Question

Evaluate: $\int \frac{e^{\log \sqrt{x}}}{x}dx$

Answer 1

It is given that,

$\int \frac{e^{log\sqrt{x}}}{x}dx$

=> $\int \frac{e^{\frac{1}{2}logx}}{x}dx$

=> Let, $logx=t$

=> $\frac{1}{x}dx=dt$

=> $\int e^{\frac{t}{2}}dt$

=> $\frac{1}{2}.e^{\frac{t}{2}}+C$

=> $\frac{1}{2}.e^{\frac{logx}{2}}+C$