88. Incorrect Calculation

b. Evaluate ∫(from -1 to 1) dx/x or show that the integral does not exist.

82-88. Improper integrals Evaluate the following integrals or show that the integral diverges.

82. ∫ (from -∞ to -1) dx/(x - 1)⁴

82-88. Improper integrals Evaluate the following integrals or show that the integral diverges.

84. ∫ (from 0 to π) sec²x dx*(Note: Potential improperness at x = π/2)*

82-88. Improper integrals Evaluate the following integrals or show that the integral diverges.

86. ∫ (from -∞ to ∞) x³/(1 + x⁸) dx

92. Integral with a parameter For what values of p does the integral

∫ (from 1 to ∞) dx/xlnᵖ(x) converge, and what is its value (in terms of p)?

What are the two general ways in which an improper integral may occur?

7–58. Improper integrals Evaluate the following integrals or state that they diverge.

28. ∫ (from 1 to ∞) tan⁻¹(s)/(s² + 1) ds

7–58. Improper integrals Evaluate the following integrals or state that they diverge.

31. ∫ (from 1 to ∞) 1/[v(v + 1)] dv