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Section 7.4 : Partial Fractions

Evaluate each of the following integrals.

1. \( \displaystyle \int{{\frac{4}{{{x^2} + 5x - 14}}\,dx}}\) Solution
2. \( \displaystyle \int{{\frac{{8 - 3t}}{{10{t^2} + 13t - 3}}\,dt}}\) Solution
3. \( \displaystyle \int_{{ - 1}}^{0}{{\frac{{{w^2} + 7w}}{{\left( {w + 2} \right)\left( {w - 1} \right)\left( {w - 4} \right)}}\,dw}}\) Solution
4. \( \displaystyle \int{{\frac{8}{{3{x^3} + 7{x^2} + 4x}}\,dx}}\) Solution
5. \( \displaystyle \int_{2}^{4}{{\frac{{3{z^2} + 1}}{{\left( {z + 1} \right){{\left( {z - 5} \right)}^2}}}\,dz}}\) Solution
6. \( \displaystyle \int{{\frac{{4x - 11}}{{{x^3} - 9{x^2}}}\,dx}}\) Solution
7. \( \displaystyle \int{{\frac{{{z^2} + 2z + 3}}{{\left( {z - 6} \right)\left( {{z^2} + 4} \right)}}\,dz}}\) Solution
8. \( \displaystyle \int{{\frac{{8 + t + 6{t^2} - 12{t^3}}}{{\left( {3{t^2} + 4} \right)\left( {{t^2} + 7} \right)}}\,dt}}\) Solution
9. \( \displaystyle \int{{\frac{{6{x^2} - 3x}}{{\left( {x - 2} \right)\left( {x + 4} \right)}}\,dx}}\) Solution
10. \( \displaystyle \int{{\frac{{2 + {w^4}}}{{{w^3} + 9w}}\,dw}}\) Solution