Question

‎1) Integral of 1/ ( x^2 - x ) dx

2) x / (x^2+1) dx = (y^2 + 1) / (y+1) dy

Answer 1

We'll decompose the fraction 1/ ( x^2 - x ) into elementary fractions
Int dx/ ( x^2 - x ) = -Int dx/x + Int dx/(x-1)
Int dx/ ( x^2 - x ) = -ln|x| + ln|x-1| + C
Int dx/ ( x^2 - x ) = ln|(x-1)/x| + C

Answer 2

Thank you.