Challenge Question: int[0,1] (5x^4(1+x^10080)) / (1+x^5)^2018

[Dhartju]

Hi guys, I am working on this challenge question but got stuck.
Problem : Integral from 0 to 1 of (5x^4(1+x^10080)) / (1+x^5)^2018. Hint is: 10080 = 5(2016).
First, I let u = x^5+1, then becomes du = 5x^4 dx. Then I plugged in 0 and 1 to the function u. It then becomes
integral from 1 to 2 of ((u-1)^2016 + 1) / u^2018 du.
I don't know how else to continue. Please help. Need it by tomorrow. Thank you!!

 

[tkhunny]

First, never "plug in". There is an appropriate method of "substitution" that you should find helpful.

Well, why not try some other substitution? Maybe take the whole denominator? Give it a go.