Mathematics

# $\displaystyle \int \frac{co\sec^{2}x-203}{\left ( \cos x \right )^{203}}dx$

$\displaystyle \frac{-\cot x}{\left ( \cos x \right )^{203}}$

##### SOLUTION
$\displaystyle \int \left ( \cos^{-203} x\right )co\sec^{2}xdx-\int \frac{203}{\left ( \cos x \right )^{203}}dx$
$\displaystyle =I_{1}-I_{2}$
Integrate $\displaystyle I_{1}$ by parts
$\displaystyle \therefore I_{1}=\left ( \cos ^{-203}x \right )\left ( -\cot x \right )-\int \cot x.203\cos ^{-204}x\left ( -\sin x \right )dx$
$\displaystyle I_{1}=-\frac{\cot x}{\left ( \cos x \right )^{203}}+\int \frac{203}{\left ( \cos x \right )^{203}}dx +C$
$\displaystyle \therefore I_{1}-I_{2}=-\frac{\cot x}{\left ( \cos x \right )^{203}}+C$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114

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