2–74. Integration techniques Use the methods introduced in Sections 8.1 through 8.5 to evaluate the following integrals.
43. ∫ eˣ sin(x) dx

60. Two Methods

a. Evaluate ∫(x · ln(x²)) dx using the substitution u = x² and evaluating ∫(ln(u)) du.

60. Two Methods

c. Verify that your answers to parts (a) and (b) are consistent.

62. Two integration methods Evaluate ∫ sin x cos x dx using integration by parts. Then evaluate the integral using a substitution. Reconcile your answers

79–82. {Use of Tech} Double table look-up The following integrals may require more than one table look-up. Evaluate the integrals using a table of integrals, and then check your answer with a computer algebra system.

79. ∫ x sin⁻¹(2x) dx

79–82. {Use of Tech} Double table look-up The following integrals may require more than one table look-up. Evaluate the integrals using a table of integrals, and then check your answer with a computer algebra system.

82. ∫ (sin⁻¹(ax)) / x² dx, a > 0

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

38. ∫ (from π/4 to π/2) x csc²x dx

78. Practice with tabular integration Evaluate the following integrals using tabular integration (refer to Exercise 77).

e. ∫ (2x² - 3x) / (x - 1)³ dx

Find the integral.

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