MarcLeclair
How can you solve the following integrals:



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

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

MarcLeclair
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*dx

hartnn
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u=1+e^x
du = e^x dx
e^{2x} = e^x *e^x
where e^x = u1

MarcLeclair
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yea im stuck at u1/ u du

hartnn
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for 2nd, 1+x^2=u

hartnn
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(u1)/u = u 1/u

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

MarcLeclair
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Sorry the x.x isn't part of it

hartnn
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yes, you can, easily.

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

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

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

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

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

hartnn
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not necessary always, forst try substitution

hartnn
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*first

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

hartnn
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thats correct :)
welcome ^_^