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[x^2/sqrt(1-x^2)dx] = |замена x = sint| = (x^2/2)*arcsinx - (1/2)int[sin^2(t)/sqrt(1-sin^2(t)dt] = (x^2/2)*arcsinx - (1/2)int[sin^2(t)/sqrt(cos^2(t))dt] = (x^2/2)*arcsinx - (1/2)int[sin^2(t)/cos(t)dt]... а дальше как? int[sin^2(t)/cos(t)dt] = int[sint*tgt dt]?