Integral of (e^x)/(e^(2x)+3) dx

U-substitution and integration by parts doesn't seem to be working for me...:(

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- Feb 14th 2009, 05:24 PMpianopianoA 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 PMKrizalid
There's no much here, just put $\displaystyle u=\sqrt3e^x$ and the remaining integral is an arctangent.

- Feb 14th 2009, 06:17 PMpianopiano
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 PMmr fantastic
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 PMKrizalid
Ahhh, yes, that's the substitution, my head is in other place. :(