Find the indefinite integral 1. integral (6+9)(9)dx 2. integral squareroot 4- 2x

Question

Find the indefinite integral 1. integral (6+9)(9)dx 2. integral squareroot 4- 2x^2 (-4x)dx 3. integral x/(4x-5x^2)^3 dx 4. integral (4x^3 + 1/(3x)^2 dx 5. integral 5 cos (5x)dx 6. integral sec^3 (x/3) 11. Find the indefinite integral and check the result by differeniation. 7. intergral x^2 + 4x + 7) dx 8. integral (7 cos x + sin x)dx 9. integral i squareroot 1 + squareroot t/t^2 dt 10. integral 3 cos 5 theta d theta III. use integral^4_0 x^4 = 81/4 to evaluate each definite integral without using the Fundamental Theorem of Calculus 11. integral^0_-4 x^5 dx 12. integral^4_-4 x^3 dx 13. integral^4_0 -x^3 dx 14. integral^0_-4 3x^3 dx IV. Evaluate each definite integral 15. integral (8/x^2 - 1)dx 16. integral^4_0 (3-t)squareroot t dt 17. integral^7_2 (3-|x-4|)dx

Explanation / Answer

You did not mention question number.

So, I am answering question 1.

1.) a. Use u substitution

6+9x=u

Using differentiation,

9 dx = du

So, we get

u du

On integrating

u^2/2 + c

So, (6+9x)^2/2 + c

b.) Question is not clear

Still I am considering sqrt(4-2x^2)

4 - 2x^2 = u^2

On differentiating,

-4x dx = 2u du

So, we get

2u^3 du

u^4/2 + c

So, we get

(4-2x^2)^2/2 + c

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