# Integration problem

#### karfag

Hello everyone,
I've been preparing for my cal exam and I got stuck on this problem:
Evaluate the infinite integral
$$\displaystyle \int \frac {\sec^4 x}{\sqrt(tan 2x)} dx$$
I would really appreciate if you give me a clue on how I should do it because I've been trying different trigonometric identities and other methods for quite some time with no results.
Thank you

#### AllanCuz

Hello everyone,
I've been preparing for my cal exam and I got stuck on this problem:
Evaluate the infinite integral
$$\displaystyle \int \frac {\sec^4 x}{\sqrt(tan 2x)} dx$$
I would really appreciate if you give me a clue on how I should do it because I've been trying different trigonometric identities and other methods for quite some time with no results.
Thank you

Last edited:

#### karfag

I think you did not notice that it is a square root of tan(2x)... That is exactly what I was doing except that with square root it does not seem to lead anywhere.

#### AllanCuz

I think you did not notice that it is a square root of tan(2x)... That is exactly what I was doing except that with square root it does not seem to lead anywhere.
Edit- lag. You're right, give me a moment i'll try something

#### Sudharaka

Hi everyone,

I don't think we can solve this integral using general methods. I mean it needs some advanced mathematics. Please refer, Wolfram Mathematica Online Integrator

karfag and AllanCuz

karfag

#### karfag

Eh, well I found it in previous final exam. First year college calculus.. I know the answer but I wanted to know how to get it. Well thanks for a try, if I'll figure it out, I'll post it lol

#### Sudharaka

Eh, well I found it in previous final exam. First year college calculus.. I know the answer but I wanted to know how to get it. Well thanks for a try, if I'll figure it out, I'll post it lol
Dear karfag,

#### karfag

(tan(2x))^1/2 + 1/5 * (tan(2x))^5/2 + C

Sorry for not writing it the correct way, I'm not very familiar with the math tags syntax

#### Sudharaka

Differentiate $$\displaystyle (tan(2x))^{1/2} + \frac{1}{5} (tan(2x))^{5/2}+C$$ and you would obtain, $$\displaystyle \frac {\sec^{4} 2x}{\sqrt{tan 2x}}$$. Hence the integration should be $$\displaystyle \int\frac {\sec^{4} 2x}{\sqrt{tan 2x}}$$