Integrate y= arctan x for 0< x <1

[3ephemeralwnd]

the question: integrate y= arctanx for 0< x <1

i know to solve this question you should use the method of integral by parts, so i tried doing that and at some point i got
x arctanx - integral of x/1+x^2 (between 0 and 1)
.. from this point on i tried using the substitution method, w = 1 + x^2, and dx = dw / 2x
i plugged in those in and solved, but i didnt end up with the right answer

turns out the integral of x/1+x^2 is ln|1+x^2| ...
but shoudln't the method of substitution work as well? or did i do something wrong?

 

[tiny-tim]

hi 3ephemeralwnd!

(try using the X² icon just above the Reply box )

… x arctanx - integral of x/1+x^2 (between 0 and 1)
.. from this point on i tried using the substitution method, w = 1 + x^2, and dx = dw / 2x
i plugged in those in and solved, but i didnt end up with the right answer

should have worked …

(btw, it would be easier to write 2xdx = dw)

show us exactly what you did ​

 

[3ephemeralwnd]

oh sorry! i figured out my mistake

after the substituion i accidentally wrote it as w/2 instead of 1/2w

thanks for the reply though :)