How to do the following integral: ∫01xa−1log(x)dx where a≥0 ?
How to do the following integral:
Answer & Explanation
Beginner2022-01-04Added 35 answers
Call your integral . Then as long as . Now you need to solve the differential equation This is a very easy differential equation to solve, and the solution is where C is some constant. Now we ask, what is that constant? Notice that so we need , or rather . So we conclude that , as you suggested.
Beginner2022-01-05Added 38 answers
We can utilize
combined with the substitution , to get
Plainmath is a platform aimed to help users to understand how to solve math problems by providing accumulated knowledge on different topics and accessible examples. Plainmath.net is owned and operated by RADIOPLUS EXPERTS LTD.