The graph is a translation of one of the basic functions ​, ​, ​, . Find the equation that defines the function.

The basketball will reach its maximum height 1.735 seconds after it has been thrown vertically into the air.

A function is a relationship between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. A function can be represented as an equation, a graph, a table of values, or a verbal description. For example, the function f(x) = 2x + 1 represents a relationship between the input x and the output 2x + 1.

To find the maximum height of the basketball, we need to find the vertex of the parabola represented by the function f(x). The vertex of x-coordinate is:

x = -b/2a

The coefficients of the quadratic equation a[tex]x^2[/tex] + b[tex]x[/tex] + c are a, b, and c. In this case, a = -4.9 and b = 17, so:

x = -17/(2*(-4.9)) = 1.735 (rounded to 3 decimal places)

Therefore, the basketball will reach its maximum height 1.735 seconds after it has been thrown vertically into the air.

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The values of the variables can be proved by solving the the equations to get;

8. y = 3

9. k = -2

10. w = 14

11. x = -9

An equation is a statement that indicates that two expressions are equivalent by joining them with the '=' sign.

The method used to prove the value of the variable is by solving the equations as follows;

8. (5·y - 1)/2 = 7

Therefore;

2 × 7 = 5·y - 1

14 = 5·y - 1

5·y = 14 + 1 = 15

y = 15/5 = 3

y = 3

9. 10·k - 4 = 2·k - 20

Therefore;

10·k - 2·k = 8·k = 4 - 20 = -16

8·k = -16

k = -16/8 = -2

Therefore;

k = -2

10. -8·(w + 1) = -5·(w + 10)

-8·w - 8 = -5·w - 50

Therefore;

-5·w + 8·w = 50 - 8 = 42

3·w = 42

w = 42/3 = 14

Therefore;

w = 14

11. 14 - 2·(x + 8) = 5·x - (3·x - 34)

Therefore;

14 - 2·x - 16 = 5·x - 3·x + 34

14 - 2·x - 16 = -2·x - 2

5·x - 3·x + 34 = 2·x + 34

Therefore;

-2·x - 2 = 2·x + 34

2·x + 2·x = -2 - 34 = -36

4·x = -36

x = -36/4 = -9

x = -9

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Answer:

To show how x² + 6x + 5 is equivalent to (x + 5)(x + 1), we can use the FOIL method, which stands for First, Outer, Inner, and Last.

First, we multiply the first term of each factor: x and x, which gives x².

Next, we multiply the outer terms of each factor: x and 1, which gives x.

Then, we multiply the inner terms of each factor: 5 and x, which gives 5x.

Finally, we multiply the last term of each factor: 5 and 1, which gives 5.

Adding up these terms, we get:

x² + x + 5x + 5

Simplifying by combining like terms, we get:

x² + 6x + 5

This is the same as the original expression. Therefore, we have shown that:

x² + 6x + 5 = (x + 5)(x + 1)

Step-by-step explanation:

The sum οf [tex](x - 5x^2 - 12)[/tex] and [tex](4 + 11x - 3x^2)[/tex] is [tex]12x - 8x^2 - 8.[/tex]

The term "sum" can alsο be used tο describe a specific sum οf mοney. Yοu cοuld spend a cοnsiderable amοunt οf mοney οn a new car. Hοwever, if yοu tοtal up οr add up all οf its advantages, yοu might be able tο justifiably justify spending sο much.

When yοu add up the cοsts οf everything yοu οrdered at the restaurant, yοu can determine the final tοtal. It's nοt necessary fοr sum tο οnly refer tο numerical values. A summary οr general statement abοut sοmething is what yοu are giving when yοu sum sοmething up.

Tο find the sum οf [tex](x - 5x^2 - 12)[/tex] and [tex](4 + 11x - 3x^2)[/tex], we need tο add the like terms. Like terms are thοse terms that have the same variable raised tο the same pοwer.

Sο, the sum οf  [tex](x - 5x^2 - 12)[/tex] and [tex](4 + 11x - 3x^2)[/tex] is:

[tex](x + 11x) + (-5x^2 - 3x^2) + (-12 + 4)[/tex]

Simplifying, we get:

[tex]12x - 8x^2 - 8[/tex]

Therefοre, the sum οf [tex](x - 5x^2 - 12)[/tex] and [tex](4 + 11x - 3x^2)[/tex]  is [tex]12x - 8x^2 - 8.[/tex]

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The distance from first base to dead center field in a certain baseball stadium is 338 feet.

Explanation:

The distance from first base to dead center field in a certain baseball stadium is 338 feet. Given,The distance from home plate to dead center field in a certain baseball stadium is 407 feet.A baseball diamond is a square with a distance from home plate to first base of 90 feet.

To find,How far is it from first base to dead center field?

Solution:Given that the distance from home plate to dead center field is 407 feet.The baseball diamond is a square with a distance from home plate to first base of 90 feet.Now we have to find the distance from first base to dead center field.We can find the distance by using the Pythagorean theorem which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.Let us consider a right triangle ABC where AB represents the distance from home plate to first base, AC represents the distance from home plate to dead center field, and BC represents the distance from first base to dead center field.

As per the Pythagorean theorem, we have

AC² = AB² + BC²

Putting the values, we have

AC² = (90)² + BC²AC² = 8100 + BC²AC² - BC² = 8100

Taking the square root on both sides, we getAC = √(8100 + BC²)

Now we have AC = 407 ft,AB = 90 ftAC² = AB² + BC²407² = 90² + BC²BC² = 407² - 90²BC² = 165649BC = √165649BC = 407 ft - 90 ft

BC = 338 ft

Therefore, the distance from first base to dead center field in a certain baseball stadium is 338 feet.

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Answer:

vro I guess this is locating root 5

Step-by-step explanation:

mark me BRAINLIST

√111: Irrational number

0: Whole number, Rational number

Π (Pi): Irrational number

71: Natural number, Whole number, Rational number

√-81: Non-real number

√111: Irrational number - The square root of 111 is an irrational number because it cannot be expressed as a fraction or a terminating or repeating decimal.

0: Whole number, Rational number - Zero is a whole number because it is a non-negative integer. It is also a rational number because it can be expressed as the ratio 0/1.

Π (Pi): Irrational number - Pi is an irrational number because it is a non-repeating, non-terminating decimal. It cannot be expressed as a fraction.

71: Natural number, Whole number, Rational number - 71 is a natural number because it is a positive integer. It is also a whole number and a rational number because it can be expressed as the ratio 71/1.

√-81: Non-real number - The square root of -81 is a non-real number because it involves the square root of a negative number. It cannot be expressed as a real number.

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The function that models the amount of money in Yasmin's savings account for a given week can be written as: f(x) = 3x + 5

where x represents the number of weeks since Yasmin opened the account.

The constant term of 5 represents the initial amount Yasmin deposited into the account when she opened it, and the coefficient of 3 represents the amount she adds at the end of each week.

For example, after 1 week, the amount of money in the account would be:

f(1) = 3(1) + 5 = 8

After 2 weeks:

f(2) = 3(2) + 5 = 11

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Answer:

We can start by using the formula:

distance = speed x time

We know that Oliver traveled 66 miles in 4 hours, so we can use this information to find his speed:

speed = distance / time

speed = 66 miles / 4 hours

speed = 16.5 miles per hour

Now that we know Oliver's speed, we can use the same formula to find how many miles he could travel in 14 hours:

distance = speed x time

distance = 16.5 miles per hour x 14 hours

distance = 231 miles

Therefore, Oliver could travel 231 miles in 14 hours at this speed.

Answer:

102

Step-by-step explanation:

(b•h)/2

(12•17)/2

204/2

The coordinates of point Y are (10 - x1, 4y1 - 10), where (x1, y1) are the coordinates of point T.

If W is the midpoint of segment TY, then the coordinates of W are the average of the coordinates of T and Y. Using the midpoint formula, we can find the coordinates of Y:

Let the coordinates of T be (x1, y1) and the coordinates of Y be (x2, y2).

x-coordinate of W = (x-coordinate of T + x-coordinate of Y) / 2

y-coordinate of W = (y-coordinate of T + y-coordinate of Y) / 2

Putting in the coordinates of W and T, we get:  5 = (x1 + x2) / 2

y-coordinate of Y = 2y1 - y-coordinate of W

y-coordinate of Y = 2y1 - (y1 + y2) / 2

Simplifying these equations, we get:

x1 + x2 = 10

y2 = 4y1 - 10

From the first equation, we can solve for x2:  x2 = 10 - x1

Putting this into the second equation, we get:  y2 = 4y1 - 10

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1. 55%

2. 60%

3. 35%

4. 95%

5. 40%

1. The probability that a randomly selected student is male is 0.55 (55%).

2. The probability that a randomly selected female student is registered in the 2-year diploma program is 0.6 (60%).

3. The probability that a randomly selected male student is registered in the 1-year certificate program is 0.35 (35%).

4. The probability that a randomly selected student is female or is registered in a 2-year diploma program is 0.95 (95%).

5. The events “1-year program” and “male” are not independent as the probability of one event affects the probability of the other event. For example, the probability of a randomly selected male student being registered in the 1-year certificate program is 0.35 (35%), which is lower than the overall probability of a randomly selected student being registered in the 1-year certificate program (0.4 or 40%).

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Answer:

3.8

Step-by-step explanation:

using sinθ = opp/hypo

sin(25) = x/9

0.4226 = x/9

x = 9(0.4226) = 3.8

Answer:

One possible rational expression that simplifies to 2x/(x+1) and meets the given restrictions is:

(4x^2 - 2x - 3) / [(x + 1)(x - 3)(x - 2)]

To see why this expression simplifies to 2x/(x+1), we can simplify the numerator and denominator separately:

Numerator:

2x(2x-1) = 4x^2 - 2x

Denominator:

(x+1)(x-3)(x-2)

Multiplying the numerator and denominator by -1 gives:

(-2x)(2x-1) / [(3-x)(2-x)(1+x)]

Then, we can rearrange the factors in the denominator to get:

(-2x)(2x-1) / [(x+1)(x-2)(x-3)]

Now we have the desired rational expression that simplifies to 2x/(x+1) and has the given restrictions on x.

Step-by-step explanation:

The correct option is C. Green image of triangle ABC.

How to find the rotated shape or coordinates of image about origin?

As we know that triangle ABC, is rotated 270° counterclockwise about the origin. So, the algebraic rule for a figure is,

90° Clockwise or 270° counter clockwise, (x,y) = (y,-x)

As, C(-3,3) which is equal to (3,3) from the algebraic rule.

And (3,3) belongs to 1st quadrant i.e. green image is the correct answer.

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Triangle below represents is  option  C. Green image of triangle ABC.

A triangle is a geometric shape with three sides and three angles. It is one of the most fundamental shapes in geometry and is used extensively in mathematics, physics, engineering, and many other fields. Triangles are often classified based on their angles and sides.

As we know that triangle ABC, is rotated 270° counterclockwise about the origin. So, the algebraic rule for a figure is,

90° Clockwise or 270° counter clockwise, (x,y) = (y,-x)

As, C(-3,3) which is equal to (3,3) from the algebraic rule.

And (3,3) belongs to 1st quadrant i.e. green image is the correct answer.

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The approximate volume of rubber used to make the ball is 636.24 cubic centimeters.

To find the volume of the concave space inside the ball, we need to abate the volume of the ball with a  lower compass. The compass of the inside  face of the ball can be  set up by abating the consistence of the rubber from the compass of the outside  face   = r_outside-

consistence  =  6- 2  =  4 centimeters  

The volume of the concave space inside the ball can be  set up using the same formula as below but with the  lower compass   = (4/3)πr_i

nside3  = (4/3) π( 4) 3  

= (4/3) π( 64)

≈268.08 boxy centimeters  

Eventually, the volume of rubber used to make the ball is the difference between the volume of the entire ball and the volume of the concave space inside   =  V-V_hollow  ≈

=904.32-268.08  

=636.24 cubic centimeters

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Answer:

Step-by-step explanation:

708588 hope this helps

Answer:

6 + 5h
h = The number of hours he can work in the yard.

Answer:

1

Step-by-step explanation:

i think

Answer: -6(p - 6) can be simplified using the distributive property of multiplication:

-6(p - 6) = -6 * p - (-6 * 6)

= -6p - (-36)

= -6p + 36

Therefore, -6(p - 6) is equivalent to -6p + 36.

Step-by-step explanation:

False: It is the same to reflect the graph of y = cos x across the y-axis as it is across the x-axis.

A 180° rotation about the origin is a transformation that would have the same outcome as a reflection over the x-axis followed by a reflection over the y-axis. The x-coordinate of each point must be negated while reflecting across the Y axis, but the -value must remain unchanged.

By graphing y=-f(x), we may reflect the graph of any function f about the x-axis, and by graphing y=f, we can reflect the graph about the y-axis (-x). By graphing y=-f, we can even reflect it about both axes (-x).

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a. Covariance = 10.11
b. Correlation coefficient = 0.376

Considering the following sample data:

x 12 18 20 22 25

y 15 20 25 22 27

a. Calculation of covariance

Covariance can be calculated by the formula:

Cov (X, Y) = [Σ(X - μx) (Y - μy)] / n

where, Σ denotes the sum of, X and Y are the variables, μx and μy are the means of X and Y respectively, and n is the sample size.

x  y  x-μx  y-μy  (x-μx)(y-μy) (-)^2  (-)^2

12  15  -6.6  -5.6  37.12  43.56  31.36

18  20  -0.6  -0.6  0.36  0.36  0.36

20  25  1.4  4.4  6.16           1.96  19.36

22  22  3.4  -2.6  -8.84  11.56  6.76

25  27  6.4  2.4  15.36  41.16  5.76

Σx = 97, Σy = 109, Σ(x-μx) = 5.00, Σ(y-μy) = -2.00, Σ(x-μx)(y-μy) = 50.56

Covariance is: Cov (X, Y) = [Σ(X - μx) (Y - μy)] / n= 50.56/5= 10.11

Thus, the covariance between the variables is 10.11.

b-1. Calculation of correlation coefficient.

Correlation coefficient is a statistical measure that measures the degree to which two random variables are associated. It can be calculated by the formula:

= Cov (X, Y) /  where, Cov (X, Y) is the covariance between X and Y, σX and σY are the standard deviations of X and Y respectively.

σx2 = [Σ(x-μx)2] / (n-1)σy2 = [Σ(y-μy)2] / (n-1)σx = √[Σ(x-μx)2] / (n-1)σy = √[Σ(y-μy)2] / (n-1)

x  y  (x-μx)  (y-μy)  (x-μx)2  (y-μy)2  (-)(-)

12  15  -6.6          -5.6         43.56  31.36               1  

18  -0.6  -0.6          0.36         0.36  0.32                5

20  25    1.4          4.4          1.96          19.36               22  

22  3.4  -2.6          11.56  6.76          -8.84                25  

27  6.4  2.4          41.16  5.76          15.36

Σx = 97, Σy = 109, Σ(x-μx) = 5.00, Σ(y-μy) = -2.00, Σ(x-μx)(y-μy) = 50.56

σx2 = 30.70

σy2 = 25.70

σx = √30.70 = 5.54

σy = √25.70 = 5.07

Correlation coefficient is:

= Cov (X, Y) /  = 10.11 / (5.54*5.07)= 0.376

Thus, the correlation coefficient is 0.376.

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The percentage gain is 45%

To calculate the percentage gain on your investment, you need to find the difference between the selling price and the buying price, divide that difference by the buying price, and then multiply by 100 to get the percentage.

The difference between the selling price and the buying price is:

$21.75 - $15 = $ 6.75

So the gain on the investment is $ 6.75 per share.

To find the percentage gain, you divide the gain by the buying price:

$6.75 ÷ $15 = 0.45

Then, multiply by 100 to convert this into a percentage :

0.45 x 100% = 45%

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Answer:

Step-by-step explanation:

[tex]y=x^2+10x+8=(x+5)^{2}-17[/tex]

Answer:

y = (x + 5)^2 - 17

Step-by-step explanation:

To write the quadratic function y = x^2 + 10x + 8 in vertex form, we need to complete the square. We start by adding and subtracting the square of half of the coefficient of x, which is (10/2)^2 = 25:

y = x^2 + 10x + 8

= (x^2 + 10x + 25) - 25 + 8

= (x + 5)^2 - 17

Therefore, the quadratic function in vertex form is:

y = (x + 5)^2 - 17

The vertex of this parabola is at the point (-5, -17), and the axis of symmetry is the vertical line x = -5. The term (-17) represents the minimum value of the function.

Answer:

The answer is B

Step-by-step explanation:

it looks right

I disagree with Brian's assertion that there is less fluctuation in the number of mystery novels simply because the mean number of mystery books is fewer than the mean number of adventure books.

The mean is merely one measure of central tendency and provides no information about the data's dispersion or variability. We would need to look at a measure of dispersion such as the range, variance, or standard deviation to see whether there is less variety in the quantity of mystery novels. If the range or standard deviation of the number of mystery books is less than that of adventure novels, we may claim that the number of mystery books is less variable. If, however, the If the range or standard deviation of the number of mystery novels is greater than that of adventure books, Brian's statement is false. As a result, we cannot establish whether or not there is less fluctuation in the quantity of mystery novels without knowing the dispersion of the data.

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From the given data, the effectiveness of epoetin alfa, which is a medication used to treat anemia, can be determined through a blood test called a complete blood count (CBC).

The CBC measures the number of red blood cells, white blood cells, and platelets in the blood, as well as the levels of hemoglobin and hematocrit.

In patients receiving epoetin alfa, the goal is to increase the hemoglobin level and hematocrit to a target range that is appropriate for their condition. Therefore, monitoring these levels through regular CBCs can help determine whether the medication is effective and whether the dosage needs to be adjusted.

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The probability of observing an 84°F temperature or higher in LA during a randomly chosen day in June is 0.1151 and the temperature of the coldest 10% of the days (days with lowest average high temperature) during June in LA is approximately 71.6°F.

Let X be the random variable that represents the average daily high temperature in LA in June. Then X ~ N(μ = 78, σ = 5). The probability of observing an 84°F temperature or higher in LA during a randomly chosen day in June is given by: P(X > 84) = P(Z > (84 - 78) / 5) = P(Z > 1.2) = 0.1151 (rounded to 4 decimal places)

To find the temperature of the coldest 10% of the days (days with lowest average high temperature) during June in LA, we need to find the 10th percentile of the distribution. Using a z-score table, we can find the z-score corresponding to the 10th percentile: z = -1.28. Thus, the temperature of the coldest 10% of the days during June in LA is given by: x = μ + zσ= 78 + (-1.28)(5)≈ 71.6°F (rounded to 1 decimal place)

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The final answer is: ∫(2x-1)÷[(x-3)(x+2)]dx = ln|x-3| + ln|x+2| + C

What is Integration ?

In calculus, integration is the inverse operation of differentiation. It is a mathematical technique used to find the integral of a function. The integral of a function f(x) is another function F(x), which gives the area under the curve of f(x) from a certain point to another.

To perform the integration of the given function:

∫(2x-1)÷([tex]x^{2}[/tex]-x-6)dx

First, we need to factor the denominator:

[tex]x^{2}[/tex]- x - 6 = (x-3)(x+2)

So we can rewrite the integral as:

∫(2x-1)÷[(x-3)(x+2)]dx

Next, we need to decompose the fraction into partial fractions:

(2x-1)÷[(x-3)(x+2)] = A÷(x-3) + B÷(x+2)

Multiplying both sides by (x-3)(x+2), we get:

2x-1 = A(x+2) + B(x-3)

Substituting x=3, we get:

5A = 5

A = 1

Substituting x=-2, we get:

-5B = -5

B = 1

So we have:

(2x-1)÷[(x-3)(x+2)] = 1÷(x-3) + 1÷(x+2)

Substituting this back into the integral, we get:

∫(2x-1)÷[(x-3)(x+2)]dx = ∫[1÷(x-3) + 1÷(x+2)]dx

Using the first rule of integration, we get:

∫[1÷(x-3) + 1÷(x+2)]dx = ln|x-3| + ln|x+2| + C

where C is the constant of integration.

Therefore, the final answer is: ∫(2x-1)/[(x-3)(x+2)]dx = ln|x-3| + ln|x+2| + C

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[tex] \displaystyle \int \rm \: \dfrac{2x - 1}{ {x}^{2} - x - 6 } dx[/tex]

Answer:

[tex] \underline{\boxed{\rm = ln |x + 2| + ln |x - 3| + C}}[/tex]

Step-by-step explanation:

[tex] = \displaystyle \int \rm \: \dfrac{2x - 1}{ {x}^{2} - x - 6 } dx[/tex]

[tex] = \displaystyle \int \rm \: \dfrac{2x - 1}{ {x}^{2} - 3x + 2x - 6 } dx[/tex]

[tex] = \displaystyle \int \rm \: \dfrac{2x - 1}{ x(x - 3) + 2(x - 3) } dx[/tex]

[tex] = \displaystyle \int \rm \: \dfrac{2x - 1}{ (x + 2) (x - 3)} dx[/tex]

[tex] \rm \: Let : \displaystyle \rm \: \dfrac{2x - 1}{ (x + 2) (x - 3) } = \dfrac{A }{x + 2} + \dfrac{B}{x - 3} [/tex]

[tex]\rm\implies\displaystyle \rm \: \dfrac{2x - 1}{ (x + 2) (x - 3) } = \dfrac{A(x - 3) + B(x + 2) }{(x + 2)(x - 3)} \\ [/tex]

[tex] \rm \implies\displaystyle \rm \: {2x - 1}{ } = {A(x - 3) + B(x + 2) } \\ [/tex]

Put x = 3 , we get

[tex] \rm \implies\displaystyle \rm \: {6 - 1}{ } = {A(3- 3) + B(3 + 2) } \\ [/tex]

[tex] \rm \implies\displaystyle \rm \: {5}{ } = 5 B \\ [/tex]

[tex] \implies \rm \: B = 1[/tex]

Again

put put x = -2

[tex] \rm \implies\displaystyle \rm \: { - 4- 1}{ } = {A( - 2- 3) + B( - 2 + 2) } \\ [/tex]

[tex] \rm \implies\displaystyle \rm \: { - 5}{ } = {A( - 5) } \\ [/tex]

[tex] \rm \implies\displaystyle \rm A = 1 \\ [/tex]

Thus ,

[tex] \displaystyle \int \rm \: \dfrac{2x - 1}{ (x + 2) (x - 3)} dx = \int\dfrac{1}{x + 2} dx + \int \dfrac{1}{x - 3} dx[/tex]

[tex] \rm = ln |x + 2| + ln |x - 3| + C[/tex]

[tex] \tt\int \dfrac{dx}{ {x}^{2} + {a}^{2} } = \frac{1}{a} { \tan}^{ - 1} \frac{x}{a} + c \\ [/tex]

[tex] \tt\int \dfrac{dx}{ {x}^{2} - {a}^{2} } = \frac{1}{2a} log \frac{x - a}{x + a} + c \\ [/tex]

[tex] \tt\int \dfrac{dx}{ {a}^{2} - {x}^{2} } = \frac{1}{2a} log \frac{a + x}{a - x} + c \\ [/tex]

[tex] \tt\int \: \dfrac{dx}{ \sqrt{ {x}^{2} + {a}^{2} } } = log|x + \sqrt{ {a}^{2} + {x}^{2} } | + c \\ [/tex]

[tex] \tt\int \: \dfrac{dx}{ \sqrt{ {x}^{2} - {a}^{2} } } = log|x + \sqrt{ {x}^{2} - {a}^{2} } | + c \\ [/tex]

[tex] \tt \int \: \dfrac{dx}{ {a}^{2} - {x}^{2} } = { \sin }^{ - 1} \bigg(\dfrac{x}{a} \bigg) + c \\ [/tex]

[tex] \tt \int \: \sqrt{ {x}^{2} + {a}^{2} } dx \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\= \tt \dfrac{x}{2} \sqrt{ {a}^{2} + {x}^{2} } + \dfrac{ {a}^{2} }{2} log |x + \sqrt{ {x}^{2} + {a}^{2} }| + c[/tex]