Calculus Examples

$\int e^{x} \ln (x) d x$

Integrate by parts using the formula $\int u d v = u v - \int v d u$ , where $u = \ln (x)$ and $d v = e^{x}$ .

$\ln (x) e^{x} - \int e^{x} \frac{1}{x} d x$

Combine $e^{x}$ and $\frac{1}{x}$ .

$\ln (x) e^{x} - \int \frac{e^{x}}{x} d x$

$\int \frac{e^{x}}{x} d x$ is a special integral. The integral is the exponential integral function.

$\ln (x) e^{x} - (E i (x) + C)$

Simplify.

$\ln (x) e^{x} - E i (x) + C$