How do you find the integral of $tan (x) sec^3(x) dx$ ?

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Answer 1 · 2015-03-06T21:56:38

The required integral is

$I = int tanxsec^3xdx$

which can be written as

$I = intsec^2x(secxtanx)dx$

Let $secx = t$

Differentiating with respect to t,

$secxtanxdx/dt = 1$
$=> secxtanxdx = dt$

This gives us the integral

$I = intt^2dt$

which has a trivial solution of

$I = t^3/3 + C$

Replacing the value of $t = secx$ , the final answer is

$I = int tanxsec^3xdx = sec^3x/3 + C$

How do you find the integral of tan (x) sec^3(x) dxtan (x) sec^3(x) dx?