How do you integrate (x/(x+1)) dx without using substitution.

A tricky question which is actually really simple if you know the technique and will save a lot of time during the exam. The method is to simply add 1 and minus one to the numerator. so the integral becomes ((x+1-1)/x+1)dx. This simplifies to the integral of ((1/x)-1/(x+1))dx as the (x+1)/(x+1) cancels out. Integrating the simplified integral then gives you a final answer of x-ln(x+1)+C.