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# Integration by Substitution Practice Questions

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Updated on Oct 1, 2011

To review these concepts, go to Integration by Substitution Study Guide.

## Integration by Substitution Practice Questions

Evaluate the following integrals.

1. x4(x5 + 1)7 dx
2. (4x + 3)10 dx
3. x2(x3 – 1)4 dx
4. (x3 – 9x + 4) dx
5. xx2 – 1dx
6. 3√xdx
7. 3x + 4 dx
8. dx
9. 2x3cos(x4) dx
10. dx
11. (8x + 5)(4x2 – + 5x – 1)3 dx
12. dx
13. dx
14. sin(x)cos(x) dx
15. sin2(x)cos(x) dx
16. cos(4x) dx
17. 4cos(x) dx
18. sin(7x – 2) dx
19. exsin(ex) dx
20. dx
21. dx
22. xe(x2) dx
23. tan(x) dx = dx
24. dx

### Solutions

1. (x5 + 1)8 + c
2. (4x + 3)11 + c
3. x4x2 + 4x + c
4. (x2 – 1) + c
5. 14
6. 26
7. ln3x3 – 5x + c
8. sin(x4) + c
9. 3x4 – 2x + 1 + c
10. (4x2 + 5x – 1)4 + c
11. + c
12. ln|4x + 101 + c
13. Using u = sin(x), the solution is sin2 + c. Using = cos(x), the solution is – cos2(x) + c. Because sin2(x) + cos2(x) = 1, these solutions will be the same if the second + c is greater than the first one.
14. sin3(x) + c
15. sin(4x) + c
16. 4sin(x) +c
17. cos(7x – 2) + c
18. –cos(ex) + c
19. (ln(x))4 + c
20. ln|ln(x)| + c
21. e(x2) + c
22. –ln(cos(x)) + c
23. ln(1 + ex) + c

150 Characters allowed

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