# A tricky integral...

• Feb 14th 2009, 05:24 PM
pianopiano
A tricky integral...
Integral of (e^x)/(e^(2x)+3) dx

U-substitution and integration by parts doesn't seem to be working for me...:(
• Feb 14th 2009, 05:34 PM
Krizalid
There's no much here, just put $\displaystyle u=\sqrt3e^x$ and the remaining integral is an arctangent.
• Feb 14th 2009, 06:17 PM
pianopiano
Can you explain that substitution in a little more detail? I'm not sure how you would use it. Our class isn't going over trigonometric substitutions, but there it is in one of our improper integral problems...
• Feb 14th 2009, 06:32 PM
mr fantastic
Quote:

Originally Posted by pianopiano
Can you explain that substitution in a little more detail? I'm not sure how you would use it. Our class isn't going over trigonometric substitutions, but there it is in one of our improper integral problems...

Krizalid is not suggesting a trig substitution ....

Actually, I think the substitution he intended was $\displaystyle e^x = \sqrt{3} u \Rightarrow e^{2x} = 3 u^2$ and $\displaystyle \frac{du}{dx} = \frac{e^x}{\sqrt{3}} \Rightarrow dx = \frac{\sqrt{3}}{e^x} = \frac{\sqrt{3}}{u}$.

So hop to it, make the substitution ....
• Feb 14th 2009, 06:37 PM
Krizalid
Ahhh, yes, that's the substitution, my head is in other place. :(