Tricky u-Substitution

by Donny
(Atlanta GA)



I have been trying to solve the indefinite integral of (x+3)(x-1)^1/2 dx. I can't figure out how to get rid of x+3 using u=(x-1)^1/2 or u=x-1. Am I picking the wrong u substitution? Any help is appreciated!




Answer by Pablo:

This integral is quite interesting, I've never seen something similar given as an exercise before. However, it is solvable by simple substitution.

The easiest choice is taking:



If we sum 4 to both sides of the definition of u:



So, there we have everything we need to make the substitution. Now:



We distribute the product inside and then integrate directly:



Now, substituting back:



Taking the derivative you can verify that this answer is indeed correct.

Return to Integration by Substitution

Click here to post comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Your Doubts and Problems.