First slide

Methods of integration

Question

$\int \frac{1}{\sqrt{\sin^{2} x \cos^{2} x - \sin^{4} x}} d x =$

Easy

A

$- \cos^{- 1} (\cot x) + C$
B

$- \cosh^{- 1} (\cot x) + C$
C

$\cosh^{- 1} (\cot x) + C$
D

$\cos^{- 1} (\cot x) + C$

Solution

$\int \frac{1}{\sin^{2} x \sqrt{\cot^{2} x - 1}} d x$
             $= \int \frac{\cos e c^{2} x}{\sqrt{\cot^{2} x - 1}} d x$

$\cot x = t \Rightarrow - \cos e c^{2} x d x = d t$

            $= - \int \frac{1}{\sqrt{t^{2} - 1}} d t$

            $= - \cosh^{- 1} (\cot x) + C$

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