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 + 6x) / (x^2 + 3)^2 dx

Evaluate the integrals in Exercises 33–52.

∫ sec³(x) tan³(x) dx

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

∫ (r² + r + 1) e^r dr

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

∫₀¹ (−ln(x)) dx

Volume: Find the volume of the solid formed by revolving the region bounded by the graphs of y = sin x + sec x, y = 0, x = 0, and x = π/3 about the x-axis.

Evaluate the integrals in Exercises 31–56. Some integrals do not require integration by parts.

∫ (sin⁻¹ x)² / √(1 - x²) dx

Evaluate the integrals in Exercises 33–52.

∫ sec⁶(x) dx