for everyone sitting the exam this saturday - evaluate $$\int\limits_{0}^{1}\ln^5\frac1x\,dx$$ and be sure to score 90% or higher

wish you luck guys with the test!

## Thread of Luck and Happiness

### Re: Thread of Luck and Happiness

Best of luck everyone!

### Re: Thread of Luck and Happiness

It's very easy.

First change of variable is 1/x = t, then ln(t) = z, so we obtain the standard integral x^n*exp(-ax) from 0 to oo, as you should know it is equal to n!/a^(n+1). This fact can be derived from integration by parts hm.. n times. Thereby, the answer is 5! = 120.

Good luck!

З.Ы. Integrals aren't my weakness. I'm worried about topology and abstract algebra. Sometimes that's a hard nut to crack.

First change of variable is 1/x = t, then ln(t) = z, so we obtain the standard integral x^n*exp(-ax) from 0 to oo, as you should know it is equal to n!/a^(n+1). This fact can be derived from integration by parts hm.. n times. Thereby, the answer is 5! = 120.

Good luck!

З.Ы. Integrals aren't my weakness. I'm worried about topology and abstract algebra. Sometimes that's a hard nut to crack.