Evaluate the integrals in Exercises 1–22.
∫₀^π 3sin(x/3) dx

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)

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

∫ √(x) / (1 - x³) dx (Hint: Let u = x³/2)

92. Evaluate ∫ from 3 to ∞ [ dx / (x √(x² - 9))]

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 -1 to 1 of (-x ln|x| dx)

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 1 to 2 of (dx / (x ln x))

Center of gravity: Find the center of gravity of the region bounded by the x-axis, the curve y = sec x, and the lines x = -pi/4 and x = pi/4.