Integration by parts

[Subject 13]

\(\displaystyle \displaystyle{\int x*arcsin^2(x)dx=?}\)
i got to
\(\displaystyle \displaystyle{\int x*arcsin^2(x)dx=\frac{x^2}{2}*arcsin^2(x)+x*arcsin(x)*\sqrt{1-x^2}-\frac{x^2}{2}-\int arcsin(x)*\sqrt{1-x^2}}\) and i don`t know how to go further...

 

[Deleted member 4993]

\(\displaystyle \displaystyle{\int x*arcsin^2(x)dx=?}\)
i got to
\(\displaystyle \displaystyle{\int x*arcsin^2(x)dx=\frac{x^2}{2}*arcsin^2(x)+x*arcsin(x)*\sqrt{1-x^2}-\frac{x^2}{2}-\int arcsin(x)*\sqrt{1-x^2}}\) and i don`t know how to go further...

d/dx[{arcsin(x)}^2] = 2 * arcsin(x) * d/dx[arcsin(x)] = = 2 * arcsin(x) * 1/√[1-x^2]

from Wolframalfa.com