Calculus Examples

$\int \frac{1}{2} (3^{x}) d x$

Step 1

Combine $\frac{1}{2}$ and $3^{x}$ .

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

Step 2

Since $\frac{1}{2}$ is constant with respect to $x$ , move $\frac{1}{2}$ out of the integral.

$\frac{1}{2} \int 3^{x} d x$

Step 3

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

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

Step 4

Simplify the answer.

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Step 4.1

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

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

Step 4.2

Multiply $\frac{1}{2}$ by $\frac{1}{\ln (3)}$ .

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