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

∫ (x² / (x² + 1)) dx

Volume: Find the volume of the solid generated by revolving the region in Exercise 45 about the x-axis.

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 1–34 converge. Evaluate the integrals without using tables.

∫₁^∞ dx / x^1.001

Evaluate the integrals in Exercises 33–52.

∫ cot³(t) csc⁴(t) dt

Evaluate the integrals in Exercises 23–32.

∫_{π/2}^{3π/4} √(1 - sin(2x)) dx