12. Techniques of Integration

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

121. ∫ (1 + x²) / (1 + x³) dx

In Exercises 21–32, express the integrand as a sum of partial fractions and evaluate the integrals.

∫ (3t² + t + 4) / (t³ + t) dt from 1 to √3

7–84. Evaluate the following integrals.

45. ∫ from 0 to ln 2 [1 / (1 + eˣ)²] dx

Express the rational function as a sum or difference of two simpler fractions. Use a system of equations.

$\frac{1}{(2x+1)(2x-1)}$