Question

Integration:-

${\displaystyle {\int \cfrac{\sec^2x}{\cosec^2x}dx}}$​

Answer 1

SOLUTION :-

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\\ : \implies{ \tt{ \int \dfrac{e^{2x}}{e^{2x}+1} - \frac{2 {e}^{x} }{ {e}^{2x} + 1} \: dx }}\\ \\ \end{gathered}\end{gathered}\end{gathered} \end{gathered} </p><p>$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\\ : \implies{ \tt{ \int \dfrac{e^{2x}}{e^{2x}+1} \: dx - \int\frac{2 {e}^{x} }{ {e}^{2x} + 1} \: dx }}\\ \\ \end{gathered}\end{gathered}\end{gathered} \end{gathered}$

$\begin{gathered}\\ : \implies{ \tt{ \frac{1}{2} \times in \bigg( {e}^{2x} + 1 \bigg) - \int\frac{2 {e}^{x} }{ {e}^{2x} + 1} \: dx }}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\\ : \implies{ \tt{ \frac{1}{2} \times in \bigg( {e}^{2x} + 1 \bigg) - 2 \: arctan \bigg( {e}^{x} \bigg) }}\\ \\ \end{gathered}\end{gathered}\end{gathered} \end{gathered}$

Answer 2

Answer:

It is the correct answer.

Step-by-step explanation:

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