# Thread: Difficult integration

1. ## Difficult integration

I'm having some trouble with a more complicated problem.

$\displaystyle \int \frac {x^{3x}} {\sqrt {4 - e^{6x}}}$

So far I have:

$\displaystyle u = e ^{3x}$ so $\displaystyle \frac {1}{3}du = e^{3x}dx$

That gives me:

$\displaystyle \frac {1}{3}\int \frac {x^{3x}}{\sqrt{4-u^2}}dx$

I need help getting rid of that x on top and turn that 4 into a 1. I'm sure that I'm missing something obvious.

2. Originally Posted by Chicken Enchilada
I'm having some trouble with a more complicated problem.

$\displaystyle \int \frac {x^{3x}} {\sqrt {4 - e^{6x}}}$

So far I have:

$\displaystyle u = e ^{3x}$ so $\displaystyle \frac {1}{3}du = e^{3x}dx$

That gives me:

$\displaystyle \frac {1}{3}\int \frac {x^{3x}}{\sqrt{4-u^2}}dx$

I need help getting rid of that x on top and turn that 4 into a 1. I'm sure that I'm missing something obvious.
I suspect the question is meant to be $\displaystyle \int \frac {{\color{red}e}^{3x}} {\sqrt {4 - e^{6x}}} \, {\color{red}dx}$

3. Originally Posted by mr fantastic
I suspect the question is meant to be $\displaystyle \int \frac {{\color{red}e}^{3x}} {\sqrt {4 - e^{6x}}} \, {\color{red}dx}$
Good point. I will take it for a typo then. I got all the other problems done, so I think I'm set. Thank You.