First slide

Methods of integration

Question

If $\int \frac{\sin 2 x}{\cos^{4} x + \sin^{4} x} d x = \tan^{- 1} (f (x)) + C$ then

Easy

A

$f (x) = x^{2}$
B

$f (x) = \cos x$
C

$f (x) = \sin x$
D

$f (x) = \tan^{2} x$

Solution

$\frac{\sin 2 x}{\cos^{4} x + \sin^{4} x} = \frac{2 \sin x \cos x}{\cos^{4} x + \sin^{4} x} = \frac{2 \tan x \sec^{2} x}{1 + \tan^{4} x}$
Now put $\tan^{2} x = t .$

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