Mark the correct alternative in each of the following:

Question:

Mark the correct alternative in each of the following:

Evaluate $\int \frac{\sin ^{2} x}{\cos ^{4} x} d x=$

A. $\frac{1}{3} \tan ^{2} \mathrm{x}+\mathrm{C}$

B. $\frac{1}{2} \tan ^{2} \mathrm{x}+\mathrm{C}$

C. $\frac{1}{3} \tan ^{3} \mathrm{x}+\mathrm{C}$

D. none of these

Solution:

$I=\int(\tan x)^{2}(\sec x)^{2} d x$

$\Rightarrow \tan \mathrm{x}=\mathrm{t}\left[\frac{d t}{d x}=(\sec x)^{2}\right]$

$\Rightarrow \int t^{2} d t=\frac{t^{3}}{3}+c$

$\Rightarrow I=\frac{1}{3}(\tan x)^{3}+c$

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