Finding Antiderivatives — Mixed Forms

Calculus 1 · Axiom Academy

EXAMPLE Finding Antiderivatives Reverse the derivative term by term to build the general antiderivative. Find the general antiderivative of . We undo each term's derivative one at a time, then add the constant of integration. Nice work — you reversed each derivative and assembled the full antiderivative. The forms worth keeping: Power rule: the antiderivative of x^n is , valid whenever . The special case: — the absolute value covers too. Always add +C : the derivative of any constant is 0 , so the antiderivative is a whole family of curves. Check by differentiating: differentiating F(x) should hand you back f(x) . Antiderivatives are the engine of integral calculus — these basic forms are the ones you reach for again and again.

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