So that (Don't forget to use the chain rule when differentiating. (Use antiderivative rule 2 from the beginning of this section on the first integral.) (Now use trig identity A from the beginning of this section.) (Now use antiderivative rule 3 from the beginning of this section.) (Use antiderivative rule 7 from the beginning of this section on the first integral and use trig identity F from the beginning of this section on the second integral.) (Combine constant with since is an arbitrary constant.)

Weve seen how this works with specific functions like sin x and ex and now. (Use antiderivative rule 1 from the beginning of this section.) The key idea is that each derivative rule can be written as an antiderivative rule. Substitute into the original problem, getting Integration Formulas Z dx x+C (1) Z xn dx xn+1 n+1 +C (2) Z dx x lnx+C (3) Z ex dx ex +C (4) Z ax dx 1 lna ax +C (5) Z lnxdx xlnxx+C (6) Z sinxdx. First use trig identity C from the beginning of this section, getting Substitute into the original problem, replacing all forms of x, getting (Use trig identity A from the beginning of this section.) (Use antiderivative rule 5 from the beginning of this section.) (Use antiderivative rule 7 from the beginning of this section.) (Use antiderivative rule 2 from the beginning of this section.)Ĭlick HERE to return to the list of problems. Integration is essentially the reverse of dierentiation, so one might expect formulas for reversing the eects of the Product Rule, Quotient Rule and Chain Rule. Substitute into the original problem, replacing all forms of, getting

Antiderivative rules pdf