Question

find the antiderivative of f(x)=(x^2)/(x^3+5) with explanation

Answer 1

I know that if
y = ln u
derivative is u'/u
I noticed that he the derivative of the denominator x^3 + 5
appears on the top as a multiple of that

so let's start with
y = ln(x^3 + 5)
dy/dx = 3x^2/(x^3 + 5)
all we have to do is get rid of the 3

so integral (x^2)/(x^3 + 5) = (1/3)ln(x^3 + 5) + c