anonymous
  • anonymous
How to prove the indefinite integral of arctanx?
Mathematics
jamiebookeater
  • jamiebookeater
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freckles
  • freckles
the question seems incomplete do you want to prove it is an even function? is the question not to prove it and just find it?
freckles
  • freckles
what do you want to prove about it exactly?
anonymous
  • anonymous
I just want to prove its solution

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anonymous
  • anonymous
http://math.stackexchange.com/questions/629940/a-definite-integral-containing-arctan-x Don't know if this site will help you @freckles
freckles
  • freckles
you mean find it solution? because this question is incomplete
freckles
  • freckles
find its solution*
anonymous
  • anonymous
\[\int\limits_{}^{}arctanx\]
anonymous
  • anonymous
yeah the solution'
anonymous
  • anonymous
not a proof i guess then
freckles
  • freckles
oh ok because this question reminds me of saying something like prove 5 like prove 5 is what :p
freckles
  • freckles
anyways you could do a substituion let u=arctan(x) then tan(u)=x differentiating both sides gives sec^2(u) du=dx
freckles
  • freckles
\[\int\limits_{}^{} u \sec^2(u) du\]
freckles
  • freckles
try integration by parts
freckles
  • freckles
you could actually do integration by parts even before substitution
anonymous
  • anonymous
so u=arctanx and dv=dx?
freckles
  • freckles
yeah
anonymous
  • anonymous
i got xarctanx - 1/2ln(1+x^2)
anonymous
  • anonymous
+C
freckles
  • freckles
\[\int\limits_{}^{} 1 \cdot \arctan(x) dx \\ =x \arctan(x)-\int\limits x \frac{1}{1+x^2} dx\] and yes for the second integral you are right because you can just do the sub u=1+x^2
anonymous
  • anonymous
ok thank you! was a lot simpler than i realized
freckles
  • freckles
and @A.S.L. my question was not about integrating arctan(x) it was about what the prove meant before that part...
freckles
  • freckles
for example "evaluate the indefinite integral of arctan(x)" I would have no questions about this meaning
anonymous
  • anonymous
Sorry My mistake @freckles
freckles
  • freckles
no apologies necessary

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