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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
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