Answer :
integral (2x^2+4)/(x^3+4x) dx =
integral (3x^2+4)/(x^3+4x) dx - integral (x^2)/(x^3+4x) dx =
integral d(x^3+4x)/(x^3+4x) -1/2*integral d(x^2+4)/(x^2+4) =
ln|x^3+4x| -1/2*ln|x^2+4| + C =
ln|x*sqrt(x^2+4)| + C
integral (3x^2+4)/(x^3+4x) dx - integral (x^2)/(x^3+4x) dx =
integral d(x^3+4x)/(x^3+4x) -1/2*integral d(x^2+4)/(x^2+4) =
ln|x^3+4x| -1/2*ln|x^2+4| + C =
ln|x*sqrt(x^2+4)| + C
