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### Section 5.2 : Computing Indefinite Integrals

For problems 1 – 21 evaluate the given integral.

1. $$\displaystyle \int{{4{x^6} - 2{x^3} + 7x - 4\,dx}}$$ Solution
2. $$\displaystyle \int{{{z^7} - 48{z^{11}} - 5{z^{16}}\,dz}}$$ Solution
3. $$\displaystyle \int{{10{t^{ - 3}} + 12{t^{ - 9}} + 4{t^3}\,dt}}$$ Solution
4. $$\displaystyle \int{{{w^{ - 2}} + 10{w^{ - 5}} - 8\,dw}}$$ Solution
5. $$\displaystyle \int{{12\,dy}}$$ Solution
6. $$\displaystyle \int{{\sqrt[3]{w} + 10\,\,\sqrt[5]{{{w^3}}}\,dw}}$$ Solution
7. $$\displaystyle \int{{\sqrt {{x^7}} - 7\,\sqrt[6]{{{x^5}}} + 17\,\,\sqrt[3]{{{x^{10}}}}\,dx}}$$ Solution
8. $$\displaystyle \int{{\frac{4}{{{x^2}}} + 2 - \frac{1}{{8{x^3}}}\,dx}}$$ Solution
9. $$\displaystyle \int{{\frac{7}{{3{y^6}}} + \frac{1}{{{y^{10}}}} - \frac{2}{{\sqrt[3]{{{y^4}}}}}\,dy}}$$ Solution
10. $$\displaystyle \int{{\left( {{t^2} - 1} \right)\left( {4 + 3t} \right)\,dt}}$$ Solution
11. $$\displaystyle \int{{\sqrt z \left( {{z^2} - \frac{1}{{4z}}} \right)\,dz}}$$ Solution
12. $$\displaystyle \int{{\frac{{{z^8} - 6{z^5} + 4{z^3} - 2}}{{{z^4}}}\,dz}}$$ Solution
13. $$\displaystyle \int{{\frac{{{x^4} - \sqrt[3]{x}}}{{6\sqrt x }}\,dx}}$$ Solution
14. $$\displaystyle \int{{\sin \left( x \right) + 10{{\csc }^2}\left( x \right)\,dx}}$$ Solution
15. $$\displaystyle \int{{2\cos \left( w \right) - \sec \left( w \right)\tan \left( w \right)\,dw}}$$ Solution
16. $$\displaystyle \int{{12 + \csc \left( \theta \right)\left[ {\sin \left( \theta \right) + \csc \left( \theta \right)} \right]\,d\theta }}$$ Solution
17. $$\displaystyle \int{{4{{\bf{e}}^z} + 15 - \frac{1}{{6z}}\,dz}}$$ Solution
18. $$\displaystyle \int{{{t^3} - \frac{{{{\bf{e}}^{ - t}} - 4}}{{{{\bf{e}}^{ - t}}}}\,dt}}$$ Solution
19. $$\displaystyle \int{{\frac{6}{{{w^3}}} - \frac{2}{w}\,dw}}$$ Solution
20. $$\displaystyle \int{{\frac{1}{{1 + {x^2}}} + \frac{{12}}{{\sqrt {1 - {x^2}} }}\,dx}}$$ Solution
21. $$\displaystyle \int{{6\cos \left( z \right) + \frac{4}{{\sqrt {1 - {z^2}} }}\,dz}}$$ Solution
22. Determine $$f\left( x \right)$$ given that $$f'\left( x \right) = 12{x^2} - 4x$$ and $$f\left( { - 3} \right) = 17$$. Solution
23. Determine $$g\left( z \right)$$ given that $$g'\left( z \right) = 3{z^3} + \frac{7}{{2\sqrt z }} - {{\bf{e}}^z}$$ and $$g\left( 1 \right) = 15 - {\bf{e}}$$. Solution
24. Determine $$h\left( t \right)$$ given that $$h''\left( t \right) = 24{t^2} - 48t + 2$$, $$h\left( 1 \right) = - 9$$ and $$h\left( { - 2} \right) = - 4$$. Solution