# Difficult integration

• Sep 13th 2009, 07:48 PM
Difficult integration
I'm having some trouble with a more complicated problem.

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

So far I have:

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

That gives me:

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

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.
• Sep 14th 2009, 02:43 AM
mr fantastic
Quote:

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

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

So far I have:

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

That gives me:

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

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 $\int \frac {{\color{red}e}^{3x}} {\sqrt {4 - e^{6x}}} \, {\color{red}dx}$
• Sep 14th 2009, 02:49 PM
I suspect the question is meant to be $\int \frac {{\color{red}e}^{3x}} {\sqrt {4 - e^{6x}}} \, {\color{red}dx}$