Calculus Examples

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

Step 1

Rewrite the equation.

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

Step 2

Integrate both sides.

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Step 2.1

Set up an integral on each side.

$\int d y = \int \frac{\sin (x)}{x} d x$

Step 2.2

Apply the constant rule.

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

Step 2.3

$\int \frac{\sin (x)}{x} d x$ is a special integral. The integral is the sine integral function.

$y + C_{1} = S i (x) + C_{2}$

Step 2.4

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

$y = S i (x) + K$