Write a value


Write a value of $\int \tan x \sec ^{3} x d x$.


given $\int \tan x \sec ^{3} x d x$

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

Let $\sec x=t$

Differentiating on both sides we get,

$\tan x \sec x d x=d t$

Substituting above equation in $\int \tan x \sec ^{3} x d x$ we get,

$=\int t^{2} d t$


$=\frac{\sec ^{3} x}{3}+c$

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