Calculus Examples

$\frac{d y}{d x} = \frac{4 \sin (x)}{x}$

Step 1

Rewrite the equation.

$d y = \frac{4 \sin (x)}{x} d x$

Step 2

Integrate both sides.

Tap for more steps...

Step 2.1

Set up an integral on each side.

$\int d y = \int \frac{4 \sin (x)}{x} d x$

Step 2.2

Apply the constant rule.

$y + C_{1} = \int \frac{4 \sin (x)}{x} d x$

Step 2.3

Integrate the right side.

Tap for more steps...

Step 2.3.1

Since $4$ is constant with respect to $x$ , move $4$ out of the integral.

$y + C_{1} = 4 \int \frac{\sin (x)}{x} d x$

Step 2.3.2

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

$y + C_{1} = 4 (S i (x) + C_{2})$

Step 2.3.3

Simplify.

$y + C_{1} = 4 S i (x) + C_{2}$

Step 2.4

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

$y = 4 S i (x) + K$