Calculus Examples

$\int e^{x} \cdot 2 x d x$

Step 1

Since $2$ is constant with respect to $x$ , move $2$ out of the integral.

$2 \int e^{x} \cdot (x) d x$

Step 2

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

$2 (x e^{x} - \int e^{x} d x)$

Step 3

The integral of $e^{x}$ with respect to $x$ is $e^{x}$ .

$2 (x e^{x} - (e^{x} + C))$

Step 4

Simplify.

$2 (x e^{x} - e^{x}) + C$