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))

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)

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.

Use reduction formulas to evaluate the integrals in Exercises 41–50.

∫ 3 sec^4(3x) dx

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

∫ x² sin(x) dx

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

∫₁^∞ dx / [x√(x² − 1)]

Evaluate the integrals in Exercises 1–22.

∫₀^π 3sin(x/3) dx