MHB What Techniques Can Simplify Integrating \(\frac{e^x}{e^{2x} + 1}\)?

[tmt1]

I have this integral

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

And I'm not sure how to approach this. I've tried u-substitution a few ways, but it seems to go to a dead end. I'm not sure how to apply partial fractions, trig-substitution, or integration by parts to this problem.

 

[MarkFL]

I would look at:

$$u=e^x\,\therefore\,du=e^x\,dx$$

And so now you have:

$$\int \frac{1}{u^2+1}\,du$$