(Solved): Use integration by parts to prove the reduction formula. [(In(x))" dx = x(in(x))" - nf (In(x))^-1 d ...

Use integration by parts to prove the reduction formula. [(In(x))" dx = x(in(x))" - nf (In(x))^-1 dx Let u = (In(x))", then dv = dx. Then du = (n(In(x))n-¹dx By the equation a fudv= -fvdu, vdu, the integration by parts gives the following. [ (in(x))" dx = (x- (ln(x))"){(x)²° ? S ×( ½-n(ln(x)})}"?¹dx - ) ex -x(In(x)}" - nf (In(x))^- 1 dx -n Watch it Need Help? Read It u dv = uv- dx and ignoring any arbitrary constants v = X