Integration by Parts

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

1. The integration by parts formula is:
2. For ∫ x sin(x) dx, a good choice is:
3. ∫ x sin(x) dx using parts (u = x, dv = sin(x)dx) equals:
4. For ∫ x eˣ dx, the best choice is:
5. ∫ x eˣ dx using parts equals:
6. For ∫ x cos(x) dx, the best choice is:
7. ∫ x cos(x) dx equals:
8. For ∫ ln(x) dx, a good choice is:
9. ∫ ln(x) dx equals:
10. For ∫ x² eˣ dx, the first parts gives u dv where:
11. ∫ x² eˣ dx requires integration by parts:
12. For ∫ eˣ sin(x) dx, the appropriate strategy is:
13. For ∫ x² cos(x) dx, the best first choice is:
14. ∫ x² cos(x) dx gives (after simplification):
15. The LIATE rule for choosing u prioritizes:
16. For ∫ x tan⁻¹(x) dx, the LIATE rule suggests u = :
17. ∫ e^x cos(x) dx can be solved by:
18. For ∫ x√(1 + x) dx, the best approach is:
19. ∫ x³ sin(x) dx requires parts:
20. For ∫ (ln(x))² dx, the first choice is u = :
21. The product ∫ xe^(2x) dx can be solved by parts with u, dv as:
22. ∫ xe^(2x) dx equals:
23. When using integration by parts, the key is to choose u and dv such that:
24. Question?
25. Question?