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 e to e^e of (ln(ln x) dx)
For Exercises 49–52, complete the square before using an appropriate trigonometric substitution.
∫ 1 / √(x² - 2x + 5) dx
In Exercises 17–20, express the integrand as a sum of partial fractions and evaluate the integrals.
∫ (x² dx) / ((x - 1)(x² + 2x + 1))
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 1 of (dt / (t - sin t))
(Hint: t ≥ sin t for t ≥ 0)
Use any method to evaluate the integrals in Exercises 15–38. Most will require trigonometric substitutions, but some can be evaluated by other methods.
∫ √(9 - w²) dw / w²
Use any method to evaluate the integrals in Exercises 15–38. Most will require trigonometric substitutions, but some can be evaluated by other methods.
∫ (x dx) / (25 + 4x²)
