Mathematics - Definite Integration Question with Solution | TestHub

$I(B)={\int }_0^1\frac{x^B-1}{\ln x}dx$

$$\frac{\partial \mathrm{I}(\mathrm{B})}{\partial \mathrm{B}}={\int }_0^1{\mathrm{x}}^{\mathrm{B}}\mathrm{dx}=\frac{1}{\mathrm{B}+1}$$

$\mathrm{I}(\mathrm{B})=\ell \mathrm{n}(\mathrm{B}+1)$

$$\mathrm{I}(3)=2\ell \mathrm{n}2$$

$\mathrm{I}(8)=2\ell \mathrm{n}3$

$$\mathrm{I}(49)=\ell \mathrm{n}50\mathrm{I}(64)=\ell \mathrm{n}65$$