How can you solve the following integrals:

Question

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

*dx

hartnn · Answer

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

anonymous · Answer

yea im stuck at u-1/ u du

hartnn · Answer

for 2nd, 1+x^2=u

hartnn · Answer

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

anonymous · Answer

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

anonymous · Answer

Sorry the x.x isn't part of it

hartnn · Answer

yes, you can, easily.

hartnn · Answer

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

anonymous · Answer

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

hartnn · Answer

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

anonymous · Answer

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

anonymous · Answer

so you don't always have to use integration by part when using something that includes the product rule? ( I'm referring to things like xe^x

hartnn · Answer

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

hartnn · Answer

not necessary always, forst try substitution

hartnn · Answer

*first

anonymous · Answer

ah so I have to change the limits of integration then go the integration by part. ALright thanks a lot!!

hartnn · Answer

thats correct :)
welcome ^_^