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Section 7.4 : Partial Fractions

Evaluate each of the following integrals.

1. \( \displaystyle \int{{\frac{9}{{{z^2} - 12z}}\,dz}}\)
2. \( \displaystyle \int{{\frac{{7x}}{{{x^2} + 14x + 40}}\,dx}}\)
3. \( \displaystyle \int_{0}^{4}{{\frac{{8y - 1}}{{2{y^2} - 15y - 8}}\,dy}}\)
4. \( \displaystyle \int{{\frac{{9 - {w^2}}}{{\left( {w + 1} \right)\left( {3w - 5} \right)\left( {w + 4} \right)}}\,dw}}\)
5. \( \displaystyle \int_{1}^{8}{{\frac{{12}}{{{z^3} - 2{z^2} - 63z}}\,dz}}\)
6. \( \displaystyle \int{{\frac{{7x + 2{x^2}}}{{\left( {x - 4} \right)\left( {2x + 3} \right)\left( {2x + 1} \right)}}\,dx}}\)
7. \( \displaystyle \int{{\frac{{4x + 10}}{{\left( {x - 2} \right){{\left( {x - 1} \right)}^2}}}\,dx}}\)
8. \( \displaystyle \int_{1}^{2}{{\frac{{24}}{{{t^4} - 6{t^3}}}\,dt}}\)
9. \( \displaystyle \int{{\frac{{10z + 2}}{{{{\left( {z + 1} \right)}^2}{{\left( {z - 3} \right)}^2}}}\,dz}}\)
10. \( \displaystyle \int{{\frac{{8w + {w^2}}}{{\left( {w - 7} \right)\left( {{w^2} + 16} \right)}}\,dw}}\)
11. \( \displaystyle \int{{\frac{{6y - 7}}{{\left( {2y + 1} \right)\left( {4{y^2} + 1} \right)}}\,dy}}\)
12. \( \displaystyle \int{{\frac{{8{t^3} - 5{t^2} + 72t - 10}}{{\left( {{t^2} + 2} \right)\left( {{t^2} + 9} \right)}}\,dt}}\)
13. \( \displaystyle \int{{\frac{{16{w^3} + 6{w^2} + 12w + 21}}{{\left( {{w^2} + 9} \right)\left( {4{w^2} + 3} \right)}}\,dw}}\)
14. \( \displaystyle \int{{\frac{{{x^4} + 5{x^3} + 20x + 16}}{{x{{\left( {{x^2} + 4} \right)}^2}}}\,dx}}\)
15. \( \displaystyle \int{{\frac{{6 - {z^2}}}{{2{z^2} + z - 21}}\,dz}}\)
16. \( \displaystyle \int{{\frac{{4{x^3} - x}}{{{x^2} - x - 30}}\,dx}}\)
17. \( \displaystyle \int{{\frac{{8 - {t^3}}}{{\left( {t - 3} \right){{\left( {t + 1} \right)}^2}}}\,dt}}\)
18. \( \displaystyle \int{{\frac{{{x^6} - 6{x^5} + 3{x^4} - 10{x^3} - 9{x^2} + 12x - 27}}{{{x^4} + 3{x^2}}}}}\,dx\)