12. Techniques of Integration

Find the integral.

${\int }_{}^{}s{e}^{3s}ds$

Find the integral.

${\int }_{}^{}\theta \cos 2\theta d\theta$

Find the integral.

${\int }_{}^{}{x}^2\ln xdx$

Find the indefinite integral.

${\int }_{}^{}{r}^2{e}^{-r}dr$

7–40. Table look-up integrals Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they can be found in a table.

28. ∫ ln² x dx

71-74. Deriving formulas Evaluate the following integrals. Assume a and b are real numbers and n is a positive integer.

74. ∫xⁿ arcsin(x) dx (Hint: integration by parts.)

7–84. Evaluate the following integrals.

38. ∫ from π/6 to π/2 [cos x · ln(sin x)] dx

7–84. Evaluate the following integrals.

79. ∫ (arcsinx)/x² dx