Derivative and Antiderivative Rules

Justifying L’Hopital’s Rule

Long division integration

Completing the square integration

if dy/dt = k(y), then y =

y = Ce^(rt)

Method for finding y = Ce^(rt) from its rate of change dy/dt = r(y)

Integration by parts

Deriving the integration by parts method

Integration by partial fractions (core idea)

Deriving integration by partial fractions method

Set f(x)/g(x) [which is the integrand, where g(x) is factored] equal to A/first factor faction + B/second factor

Then condense the partial fractions into one fraction and multiply both sides by the factored version of g(x) to get f(x) = A(second factor) + B(first factor)

Solve for A and by by plugging in values for x that make each factor = 0

ANSWER (THE ANTIDERIVATIVE) WILL ALWAYS INVOLVE A NATURAL LOG

Arc length of a function y = f(x) on the closed, continuous interval [a, b]