Integration by Substitution

Grade 12 Maths Higher — Integration by Substitution: 25 practice questions with instant scoring and explanations.

1. Integration by substitution uses chain rule in reverse, with u = g(x):
2. To integrate ∫(2x+1)^5 dx, we use substitution u =
3. For ∫sin(3x)dx, after u = 3x, du/dx =
4. ∫sin(3x)dx =
5. ∫e^(5x)dx =
6. For ∫x√(x²+1)dx, let u = x²+1, then ∫ becomes:
7. ∫x√(x²+1)dx =
8. ∫cos(ln(x))/x dx, using u = ln(x):
9. For ∫1/(x ln(x))dx, the substitution u =
10. ∫1/(x ln(x))dx =
11. When substituting u = g(x), we must replace:
12. For definite integrals ∫_a^b f(g(x))g'(x)dx with u = g(x):
13. ∫_1^2 x(x²+1)^(1/2)dx using u = x²+1 becomes:
14. ∫x/(x²+1)dx =
15. For ∫dx/(a²+x²), the substitution x = a·tan(θ) gives:
16. Trigonometric substitution x = a·sin(θ) is useful for:
17. For ∫√(a²-x²)dx, substitution x = a·sin(θ) converts to:
18. ∫√(1-x²)dx =
19. For integrands with √(x²-a²), use substitution:
20. After integration by substitution, we must:
21. ∫sin^n(x)cos^m(x)dx with n odd uses substitution u =
22. ∫e^(ax)sin(bx)dx can be solved by:
23. Weierstrass substitution t = tan(x/2) converts sin(x) to:
24. The goal of substitution is to convert integral to:
25. Review question for Integration by Substitution