Evaluate the integrals in Exercises 9–28. It may be necessary to use a substitution first.
∫ [(3v − 7) / ((v − 1)(v − 2)(v − 3))] dv

In Exercises 17–20, express the integrand as a sum of partial fractions and evaluate the integrals.

∫ (x² dx) / ((x - 1)(x² + 2x + 1))

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

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

∫ (8x² + 8x + 2) / (4x² + 1)² dx

Expand the quotients in Exercises 1–8 by partial fractions.

(t⁴ + 9) / (t⁴ + 9t²)

Evaluate the integrals in Exercises 9–28. It may be necessary to use a substitution first.

∫ [t / (t⁴ − t² − 2)] dt

Evaluate the integrals in Exercises 9–28. It may be necessary to use a substitution first.

∫ [(x³ + 1) / (x³ − x)] dx

Evaluate the integrals in Exercises 9–28. It may be necessary to use a substitution first.

∫ [(2x³ + x² − 21x + 24) / (x² + 2x − 8)] dx

Evaluate the integrals in Exercises 9–28. It may be necessary to use a substitution first.

∫ [1 / (x (1 + ∛x))] dx