Strategy for Integration

Question

Evaluate the integral.

∫ (from pi/2 to pi/4) (1+8cot(x))/(8-cot(x)) dx

Answer 1

You can use a u substitution on cot(x). This will result in your function containing csc^2(x), which can be subbed out using the identity 1+cot^2(x) = csc^2(x) [or more usefully, 1+u^2 = csc^2(x)]. From there, you can split the integral using partial fractions. Each resulting component can be integrated using the general from for natural log integrals. Please let me know if you'd like clarification.