anonymous
  • anonymous
How can you solve the following integrals:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\int\limits_{a}^{b} e ^{2x}/(1+e^{x}) dx\] --> its just an indefinite integral
anonymous
  • anonymous
\[\int\limits_{0}^{1} xln \left| 1 + x ^{2} \right|\]
anonymous
  • anonymous
*dx

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hartnn
  • hartnn
u=1+e^x du = e^x dx e^{2x} = e^x *e^x where e^x = u-1
anonymous
  • anonymous
yea im stuck at u-1/ u du
hartnn
  • hartnn
for 2nd, 1+x^2=u
hartnn
  • hartnn
(u-1)/u = u -1/u
anonymous
  • anonymous
oh so i can integrate u/u - 1/u x.x
anonymous
  • anonymous
Sorry the x.x isn't part of it
hartnn
  • hartnn
yes, you can, easily.
hartnn
  • hartnn
for 2nd, you'll just need to integrate ln u
anonymous
  • anonymous
I thought I needed to use integration by part for expressions that had the product rule :/
hartnn
  • hartnn
when you can substitute and simplify, why go for parts ? :)
anonymous
  • anonymous
oooohh and u= 1+ x^2 and du= 2xdx and du/2 = xdx. that was helpful :D
anonymous
  • 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
hartnn
  • hartnn
still you'll need integration by parts to integrate ln u
hartnn
  • hartnn
not necessary always, forst try substitution
hartnn
  • hartnn
*first
anonymous
  • anonymous
ah so I have to change the limits of integration then go the integration by part. ALright thanks a lot!!
hartnn
  • hartnn
thats correct :) welcome ^_^

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