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\[\int\limits_{a}^{b} e ^{2x}/(1+e^{x}) dx\] --> its just an indefinite integral

\[\int\limits_{0}^{1} xln \left| 1 + x ^{2} \right|\]

*dx

u=1+e^x
du = e^x dx
e^{2x} = e^x *e^x
where e^x = u-1

yea im stuck at u-1/ u du

for 2nd, 1+x^2=u

(u-1)/u = u -1/u

oh so i can integrate u/u - 1/u x.x

Sorry the x.x isn't part of it

yes, you can, easily.

for 2nd, you'll just need to integrate ln u

I thought I needed to use integration by part for expressions that had the product rule :/

when you can substitute and simplify, why go for parts ? :)

oooohh and u= 1+ x^2 and du= 2xdx and du/2 = xdx. that was helpful :D

still you'll need integration by parts to integrate ln u

not necessary always, forst try substitution

*first

thats correct :)
welcome ^_^