Calculus Examples

$\int \frac{1}{4 \sec (x)} d x$

Step 1

Since $\frac{1}{4}$ is constant with respect to $x$ , move $\frac{1}{4}$ out of the integral.

$\frac{1}{4} \int \frac{1}{\sec (x)} d x$

Step 2

Simplify.

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Step 2.1

Rewrite $\sec (x)$ in terms of sines and cosines.

$\frac{1}{4} \int \frac{1}{\frac{1}{\cos (x)}} d x$

Step 2.2

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\cos (x)}$ .

$\frac{1}{4} \int 1 \cos (x) d x$

Step 2.3

Multiply $\cos (x)$ by $1$ .

$\frac{1}{4} \int \cos (x) d x$

Step 3

The integral of $\cos (x)$ with respect to $x$ is $\sin (x)$ .

$\frac{1}{4} (\sin (x) + C)$

Step 4

Simplify.

$\frac{1}{4} \sin (x) + C$