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### Section 5.4 : More Substitution Rule

Evaluate each of the following integrals.

1. $$\displaystyle \int {{4\sqrt {5 + 9t} + 12{{\left( {5 + 9t} \right)}^7}\,dt}}$$ Solution
2. $$\displaystyle \int {{7{x^3}\cos \left( {2 + {x^4}} \right) - 8{x^3}{{\bf{e}}^{2 + {x^{\,4}}}}\,dx}}$$ Solution
3. $$\displaystyle \int {{\frac{{6{{\bf{e}}^{7w}}}}{{{{\left( {1 - 8{{\bf{e}}^{7w}}} \right)}^3}}} + \frac{{14{{\bf{e}}^{7w}}}}{{1 - 8{{\bf{e}}^{7w}}}}\,dw}}$$ Solution
4. $$\displaystyle \int {{{x^4} - 7{x^5}\cos \left( {2{x^6} + 3} \right)\,dx}}$$ Solution
5. $$\displaystyle \int {{{{\bf{e}}^z} + \frac{{4\sin \left( {8z} \right)}}{{1 + 9\cos \left( {8z} \right)}}\,dz}}$$ Solution
6. $$\displaystyle \int {{20{{\bf{e}}^{2 - 8w}}\sqrt {1 + {{\bf{e}}^{2 - 8w}}} \, + 7{w^3} - 6\,\,\sqrt[3]{w}\,dw}}$$ Solution
7. $$\displaystyle \int {{{{\left( {4 + 7t} \right)}^3} - 9t\,\,\sqrt[4]{{5{t^2} + 3}}\,dt}}$$ Solution
8. $$\displaystyle \int {{\frac{{6x - {x^2}}}{{{x^3} - 9{x^2} + 8}} - {{\csc }^2}\left( {\frac{{3x}}{2}} \right)\,dx}}$$ Solution
9. $$\displaystyle \int {{7\left( {3y + 2} \right){{\left( {4y + 3{y^2}} \right)}^3} + \sin \left( {3 + 8y} \right)\,dy}}$$ Solution
10. $$\displaystyle \int {{{{\sec }^2}\left( {2t} \right)\left[ {9 + 7\tan \left( {2t} \right) - {{\tan }^2}\left( {2t} \right)} \right]\,dt}}$$ Solution
11. $$\displaystyle \int {{\frac{{8 - w}}{{4{w^2} + 9}}\,dw}}$$ Solution
12. $$\displaystyle \int {{\frac{{7x + 2}}{{\sqrt {1 - 25{x^2}} }}\,dx}}$$ Solution
13. $$\displaystyle \int {{{z^7}{{\left( {8 + 3{z^4}} \right)}^8}\,dz}}$$ Solution