531.

$\int \frac{1}{\sin \left(\mathrm{x}\right)\cos \left(\mathrm{x}\right)}\mathrm{dx}$ is equal to

• $\log \left|\tan \left(\mathrm{x}\right)\right| + \mathrm{C}$

• $\log \left|\sin \left(2\mathrm{x}\right)\right| + \mathrm{C}$

• $\log \left|\sec \left(\mathrm{x}\right)\right| + \mathrm{C}$

• $\log \left|\cos \left(\mathrm{x}\right)\right| + \mathrm{C}$

$\int \frac{2\mathrm{x} + \sin \left(2\mathrm{x}\right)}{1 + \cos \left(2\mathrm{x}\right)}\mathrm{dx}$ is equal to

• $\mathrm{x} + \log \left(\tan \left(\mathrm{x}\right)\right) + \mathrm{C}$

• $\mathrm{xlog}\left|\tan \left(\mathrm{x}\right)\right| + \mathrm{C}$

• $\mathrm{xtan}\left(\mathrm{x}\right) + \mathrm{C}$

• $\mathrm{x} + \tan \left(\mathrm{x}\right) + \mathrm{C}$

$\int \frac{1}{8{\sin }^2\left(\mathrm{x}\right) + 1}\mathrm{dx}$ is equal to

• ${\sin }^{-1}\left(\tan \left(\mathrm{x}\right)\right) + \mathrm{C}$

• $\frac{1}{3}{\sin }^{-1}\left(\tan \left(\mathrm{x}\right)\right) + \mathrm{C}$

• $\frac{1}{3}{\tan }^{-1}\left(3\tan \left(\mathrm{x}\right)\right) + \mathrm{C}$

• ${\tan }^{-1}\left(3\tan \left(\mathrm{x}\right)\right) + \mathrm{C}$

${\int }_0^{\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\log \left(\frac{\cos \left(\mathrm{x}\right)}{\sin \left(\mathrm{x}\right)}\right)\mathrm{dx}$ is equal to

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{4}$

• $\mathrm{\pi }$

• 0

The value of ${\int }_{- 1}^{2}4{\mathrm{x}}^2\left|\mathrm{x}\right|d\mathrm{x}$ is equal to

• 17

• 16

• 15

• 14

The value of ${\int }_2^4\left(\mathrm{x} - 2\right)\left(\mathrm{x} - 3\right)\left(\mathrm{x} - 4\right)\mathrm{dx}$ is equal to

• $\frac{1}{2}$

• 2

• 3

• 0

${\int }_0^{\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\frac{\sqrt{\sin \left(\mathrm{x}\right)}}{\sqrt{\sin \left(\mathrm{x}\right)} + \sqrt{\cos \left(\mathrm{x}\right)}}\mathrm{dx}$ is equal to

• 0

• $- \mathrm{\pi }$

• $\raisebox{1ex}{$3\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

• $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$

${\int }_{2016}^{2017}\frac{\sqrt{\mathrm{x}}}{\sqrt{\mathrm{x}} + \sqrt{4033} - \mathrm{x}}\mathrm{dx}$ is equal to

• 1/4

• 3/2

• 2017/2

• 1/2

${\int }_{- 1}^1\max \left\{\mathrm{x}, {\mathrm{x}}^3\right\}\mathrm{dx}$ is equal to

• 3/4

• 1/4

• 1/2

• 1

$\int \frac{{\mathrm{x}}^2}{1 + {\left({\mathrm{x}}^3\right)}^2}\mathrm{dx}$ is equal to

• ${\tan }^{-1}\left({\mathrm{x}}^2\right) + \mathrm{C}$

• $\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.{\tan }^{-1}\left({\mathrm{x}}^3\right) + \mathrm{C}$

• $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.{\tan }^{-1}\left({\mathrm{x}}^3\right) + \mathrm{C}$

• $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.{\tan }^{-1}\left({\mathrm{x}}^2\right) + \mathrm{C}$