In Exercises 21–32, express the integrand as a sum of partial fractions and evaluate the integrals.
∫ (s⁴ + 81) / (s(s² + 9)²) ds

The integrals in Exercises 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.

∫ (x² / (x² + 1)) dx

Evaluate the integrals in Exercises 31–56. Some integrals do not require integration by parts.

∫ e√x / √x dx

Use any method to evaluate the integrals in Exercises 65–70.

∫ cot(x) / cos²(x) dx

The integrals in Exercises 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.

∫ (tan θ + 3 / sin θ) dθ

The integrals in Exercises 1–34 converge. Evaluate the integrals without using tables.

∫₁^∞ dx / x^1.001

Evaluate the integrals in Exercises 33–52.

∫ cot³(t) csc⁴(t) dt