How do you integrate a fraction when x is on the numerator and denominator?

Firstly, ensure both numerator and denominator are factorised fully so that any possible cancellations can happen - making it easy for yourself is always a good idea. Now, turn it into partial fractions. If the denominator is a quadratic, remember to put the fractions into the form: A + B/(x+a) + C/(x+b)Once done, give each fraction its own integral, ensuring to keep the same operations in front of each fraction. Now integrate them separately - the fractions will all integrate to ln as the numerator is a differential of the denominator multiplied by a constant. After this, add +c to the end and the problem is solved!