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Ok, I give up, I have tried with $u$-substitution and integration by parts but I can't solve it. The integral is:

$$\int{\frac{e^x dx}{1+e^{2x}}}$$

I have tried $u=e^x$, $u=e^{2x}$ and also integration by parts but I can't solve it. The result should be:

$$\arctan(e^x)$$

  • 2
    $u = e^x$ works. Try it again.2012-06-24
  • 0
    You should recognize $e^x = \frac{1}{2} \frac{d}{dx} (e^x)^2$.2012-06-24

5 Answers 5