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# Antidifferentiation Practice Questions

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To review these concepts, go to Antidifferentiation Study Guide.

## Antidifferentiation Practice Questions

Evaluate the following integrals.

1. x5dx
2. x12dx
3. u6du
4. x2dx
5. xdx
6. t–3dt
7. t5dt
8. 3xdx
9. 3udu
10. 5dx
11. 5dt
12. 8dx

Evaluate the following integrals.

1. 9x4 dx
2. 8u2 du
3. (x – √x)dx
4. (6x2 – 10x + 5) dx
5. 12x3 dx
6. (3x2 + 4)dx
7. (6x – 4) dx
8. (3t11 + 9t2 + t) dt
9. (1 – t2) dt
10. (8x3 + 10x2 – 4x + 2) dx
11. (10u4 – 4u + 1) du
12. 12√xdx
13. dx
14. dx

Evaluate the following integrals.

1. (x2 – 5cos(x)) dx
2. (3ex + 2x3) dx
3. du
4. (θ + 2sin(θ)) dθ
5. (sin(x) + 2ex) dx
6. (x + ex) dx
7. 1e dx

### Solutions

1. x6 + c
2. x13 + c
3. u7 + c
4. 72
5. 40
6. t–2 + c = – + c
7. x + c
8. x + c
9. u + c
10. 5x + c
11. 5t + c
12. 40
13. x5 + c
14. u3 + c
15. x2x + c
16. 2x3 – 5x2 + 5x + c
17. 48
18. 11
19. 115
20. t12 + 3t3 + t2 + c
21. –6
22. 2x4 + x3 – 2x2 + 2x + c
23. 58
24. 208
25. + c
26. x3 – 5sin(x) + c
27. 3ex + x4 + c
28. ln|ul| + c
29. θ2 – 2cos(θ) + c
30. –cos(x) + 2ex + c
31. ( + e1) – (0 + e0) = e
32. 4ln(e) – 4ln(1) = 4 – 0 = 4
33. 4√2

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