Calculus Examples

$\int (2^{x} + 1) d x$

Step 1

Remove parentheses.

$\int 2^{x} + 1 d x$

Step 2

Split the single integral into multiple integrals.

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

Step 3

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

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

Step 4

Apply the constant rule.

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

Step 5

Simplify.

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