9. Partial Fractions

Homework

1. Compute \(\displaystyle \int_1^2 \dfrac{1-x}{x^2-7x+12}\,dx\)

2. Compute \(\displaystyle \int_{-1}^1 \dfrac{2x^3-8x+12}{x^2-4}\,dx\)

3. Compute \(\displaystyle \int_2^3 \dfrac{x-2}{x^3+x}\,dx\)

4. Write out the general partial fraction expansion for: \[ f(x)=\dfrac{x^3-5x}{(x-2)^2(x^4-16)(x^2++4x+5)^2} \]
   Don't find the coefficients.

5. Compute \(\displaystyle \int_{-1}^1 \dfrac{8x}{(x+2)(x^2-4)}\,dx\)