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