Exponential and logarithmic functions are very important for integrating. Exponential functions have their own set of integration rules and logarithmic functions are necessary in order to find the integrals of tangent, cotangent, cosecant, and secant functions.
This image shows the basics of exponential integration. The first formula on this list is one of the most important rules to follow when integrating exponential functions.
This YouTube video goes in-depth on logarithmic functions, with the beauty and style only this magnificently monotone man can.