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

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

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

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

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

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

• $\frac{1}{2}\log \left|\log \left({\mathrm{x}}^2\right)\right| + \mathrm{C}$

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

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

• $\frac{1}{4}\log \left|\log \left({\mathrm{x}}^2\right)\right| + \mathrm{C}$

${\int }_0^1\frac{1}{\left({\mathrm{x}}^2 + 16\right)\left({\mathrm{x}}^2 + 25\right)}\mathrm{dx}$ is equal to

• $\frac{1}{5}\left[\frac{1}{4}{\tan }^{-1}\left(\frac{1}{4}\right) - \frac{1}{5}{\tan }^{-1}\left(\frac{1}{5}\right)\right]$

• $\frac{1}{9}\left[\frac{1}{4}{\tan }^{-1}\left(\frac{1}{4}\right) - \frac{1}{5}{\tan }^{-1}\left(\frac{1}{5}\right)\right]$

• $\frac{1}{4}\left[\frac{1}{4}{\tan }^{-1}\left(\frac{1}{4}\right) - \frac{1}{5}{\tan }^{-1}\left(\frac{1}{5}\right)\right]$

• $\frac{1}{9}\left[\frac{1}{5}{\tan }^{-1}\left(\frac{1}{4}\right) - \frac{1}{4}{\tan }^{-1}\left(\frac{1}{5}\right)\right]$

524.

${\int }_{- 1}^1\mathrm{x}\left(1 - \mathrm{x}\right)\left(1 +\hspace{0.17em}\mathrm{x}\right)\mathrm{dx}$ is equal to

• $\frac{1}{3}$

• $\frac{2}{3}$

• 1

• 0

The value of ${\int }_{- \mathrm{\pi }}^{\mathrm{\pi }}\frac{{\sin }^2\left(\mathrm{x}\right)}{1 + 7^{\mathrm{x}}}\mathrm{dx}$ is

• 7^x

• $\mathrm{\pi }$

• $\frac{\mathrm{\pi }}{2}$

• $2^{\mathrm{\pi }}$

${\int }_0^{\raisebox{1ex}{$\sqrt{\mathrm{\pi }}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}2{\mathrm{x}}^3\sin \left({\mathrm{x}}^2\right)\mathrm{dx}$ is equal to

• $\frac{1}{\sqrt{2}}\left(1 + \frac{\mathrm{\pi }}{4}\right)$

• $\frac{1}{\sqrt{2}}\left(1 - \frac{\mathrm{\pi }}{4}\right)$

• $\frac{1}{\sqrt{2}}\left(\frac{\mathrm{\pi }}{2} - 1\right)$

• $\frac{1}{\sqrt{2}}\left(1 - \frac{\mathrm{\pi }}{2}\right)$

$\int {\left(\sec \left(\mathrm{x}\right)\right)}^{\mathrm{m}}\left({\tan }^3\left(\mathrm{x}\right) + \tan \left(\mathrm{x}\right)\right)\mathrm{dx}$ is equal to

• ${\sec }^{\mathrm{m} + 2}\left(\mathrm{x}\right) + \mathrm{C}$

• ${\tan }^{\mathrm{m} +\hspace{0.17em}2}\left(\mathrm{x}\right) + \mathrm{C}$

• $\frac{{\sec }^{\mathrm{m} + 2}\left(\mathrm{x}\right)}{\mathrm{m} + 2} +\hspace{0.17em}\mathrm{C}$

• $\frac{{\tan }^{\mathrm{m} + 2}\left(\mathrm{x}\right)}{\mathrm{m} + 2} +\hspace{0.17em}\mathrm{C}$

$\int \frac{1}{7}\sin \left(\frac{\mathrm{x}}{7} + 10\right)\mathrm{dx}$ is equal to

• $\frac{1}{7}\cos \left(\frac{\mathrm{x}}{7} + 10\right) + \mathrm{C}$

• $- \frac{1}{7}\cos \left(\frac{\mathrm{x}}{7} + 10\right)\mathrm{dx}$

• $- \cos \left(\frac{\mathrm{x}}{7} + 10\right) + \mathrm{C}$

• $- 7\cos \left(\frac{\mathrm{x}}{7} + 10\right) + \mathrm{C}$

$\int \left(\frac{\mathrm{x} - \mathrm{a}}{\mathrm{x}} - \frac{\mathrm{x}}{\mathrm{x} +\hspace{0.17em}\mathrm{a}}\right)\mathrm{dx}$ is equal to

• $\log \left|\frac{\mathrm{x} + \mathrm{a}}{\mathrm{x}}\right| + \mathrm{C}$

• $\mathrm{alog}\left|\frac{\mathrm{x} + \mathrm{a}}{\mathrm{x}}\right| + \mathrm{C}$

• $\mathrm{alog}\left|\frac{\mathrm{x}}{\mathrm{x} +\hspace{0.17em}\mathrm{a}}\right| + \mathrm{C}$

• $\log \left|\frac{\mathrm{x} + \mathrm{a}}{\mathrm{x}}\right| + \mathrm{C}$

$\int {\mathrm{x}}^4{\mathrm{e}}^{{\mathrm{x}}^5}\cos \left({\mathrm{e}}^{{\mathrm{x}}^5}\right)\mathrm{dx}$ is equal to

• $\frac{1}{3}\sin \left({\mathrm{e}}^{{\mathrm{x}}^5}\right) + \mathrm{C}$

• $\frac{1}{4}\sin \left({\mathrm{e}}^{{\mathrm{x}}^5}\right) + \mathrm{C}$

• $\frac{1}{5}\sin \left({\mathrm{e}}^{{\mathrm{x}}^5}\right) + \mathrm{C}$

• $\sin \left({\mathrm{e}}^{{\mathrm{x}}^5}\right) + \mathrm{C}$