Calculus Examples

$\int 9 \frac{\sin (2 x)}{\sin (x)} d x$

Step 1

Simplify.

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Step 1.1

Apply the sine double-angle identity.

$\int 9 \frac{2 \sin (x) \cos (x)}{\sin (x)} d x$

Step 1.2

Cancel the common factor of $\sin (x)$ .

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Step 1.2.1

Cancel the common factor.

$\int 9 \frac{2 \sin (x) \cos (x)}{\sin (x)} d x$

Step 1.2.2

Divide $2 \cos (x)$ by $1$ .

$\int 9 (2 \cos (x)) d x$

Step 1.3

Multiply $2$ by $9$ .

$\int 18 \cos (x) d x$

Step 2

Since $18$ is constant with respect to $x$ , move $18$ out of the integral.

$18 \int \cos (x) d x$

Step 3

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

$18 (\sin (x) + C)$

Step 4

Simplify.

$18 \sin (x) + C$