1. ${\displaystyle \int (x^{2}-2)^{2}dx}$

2. ${\displaystyle \int 8x^{3}dx}$

3. ${\displaystyle \int (4x^{2}+11x^{3})dx}$

4. ${\displaystyle \int (31x^{32}+4x^{3}-9x^{4})dx}$

5. ${\displaystyle \int 5x^{-2}\,dx}$

6. ${\displaystyle \int {\bigl (}\cos(x)+\sin(x){\bigr )}dx}$

7. ${\displaystyle \int 3\sin(x)dx}$

8. ${\displaystyle \int {\bigl (}1+\tan ^{2}(x){\bigr )}dx}$

9. ${\displaystyle \int {\bigl (}3x-\sec ^{2}(x){\bigr )}dx}$

10. ${\displaystyle \int -e^{x}\,dx}$

11. ${\displaystyle \int 8e^{x}\,dx}$

12. ${\displaystyle \int {\frac {dx}{7x}}}$

13. ${\displaystyle \int {\frac {dx}{x^{2}+a^{2}}}}$

14. Consider the integral ${\displaystyle \int \sin(x)\cos(x)dx}$ . Find the integral in two different ways. (a) Integrate by parts with ${\displaystyle u=\sin(x)}$ and ${\displaystyle v'=\cos(x)}$ . (b) Integrate by parts with ${\displaystyle u=\cos(x)}$ and ${\displaystyle v'=\sin(x)}$ . Compare your answers. Are they the same?