Calculus Examples

$\frac{d y}{d x} = \sec (x)$

Step 1

Rewrite the equation.

$d y = \sec (x) d x$

Step 2

Integrate both sides.

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Step 2.1

Set up an integral on each side.

$\int d y = \int \sec (x) d x$

Step 2.2

Apply the constant rule.

$y + C_{1} = \int \sec (x) d x$

Step 2.3

The integral of $\sec (x)$ with respect to $x$ is $\ln (| \sec (x) + \tan (x) |)$ .

$y + C_{1} = \ln (| \sec (x) + \tan (x) |) + C_{2}$

Step 2.4

Group the constant of integration on the right side as $C$ .

$y = \ln (| \sec (x) + \tan (x) |) + C$