Calculus Examples

$\int \frac{2}{5} \cdot (\sec (x) \tan (x)) d x$

Step 1

Simplify.

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Step 1.1

Combine $\sec (x)$ and $\frac{2}{5}$ .

$\int \frac{\sec (x) \cdot 2}{5} \cdot \tan (x) d x$

Step 1.2

Combine $\frac{\sec (x) \cdot 2}{5}$ and $\tan (x)$ .

$\int \frac{\sec (x) \cdot 2 \tan (x)}{5} d x$

Step 1.3

Move $2$ to the left of $\sec (x)$ .

$\int \frac{2 \sec (x) \tan (x)}{5} d x$

Step 2

Since $\frac{2}{5}$ is constant with respect to $x$ , move $\frac{2}{5}$ out of the integral.

$\frac{2}{5} \int \sec (x) \tan (x) d x$

Step 3

Since the derivative of $\sec (x)$ is $\sec (x) \tan (x)$ , the integral of $\sec (x) \tan (x)$ is $\sec (x)$ .

$\frac{2}{5} (\sec (x) + C)$

Step 4

Simplify.

$\frac{2}{5} \sec (x) + C$