- #1
apiwowar
- 96
- 0
the problem is find the integral of xarctan(x^2)dx
i set w = x^2, so 1/2dw = xdx
then i plug that into the integral to get
the integral of 1/2arctan(w)dw
so i let u = arctan(w) and dv = dw
so du = dw/(1+w^2) and v = w
so then the integral of udv = uv - integral of vdu
so 1/2(w*arctan(w) - integral of w * 1/(1+w^2)dw is what i end up with
but then if i would have to do integration by parts on the second integral
which gets me at
1/2(w*arctan(w) - wln(1+w^2) - integral of ln(1+w^2)dw
and that gets me stuck due to the having to take the antiderivative of the natural log
any help would be appreciated. and sorry if its hard to read
i set w = x^2, so 1/2dw = xdx
then i plug that into the integral to get
the integral of 1/2arctan(w)dw
so i let u = arctan(w) and dv = dw
so du = dw/(1+w^2) and v = w
so then the integral of udv = uv - integral of vdu
so 1/2(w*arctan(w) - integral of w * 1/(1+w^2)dw is what i end up with
but then if i would have to do integration by parts on the second integral
which gets me at
1/2(w*arctan(w) - wln(1+w^2) - integral of ln(1+w^2)dw
and that gets me stuck due to the having to take the antiderivative of the natural log
any help would be appreciated. and sorry if its hard to read