Mathematics

# Solve $\int {\frac{1}{\cos ^2x(1-\tan x)^2}dx}$

##### SOLUTION
$I = \int \frac{1}{cos^{2}x(1-tanx)^{2}}dx$
$I = \int \frac{sec^{2}x}{(1-tanx)^{2}}dx$
$1-tanx = t$
$-sec^{2}xdx = dt$
$I = -\int \frac{dt}{t^{2}}$
$= -\frac{t^{-2+1}}{(-2+1)}+c$
$I = +t^{-1}+c$
$I = \frac{1}{t}+c$
$I = \frac{1}{(1-tanx)}+c$
$\therefore \int \frac{1}{cos^{2}x(1-tanx)^{2}}dx = \frac{1}{(1-tanx)}+c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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