How can I remember the difference between differentiation and integration?

A neat trick to remember what we do to the powers when integrating and differentiating is that we INcrease the power when we INtegrate, and Decrease the power when we Differentiate! Once we've got the powers sorted, recall that for differentiation, we multiply the expression by the old power (ie x^2 becomes 2x where 2 is the old power that we are multiplying by) wherease we divide by the new power when integrating (ie x^2 becomes x^3/3 where 3 it the new power we are dividing by.)