What is the integral of $int (tan(2x))^2$ ?

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Answer 1 · 2016-08-30T19:30:13

$1/2tan(2x)-x+C$

Note that $(tan(2x))^2=tan^2(2x)$ .

We have:

$inttan^2(2x)dx$

Recall that, through the Pythagorean identity, $tan^2(x)=sec^2(x)-1$ .

$=int(sec^2(2x)-1)dx$

Split up the integral:

$=intsec^2(2x)dx-intdx$

$=intsec^2(2x)dx-x$

Now, let $u=tan(2x)$ . This means that $du=2sec^2(2x)dx$ .

$=1/2int2sec^2(2x)dx-x$

$=1/2intdu-x$

$=1/2u-x+C$

$=1/2tan(2x)-x+C$

What is the integral of int (tan(2x))^2int (tan(2x))^2?