We conclude the lesson by stating the rules for definite integrals, most of which parallel the rules we stated for the general indefinite integrals. Given these rules together with Theorem 4.1, we will be able to solve a great variety of definite integrals.

*Integral Calculus Formula Sheet Derivative Rules: 0 d c dx nn 1 d xnx dx sin cos d x x dx sec sec tan d x xx dx tan sec2 d x x dx cos sin d x x dx csc csc cot d x xx dx cot csc2 d x x dx d aaaxxln dx d eex x dx dd cf x c f x dx dx*All of these formulas can be directly proved by diﬀerentiating the right side of the equalities (for the reader it is useful to check the formulas 2.12 and 2.13). 5.3 Properties of inde nite integral Next we shall prove three properties of the indeﬁnite integrals and use them to integrate some functions. Property 3.1. ∫ [f(x)+g(x)]dx ... Calculus Cheat Sheet ... For indefinite integrals drop the limits of integration. ... and/or half angle formulas to reduce the integral into a form that can be ... List of integrals of exponential functions The following is a list of integrals of exponential functions. For a complete list of Integral functions, please see the list of integrals. Indefinite integrals Indefinite integrals are antiderivative functions. A constant (the constant of integration) may be added to the right