Integration by Substitution

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

1. In integration by substitution, if u = g(x), then:
2. For ∫ (2x + 1)⁵ dx, the best substitution is:
3. For ∫ x·e^(x²) dx, the best substitution is:
4. ∫ (3x + 1)⁴ dx using substitution u = 3x + 1 equals:
5. ∫ e^(2x) dx using substitution u = 2x equals:
6. ∫ sin(3x) dx using substitution u = 3x equals:
7. ∫ 1/(2x + 1) dx using substitution u = 2x + 1 equals:
8. ∫ cos(5x) dx using substitution u = 5x equals:
9. For ∫ x cos(x²) dx, the substitution u = x² gives:
10. ∫ (2x)(x² + 1)³ dx using substitution u = x² + 1 gives:
11. For ∫ e^(−x) dx, using u = −x gives:
12. ∫ 1/√(2x + 1) dx using substitution u = 2x + 1 equals:
13. For ∫ x(x² − 1)^(1/2) dx, the best substitution is:
14. ∫ (cos(x))sin(x) dx using u = cos(x) gives:
15. For ∫ 3e^(3x) dx, the substitution u = 3x gives:
16. ∫ x²(x³ + 2)⁴ dx using u = x³ + 2 gives:
17. For ∫ sec²(x) dx, is substitution needed?
18. ∫ sin(ax + b) dx using u = ax + b gives:
19. For ∫ f'(x)/f(x) dx, the result is:
20. ∫ (tan(x))sec²(x) dx using u = tan(x) gives:
21. For ∫ dx/(ax² + b), if a > 0, b > 0:
22. ∫ (1 + ln(x))/x dx using u = ln(x) gives:
23. In substitution, after finding ∫ f(u)du, we must:
24. Question?
25. Question?