<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass[a4paper,12pt]{article}
\newcommand\ds{\displaystyle}
\begin{document}

\parindent=0pt

QUESTION

Find $\ds\int\frac{\sec^2x}{1+\tan x}\,dx$.

\bigskip

ANSWER

$\ds\int\frac{\sec^2x}{1+\tan x}\,dx=\ln|1+\tan x|+C\\ \{u=\tan
x,du=\sec^2xdx;$ therefore $\ds
I=\int\frac{1}{2}du(u^6)=\frac{u^7}{2(7)}+c$\}




\end{document}
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