# Thread: Problem with Integration of trig functions

1. ## Problem with Integration of trig functions

$\int\frac{2cos^2(2t)-1}{1+3sin4t}dx$

$\int\frac{cot^2ln(1-x)}{1-x}dx$

$\int\frac{tan^2e^-x}{e^x}dx$

I am having problems with simplifying the given, before I can Integrate.
For example, the problem 1, my u is the denominator, but after deriving the u It is still impossible to solve it, same problem applies to problem 2. For number I just can't solve it

any help is appreciated, thank you

2. Originally Posted by honestliar
$\int\frac{2cos^2(2t)-1}{1+3sin4t}dx$

$\int\frac{cot^2ln(1-x)}{1-x}dx$

$\int\frac{tan^2e^-x}{e^x}dx$

I am having problems with simplifying the given, before I can Integrate.
For example, the problem 1, my u is the denominator, but after deriving the u It is still impossible to solve it, same problem applies to problem 2. For number I just can't solve it

any help is appreciated, thank you
1. note that $2\cos^2(2t) - 1 = \cos(4t)$ , let $u = 1+3\sin(4t)$

2. use the identity $\cot^2{t} = \csc^2{t} - 1$ , let $u = \ln(1-x)$

3. use the identity $\tan^2{t} = \sec^2{t} - 1$ , let $u = e^{-x}$