In Exercises 35–68, use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integrals for convergence. If more than one method applies, use whatever method you prefer.
∫ from 0 to ∞ of (dθ / (θ² - 1))
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.
∫ (e^{t} dt) / ((1 + e^{2t})^{3/2}) from ln(3/4) to ln(4/3)
Solve the initial value problems in Exercises 53–56 for y as a function of x.
(x² + 1)² (dy/dx) = √(x² + 1), where y(0) = 1
Use reduction formulas to evaluate the integrals in Exercises 41–50.
∫ 8 cot^4(t) dt
In Exercises 9–16, express the integrand as a sum of partial fractions and evaluate the integrals.
∫ (y + 4) / (y² + y) dy from 1/2 to 1
