The Chain Rule to Find Antiderivaties

p {margin: 0; padding: 0;} No. Date "The chain rule to find antiderivatives. The chain rule allows us to differentiate a wide variety of functions. but we are able to find antiderivatives for only a limited range of functions We can sometimes use substitution to resulte functions in A form that we can integrate S (x+2)5 dx Let us x + 2 Sus du du =dx I u' + 6 Don't forget to subtitute the (x +2) + value for u back into the C Problem ! r I tx 1 2xdx One of the clues that we look 4= du for is if we can find a function 2 is + C and its derivative in the integrand 3 2 (1+x1)7 + C The derivative of x2 is 2x dx 3 Let u = 1+x du = 2xdx Note Note that this only worked because of the 2x in the original Many integrals can not be done by subtitution