Calculus Examples

$\int (2^{x} + 3^{x}) d x$

Step 1

Remove parentheses.

$\int 2^{x} + 3^{x} d x$

Step 2

Split the single integral into multiple integrals.

$\int 2^{x} d x + \int 3^{x} d x$

Step 3

The integral of $2^{x}$ with respect to $x$ is $\frac{2^{x}}{\ln (2)}$ .

$\frac{2^{x}}{\ln (2)} + C + \int 3^{x} d x$

Step 4

The integral of $3^{x}$ with respect to $x$ is $\frac{3^{x}}{\ln (3)}$ .

$\frac{2^{x}}{\ln (2)} + C + \frac{3^{x}}{\ln (3)} + C$

Step 5

Simplify.

$\frac{1}{\ln (2)} \cdot 2^{x} + \frac{1}{\ln (3)} \cdot 3^{x} + C$