Integration of Inverse Tangent Function

[Lanza52]

[SOLVED] Integration of Inverse Tangent Function

\int \frac{e^{x}}{4+9e^{2x}}dx

Saw the problem, looked at it for a bit. Noticed that it is a inverse Tangent function. Played with some integration by parts and substitution and couldn't figure it out. Can anybody toss me a starting point on this problem?

Thanks

 

[hotcommodity]

Think of 9e^(2x) as (3e^x)^2, that should get you started.

 

[rocomath]

you're aim should be to put your integral in this form \int\frac{1}{a^{2}+x^{2}}dx so algebraically manipulate it as hotcommodity suggested.

 

[Lanza52]

Ahh...thank you guys =P

For some reason I wasn't letting myself put the 9e^2x as (3e^x)^2. Basic order of operations tricks me again.