Question

How to prove the indefinite integral of arctanx?

Answer 1

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?

Answer 2

what do you want to prove about it exactly?

Answer 3

I just want to prove its solution

Answer 4

http://math.stackexchange.com/questions/629940/a-definite-integral-containing-arctan-x
Don't know if this site will help you @freckles

Answer 5

you mean find it solution?

because this question is incomplete

Answer 6

find its solution*

Answer 7

\[\int\limits_{}^{}arctanx\]

Answer 8

yeah the solution'

Answer 9

not a proof i guess then

Answer 10

oh ok
because this question reminds me of saying something like
prove 5
like prove 5 is what :p

Answer 11

anyways you could do a substituion
let u=arctan(x)
then tan(u)=x
differentiating both sides gives
sec^2(u) du=dx

Answer 12

\[\int\limits_{}^{} u \sec^2(u) du\]

Answer 13

try integration by parts

Answer 14

you could actually do integration by parts even before substitution

Answer 15

so u=arctanx and dv=dx?

Answer 16

yeah

Answer 17

i got xarctanx - 1/2ln(1+x^2)

Answer 18

+C

Answer 19

\[\int\limits_{}^{} 1 \cdot \arctan(x) dx \\ =x \arctan(x)-\int\limits x \frac{1}{1+x^2} dx\]

and yes for the second integral you are right
because you can just do the sub u=1+x^2

Answer 20

ok thank you! was a lot simpler than i realized

Answer 21

and @A.S.L. my question was not about integrating arctan(x)
it was about what the prove meant before that part...

Answer 22

for example
"evaluate the indefinite integral of arctan(x)" I would have no questions about this meaning

Answer 23

Sorry My mistake @freckles

Answer 24

no apologies necessary