Ah ok. Was having trouble visualizing the exponents.
So rewrite $$e^{2x}$$ as $$(e^{x})^{2}$$ then replace the $$e^{x}$$ with u.
I was stuck on having to replace the $$e^{x}$$ with a $$e^{2x}$$ whole.
Thanks!
Re: Intergral of Rational Exponential
No I have not seen that exact form. It looks similar to the anti-derivative of arctan:
$$\int \frac{1}{1 + {x}^{2}} dx = arctan$$
Not sure where the $${u}^{'} $$ comes from unless you are referring to the du from the u substitution in prime notation...
Hi,
I'm new to this forum. This semester I took Calculus I and just took the final yesterday. There were a few questions that were unexpected that I didn't know how to handle. This integral has got me stumped.$$\int_{0}^{1} e^{x}/(1 + e^{2x}) \,dx$$
The techniques I know at this point...