Assistance on beginning the integral $\int\frac{dx}{(x+1)(n-x)}$

Question

This is the integral $$\int\frac{dx}{(x+1)(n-x)}=\int kdt$$ I just need some assistance on how to begin the left side integral and I will most likely be able to continue it from there thank you.

Answer 1

All what you need to do is partial fractions for the left hand sided term then you will have two fractions and their integration will be in the form of $ln(x)$.

Answer 2

HINT : there is $(a,b)$ such as $$1/((x+1)(n-x)) = a/(x+1) +b/(n-x)$$ if $n\ne-1$