Question

What is the integral of ${\tan }^{2}x$?

Answer 1

Find the integral of ${\tan }^{2}x$.

$$\begin{gathered} \int {\tan }^{2}xdx=\int \left(se{c}^{2}x-1\right)dx\left\{\because \mathit{s}\mathit{e}{\mathit{c}}^{\mathbf{2}}\mathit{x}\mathbf{-}\mathit{t}\mathit{a}{\mathit{n}}^{\mathbf{2}}\mathit{x}\mathbf{=}\mathbf{1}\right\} \\ \int {\tan }^{2}xdx=\tan x-x+C\left\{\because \int se{c}^{2}xdx=\tan x,\int 1dx=x.\right\} \end{gathered}$$

Hence, the required integral is $\int {\tan }^{2}xdx=\tan x-x+C$ ,where $C$ is a constant of integration .