int [x*arcsin(x)dx] = |u=arcsinx; dv = xdx| = (x^2/2)*arcsinx - int [x^2/(2*sqrt(1-x^2))dx] = (x^2/2)*arcsinx - (1/2)int[{(1-x^2)+1}/sqrt(1-x^2)dx] = |замена x = sint| = (x^2/2)*arcsinx - (1/2)int[(1-sin^2(t)+1)/sqrt(1-sin^2(t)) dt = (x^2/2)*arcsinx - (1/2)int[(cos^2(t)+1)/sqrt(1-sin^2(t)) dt = (x^2/2)*arcsinx - (1/2)int[d(1-sin^2(t)/sqrt(1-sin^2(t)) = (x^2/2)*arcsinx - 1/2arcsin(sint) = (x^2/2)*arcsinx - 1/2arcsinx
вот так, но я не уверена...