Integral of sqrt(1 + e^(2x)) u = 1 + e^(2x) ?? Please point me in the right direction. Thank you.
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Originally Posted by jsel21 Integral of sqrt(1 + e^(2x)) u = 1 + e^(2x) ?? Please point me in the right direction. Thank you. Try this.
Originally Posted by jsel21 Integral of sqrt(1 + e^(2x)) u = 1 + e^(2x) ?? Please point me in the right direction. Thank you. integrate Sqrt[1 + Exp[2x]] - Wolfram|Alpha+ Click on Show steps.
Where Let , so that , then: Thus
Last edited by TheCoffeeMachine; Feb 8th 2011 at 05:18 PM.
Originally Posted by dwsmith Try this. Interesting... Make the substitution and the integral becomes . And now making the substitution the integral becomes which can be solved using partial fractions
Originally Posted by Prove It Interesting... Make the substitution and the integral becomes That was the first thing that came to mind.
Thanks guys, these posts were very helpful.
there's no much here, just clearing out the clutter and it's easy.
Also
take u^2 = 1 + e^(2x) so 2udu = 2e^(2x) which is 2(u^2-1)dx 2udu = 2(u^2-1)dx dx = u/(u^2-1) du put it in the question.. it will be u^2/(u^2-1) du = (u^2 - 1 + 1)/(u^2-1)du
you did the same as me.
hmm.. sorry
Originally Posted by Prove It I hate it when trig substitutions do this kind of thing. But the original integrand is positive definite, so we can discard the negative solution. Correct? Or is it more complicated than that? -Dan
In this case, on Prove's substitution, that forces to and we have that Of course we coulda taken but that makes non positive. It all depends on how you fix the angle, but that's more a matter of dealing with definite integrals.
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