How to Solve complex indefinite integrals in calculus

In this video the math teacher explains the meaning of the indefinite integral formula in calculus by stating it in terms of antiderivatives. He then shows in general terms how this indefinite integral formula has a related derivative formula, i.e. if the derivative of F(x) is f(x) then the indefinite integral of f(x) is F(x) plus a constant term (C). With this general relationship the teacher takes us through three related examples where he converts a derivative formula to an integral formula. This is done merely by changing the operation from derivation to integration and reversing the positions of f(x) and F(x) as is seen in the general formula, never forgetting the constant term (C).