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Section 7.6 : Integrals Involving Quadratics

Evaluate each of the following integrals.

1. \( \displaystyle \int{{\frac{{x + 1}}{{{x^2} + 10x + 18}}\,dx}}\)
2. \( \displaystyle \int{{\frac{{15}}{{3{y^2} - 4y + 4}}\,dy}}\)
3. \( \displaystyle \int{{\frac{{12 - 9z}}{{1 - 4z - 4{z^2}}}\,dz}}\)
4. \( \displaystyle \int{{\frac{{3 - 7t}}{{{{\left( {{t^2} + 12t + 40} \right)}^2}}}\,dt}}\)
5. \( \displaystyle \int{{\frac{{11w + 4}}{{{{\left( {3 + 6w - {w^2}} \right)}^2}}}\,dw}}\)
6. \( \displaystyle \int{{\frac{3}{{{{\left( {2{x^2} + 10x + 4} \right)}^{\frac{7}{2}}}}}\,dx}}\)