Question

Solve :
$\int e^x(logx+\frac{1}{x^2})dx$

Answer 1

$\begin{array}{c}\int e^x\left(\log x+\frac{1}{x^2}\right)dx\\ \int e^x\left(\log x+\frac{1}{x}-\frac{1}{x}+\frac{1}{x^2}\right)dx\\ \int e^x\left(f\right(x)-f^{\prime }(x\left)\right)dx=e^{x}f\left(x\right)\\ =e^x\left(\log x-\frac{1}{x}\right)+C\end{array}$

Hence,

Solved.