Use reduction formulas to evaluate the integrals in Exercises 41–50.
∫ 16x^3 (ln(x))^2 dx

In Exercises 39–48, use an appropriate substitution and then a trigonometric substitution to evaluate the integrals.

∫ √(x - 2) / √(x - 1) dx

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

∫ x cos³(x) dx

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

∫ x·sec²x dx

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

∫ cotx·csc³x dx

Evaluate the limits in Exercise 9 and 10 by identifying them with definite integrals and evaluating the integrals.

lim (n → ∞) Σ (from k=1 to n) ln √(1 + k/n)

Evaluate the integrals in Exercises 1–24 using integration by parts.

∫ θ cos(πθ) dθ

Evaluate the integrals in Exercises 1–24 using integration by parts.

∫ x² sin(x) dx

Evaluate the integrals in Exercises 1–24 using integration by parts.

∫(from 1 to e) x³ ln(x) dx