A tricky integral...

**pianopiano** · February 14th 2009, 05:24 PM

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

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

**Krizalid** · February 14th 2009, 05:34 PM

There's no much here, just put $u=\sqrt3e^x$ and the remaining integral is an arctangent.

**pianopiano** · February 14th 2009, 06:17 PM

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...

**mr fantastic** · February 14th 2009, 06:32 PM

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 $e^x = \sqrt{3} u \Rightarrow e^{2x} = 3 u^2$ and $\frac{du}{dx} = \frac{e^x}{\sqrt{3}} \Rightarrow dx = \frac{\sqrt{3}}{e^x} = \frac{\sqrt{3}}{u}$ .

So hop to it, make the substitution ....

**Krizalid** · February 14th 2009, 06:37 PM

Ahhh, yes, that's the substitution, my head is in other place.

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