1. Math 229 Integration Worksheet – Substitution Method
Integrate
1. (5x + 4)5 dx 2. 3t2 (t3 + 4)5 dt
√
3. 4x − 5 dx 4. t2 (t3 + 4)−1/2 dt
5. cos(2x + 1) dx 6. sin10 x cos x dx
√
sin x ( x − 1)2
7. dx 8. √ dx
(cos x)5 x
1
x+1
9. x3 + x2 (3x2 + 2x) dx 10. dx
−1 (x2 + 2x + 2)3
π √
11. cos x sin x dx 12. (x + 1) sin(x2 + 2x + 3) dx
0
3 1
1 1
13. 1+ dt 14. x2 x3 + 1 dx
t t2 −1
4
2 1
15. √ dx 16. √ √ dx
3x − 7 1 x( x + 1)2
1 √
x
17. √ dx 18. x 2x + 1 dx
0 x+1
√ √
19. x x x + 1 dx 20. x3 x2 − 1 dx
√ x2 + 2x
21. (x2 + 1) x − 2 dx 22. dx
x2 + 2x + 1
1 sec2 x
23. dx 24. dx
x2 + 6x + 9 (1 + tan x)3
sin x
25. dx 26. x tan(x2 ) sec(x2 ) dx
(2 + 3 cos x)2
27. 3t3 (t2 + 4)5 dt 28. (tan 2x + cot 2x)2 dx
1