Question Type 5: Integrating rational functions using partial fractions (linear factors) Exercises

Find $\displaystyle \int \frac{1}{x^2 - 7x + 10}\,dx$.

Compute $\displaystyle \int \frac{2x - 3}{x^2 - 5x + 6}\,dx$.

Find $\displaystyle \int \frac{2x + 1}{x^2 + 4x + 3}\,dx$.

Evaluate $\displaystyle \int \frac{5x + 2}{x^2 - 9}\,dx$.

Find $\displaystyle \int \frac{3x - 2}{x^2 + x - 12}\,dx$. [6]

Evaluate the integral $\displaystyle \int \frac{3x + 5}{x^2 - x - 6}\,dx$.

Compute $\displaystyle \int \dfrac{2x + 3}{x^2 + 2x - 8}\,dx$.

Evaluate $\displaystyle \int \frac{x + 4}{x^2 - 6x + 5}\,dx$.

Find $\displaystyle \int \frac{4x + 7}{x^2 - 2x - 3}\,dx$.

Evaluate $\displaystyle \int \frac{4x - 1}{x^2 - 4}\,dx$.

Find $\displaystyle \int \frac{1}{(x - 2)(x + 3)}\,dx$.

Evaluate the integral $\displaystyle \int \frac{x}{x^2 - 3x - 28}\,dx$.