4. How is integration by parts used to evaluate a definite integral?

9–40. Integration by parts Evaluate the following integrals using integration by parts.

11. ∫ t · e⁶ᵗ dt

9–40. Integration by parts Evaluate the following integrals using integration by parts.

17. ∫ x · 3x dx

9–40. Integration by parts Evaluate the following integrals using integration by parts.

20. ∫ sin⁻¹(x) dx

1. On which derivative rule is integration by parts based?

9–40. Integration by parts Evaluate the following integrals using integration by parts.

14. ∫ s · e⁻²ˢ ds

9–40. Integration by parts Evaluate the following integrals using integration by parts.

26. ∫ t³ sin(t) dt

9–40. Integration by parts Evaluate the following integrals using integration by parts.

23. ∫ x² sin(2x) dx

Use a substitution to reduce the following integrals to ∫ ln u du. Then evaluate using the formula for ∫ ln x dx.

7. ∫ (sec²x) · ln(tan x + 2) dx