In Exercises 27–40, use a substitution to change the integral into one you can find in the table. Then evaluate the integral.
∫ x^2 √(2x - x^2) dx

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

∫₀² (s + 1) / √(4 − s²) ds

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

∫ sin³(x) / cos⁴(x) dx

Solve the initial value problems in Exercises 53–56 for y as a function of x.

√(x² - 9) (dy/dx) = 1, where x > 3, y(5) = ln 3

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.

∫ (sec t + cot t)² dt

In Exercises 69–80, determine whether the improper integral converges or diverges. If it converges, evaluate the integral.

∫₋∞⁴ [x / (x² + 9)^(2/5)] dx

Exercises 59–64 require the use of various trigonometric identities before you evaluate the integrals.

∫ sin³(θ) cos(2θ) dθ