Back7–40. 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
92–98. Evaluate the following integrals.
97. ∫ tan⁻¹(∛x) dx
7-56. Trigonometric substitutions Evaluate the following integrals using trigonometric substitution.
51. ∫ x²/√(4 + x²) dx