anonymous one year ago How to prove the indefinite integral of arctanx?

1. 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?

2. freckles

what do you want to prove about it exactly?

3. anonymous

I just want to prove its solution

4. anonymous

5. freckles

you mean find it solution? because this question is incomplete

6. freckles

find its solution*

7. anonymous

$\int\limits_{}^{}arctanx$

8. anonymous

yeah the solution'

9. anonymous

not a proof i guess then

10. freckles

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

11. freckles

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

12. freckles

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

13. freckles

try integration by parts

14. freckles

you could actually do integration by parts even before substitution

15. anonymous

so u=arctanx and dv=dx?

16. freckles

yeah

17. anonymous

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

18. anonymous

+C

19. 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

20. anonymous

ok thank you! was a lot simpler than i realized

21. freckles

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

22. freckles

23. anonymous

Sorry My mistake @freckles

24. freckles

no apologies necessary