7. What integrals lead to logarithms? Give examples. What are the integrals of tan x, cot x, sec x, and csc x?

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

∫ sin(2θ) dθ / (1 + cos(2θ))²

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

∫ (sin5t) dt / [1 + (cos5t)²]

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

133. ∫ (sin²x) / (1 + sin²x) dx

Evaluate the integrals in Exercises 33–54.

∫₀^(π/4) (1 + e^(tan θ)) sec²θ dθ

Use reduction formulas to evaluate the integrals in Exercises 41–50.

∫ 8 cos^4(2πt) dt

Use reduction formulas to evaluate the integrals in Exercises 41–50.

∫ 2 sin^2(t) sec^4(t) dt

Use any method to evaluate the integrals in Exercises 15–38. Most will require trigonometric substitutions, but some can be evaluated by other methods.

∫ dx / √(1 - x²)

Use reduction formulas to evaluate the integrals in Exercises 41–50.

∫ 8 cot^4(t) dt