Consider the function F(k)=∫01xkdxF(k) = \int_0^1 x^k dxF(k)=∫01xkdx. What is the value of ∫01xa−xblnxdx\int_0^1 \frac{x^a - x^b}{\ln x} dx∫01lnxxa−xbdx for a,b>−1a, b > -1a,b>−1?
ln(a+1b+1)\ln(\frac{a+1}{b+1})ln(b+1a+1)
ln(b+1a+1)\ln(\frac{b+1}{a+1})ln(a+1b+1)
1a−b\frac{1}{a-b}a−b1
a−ba+b\frac{a-b}{a+b}a+ba−b