Finding Antiderivatives — Basics

Calculus 1 · Axiom Academy

EXAMPLE Finding Antiderivatives Reverse the power rule, term by term, to find a general antiderivative Find the general antiderivative . We will integrate one term at a time with the power rule for integration, then add the constant of integration. Nice work — you reversed the power rule term by term to build the general antiderivative. Power rule for integration: for , — raise the exponent by one and divide by the new exponent. Integrate term by term: the integral of a sum is the sum of the integrals, so each term can be handled on its own. Always add +C : an indefinite integral is a whole family of functions, so the constant of integration is part of the answer. Check by differentiating: , which is the original integrand — so the answer is correct. Practice the power rule on polynomials of varying degree to make this fast and automatic.

This is the written version of the interactive lesson above. See the full Calculus 1 course.