## anonymous 3 years ago How can you solve the following integrals:

1. anonymous

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

2. anonymous

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

3. anonymous

*dx

4. hartnn

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

5. anonymous

yea im stuck at u-1/ u du

6. hartnn

for 2nd, 1+x^2=u

7. hartnn

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

8. anonymous

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

9. anonymous

Sorry the x.x isn't part of it

10. hartnn

yes, you can, easily.

11. hartnn

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

12. anonymous

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

13. hartnn

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

14. anonymous

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

15. anonymous

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

16. hartnn

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

17. hartnn

not necessary always, forst try substitution

18. hartnn

*first

19. anonymous

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

20. hartnn

thats correct :) welcome ^_^