Efficient Methods for Solving Integrals with Trigonometric Substitution

[soe236]

1. integral(e^(2x)/$$\sqrt{}(e^2^x+1)$$)dx and integral(e^(x)/$$\sqrt{}(e^2^x+1)$$)dx







3. I tried solvign by letting u=e^x and used trig substitution for $$\sqrt{}u^2+1$$ where x=tan(theta), d(theta)=sec^2(theta), $$\sqrt{}u^2+1$$=sec(theta) but got stuck

 

[sutupidmath]

$$\int\frac{e^{2x}}{\sqrt(e^{2x}+1)}dx$$ letting

$$t^{2}=e^{2x}+1=>2tdt=2e^{2x}dx=>tdt=e^{2x}dx$$,
I think you can go from here, right? Similarly try the other, and show a little more work please!