6. Use properties of integration and properties of functions to find the exact value of L(x* – 5x² + 1)dx.

Q: Find the indefinite integral. (Use C for the constant of integration.) |(2x - 1)(6x2 - 6x + 1)/3 dx

A: Using method of substitution

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) x3 dx 1 + x8

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) | x³ sin(x*) dx

A: Let’s put u = x4 and then solve the integration:

Q: Find the indefinite integral. (Use C for the constant of integration.) -cos X dx sin5 x

A:

Q: Use integration by parts to find the indefinite integral ∫x e1-x dx

A:

Q: 5. Find the indefinite integral and check the result by differentiation. (Use C for the constant of…

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) (7x2 + 5x-2) dx

A:

Q: 4. For some integrals, you may need to use integration by parts more than once. Evaluate the…

A: Given: The integral

Q: Find the general indefinite integral. (Use C for the constant of integration.) | (x1.3 + 9x3.5) dx

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) 4x - 9/x dx

A: To find the indefinite integral: ∫4x3-9xxdx Solution: Evaluating the given integral.…

Q: Evaluate the indefinite integral. (use C for the constant of integration.) x3 – 3x2 + 4x – 8 dx

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) ーx)3(2 - x) dx

A:

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

A: Find your answer below

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) COS X dx (sin x)20

A: Given, ∫cosxsinx20dx We have to evaluate the indefinite integral.

Q: Evaluate the integral. (Use C for the constant of integration.) fu- (x – 3)sin(Tx) dx

A:

Q: Find the indefinite integral. (Use C for the constant of integration. sin 4x sin 3x dx sin x sin 7x…

A: Solution is given in step 2

Q: Find the general indefinite integral. (Use C for the constant of integration.) + 9x3.5) dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) x²e&x3 dx

A:

Q: (x2 + 7)(x1/2 − 7) dx

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) (5x2 + 6x-2) dx

A:

Q: Find the indefinite integral. (Use C for the constant of integration.)

A: The given integral is,

Q: Find the indefinite integral. (Use C for the constant of integration.) 5 8x3 + x2 X dx

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) dx (6x – 5)2

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) 2 4x2 + 8 + dx x2 + 1

A:

Q: Evaluate the integral. (Use C for the constant of integration.) (ln(x))2 dx

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) (x1.7 + 9x3.5) dx

A:

Q: Use integration by parts to evaluate the integral. (Use C for the constant of integration.) In(5x)…

A: Given , the integral We have to evaluate the integral by using by parts formula.

Q: please answer the question and show all of your work

A:

Q: Evaluate the ∫ from 0 to 1 of xe−2x dx using integration by parts

A: Given, I=∫01xe-2xdx

Q: 9. Using integration by parts, evaluate fe* sin 3x dx.

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) x* + x – 25 dx x2 + 5 1 3 -…

A:

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

A:

Q: Calculate the integral. (Use C for the constant of integration.)   dx x   4x4 − 1

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) 3 8x2 + 7 + dx x2 + 1

A: Given : ∫8x2 + 7 + 3x2+1dx

Q: Evaluate the integral ∫6x^2−4/(x^3−2x−8) dx       Note: Use an upper-case "C" for the constant of…

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) tan-(5x) dx 1 + 25x2

A: To evaluate the given integral:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos(x)/sin^20(x)    dx

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) 3 4x2 + 5 + dx 2 X +…

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) + 8x + 7) dx

A:

Q: Evaluate the integral -1 dx x² + 16 Note: Use an upper-case "C" for the constant of integration.

A: LetI=∫-1x2+16dxTake the constant out:  ∫a·fxdx=a·∫fxdxI=-∫1x2+16dxI=-∫1x2+42dxPur x=4tany…

Q: Find the indefinite integral. (Use C for the constant of integration.) e2x dx

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) sin 2x 9. dx sin x

A: Explanation of the answer is as follows

Q: Use the basic integration rules to find or evaluate the integral ∫x/ 3√(4 − x2) dx

A: The given integral is ∫x4-x23dx.

Q: Find the indefinite integral. (Use C for the constant of integration.) (1 - e2x dx

A: We need to find the following indefinite integral.                ∫ex1-e2xdx

Q: Find the indefinite integral. (Use C for the constant of integration.) cos 2x dx

A:

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

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 4x 4 + 4x dx e

A: We have to find

Q: valuate the definite integral: 4 x* — 2ух + 2 - -dx. x2

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) (x1.8 + 9x3.5) dx

A: Given, ∫ x1.8+9x3.5dx