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.)

Given that ${\int }_1^{3}f\left(x\right) dx$=$-3$ and ${\int }_k^{1}f\left(x\right) dx$=$4$, what is the value of ${\int }_3^{k}f\left(x\right) dx$?

If n is a known positive integer, for what value of k does the following hold: ${\int }_{}^{}k{x}^{n-1}dx$ = $\frac{1}{n}$?

For the integral ${\int }_{}^{}x{e}^{x}dx$, which of the following correctly identifies $u$ and $du$ for use in integration by parts?

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

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

92–98. Evaluate the following integrals.

97. ∫ tan⁻¹(∛x) dx

2–74. Integration techniques Use the methods introduced in Sections 8.1 through 8.5 to evaluate the following integrals.

60. ∫ x² coshx dx