Evaluate the integral dx (x+ a)(x + b) for the cases where a = b and where a + b. Note: For the case where a = b, use only a in your answer. Also, use an upper-case "C" for the constant of integration. If a = b: -6/(x+a) + C If a + b: (-6log ( ( -a + x) / (b + x))) / (a - b) ) + C

Q: (2x- 1) dx x2 - 15x + 56

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Q: Evaluate the integral. (Use C for the constant of integration.) dx 81 - x2

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Q: Evaluate the integral. (Use C for the constant of integration.) 9x3 + 2x2 + 27x + 2 dx (x2 + 1)(x2 +…

A: We have to evaluate the integral by using partial fraction

Q: Use the basic integration rules to find or evaluate the integral ∫x2 √(x3 − 27) dx

A: Now put

Q: Evaluate the integral. (Use C for the constant of integration.) (x2 - 9x) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) √x²√3 dx √3+2x-x²

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Q: Evaluate the integral. (Use C for the constant of integration.) x² dx 81 - x2

A: Given,             ∫x281 - x2dx

Q: Evaluate the integral. (Use C for the constant of integration.) 7x2 + x + 7 dx (x² + 1)2

A: The given integral is: ∫7x2+x+7x2+12dx To evaluate the given integral.

Q: Evaluate the integral. (Use C for the constant of integration.) 1 - 4x2 dx

A: Given that∫ 1-4x2 dxwe need to evaluate it

Q: First make a substitution and then use integration by parts to evaluate the integral. (Use C for the…

A: I = ∫ x ln (5+x) dxLet  5 + x = u       dx  = duand,          x = 4 - 5

Q: Evaluate the integral. (Use C for the constant of integration.) dx /x² + + 81

A: In this question given that a integration and solve it.  We use here integration formula and solve…

Q: Evaluate the integral. (Use C for the constant of integration.) dr

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Q: Evaluate the integral. (Use C for the constant of integration.) | (4x4 - 3x-2 + 5x-5 + 2) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) dx x2 + 25

A: SOLUTION-

Q: Evaluate the integral. (Use C for the constant of integration.) | (3x5 - x4 + 1) dx

A: The objective is to evaluate the integrals

Q: Evaluate the integral. (Use C for the constant of integration.) 8x2 dx

A: Explanation of the solution is given below....

Q: Evaluate the integral. (Use C for the constant of integration.) dx x² + 81

A: Use substitution method to integrate. or   use ∫secθ dθ = logsecθ + tanθ + C1…

Q: Evaluate the integral. (Use C for the constant of integration.) x² - 64 dx - +8

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration. -6x…

A: We have to evaluate ∫e-6xdx ,   by substituting u=-6xWe have to evaluate ∫dt1-7t6 ,   by…

Q: Evaluate the integral. (Use C for the constant of integration.) 9x dx

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Q: Evaluate the integral. (Use C for the constant of integration.) x2 dx 25 – x2

A: Let, Integrate using substitution,

Q: Evaluate the integral 8 dx x² V25 – x2 Note: Use an upper-case "C" for the constant of integration.

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Q: Evaluate the integral. (Use C for the constant of integration.) | (4x* - 2x-2 + 3x-5 + 5) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) (4x4 3x-2 + 5x-5 + 2) dx

A: By using integration formula we can easily solve it. See attached file for a step by step…

Q: Evaluate the integral. (Use C for the constant of integration.) 1- 36x2 dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 9xV1- x4 dx

A: Formula used: ∫a2-x2dx=xa2-x22+a22sin-1xa+C Calculation: Simplify the integral as follows:…

Q: Evaluate the integral. (Use C for the constant of integration.) √3x√1- 3x√ 1 - x4 dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 5xV1 - x4 dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 45x-5 dx

A: Consider the given integral. ∫45x-5dx The objective of the problem is to evaluate the given…

Q: Evaluate the integral. (Use C for the constant of integration.) 16 In(Vx) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) dx 3 - 3x9

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Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) dx x2…

A: Given: ∫dxx24x2+81

Q: Evaluate the integral. (Use C for the constant of integration.) x2 - 64 dx

A: The given integral is ∫x2-64x3dx. Let us assume u=x2-64 and v'=1x3. Differentiate u with respect to…

Q: Evaluate the integral. (Use C for the constant of integration.) 3 + 2x - x2 dx

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Q: Evaluate the integral 5(x – 9) dx (x + 5)(x – 2) Note: Use an upper-case "C" for the constant of…

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Q: Evaluate the integral. (Use C for the constant of integration.) 11 dx x²V 4x² - 1

A: Given integral ∫11dxx24x2-1=11∫dxx24x2-1 Now consider ∫dxx24x2-1 Use substitution method to solve…

Q: Evaluate the integral. (Use C for the constant of integration.) (2× – 5*) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) | 8x2 + 7x + 8 dx (x2 + 1)2

A: Given query is to find the value of the integral.

Q: Evaluate the integral. (Use C for the constant of integration.) dx 5x(1 +5x)

A: Evaluate the integral using trigonometric substitution

Q: Evaluate the integral. (Use C for the constant of integration.) 4e2x dx 5 + ex

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Q: Evaluate the integral. (Use C for the constant of integration.) ∫ 3 tan2(x) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) dx 49 - x2

A: We have to find the integral

Q: Evaluate the integral. (Use C for the constant of integration.) 13 dx xV 9x2 - 1

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Q: Evaluate the integral. (Use C for the constant of integration.) 7 In(x) dx XV 5 + (In(x))²

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Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 4 +…

A: Given

Q: Evaluate the integral. (Use C for the constant of integration.) 27 – 6x – x2 dx

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Q: Evaluate the integral 8(x – 9) J (x + 5)(x – 2) ** Note: Use an upper-case "C" for the constant of…

A: Solve by substitution and simplify.

Q: Evaluate the integral. (Use C for the constant of integration.) 25x-5 dx

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Q: Evaluate the integral. (Use C for the constant of integration.) | VER-X² dx 81 x

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Q: Evaluate the integral. (Use C for the constant of integration.) | (x – 3)sin(xx) dx

A: The given integral:∫x-3sinπxdxWe need to evaluate the above integral.We will use integral by parts…