Calculus Examples

$\int \frac{3 (\sin (2 x))}{\sin (x)} d x$

Step 1

Simplify the numerator.

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Step 1.1

Apply the sine double-angle identity.

$\int \frac{3 \cdot 2 \sin (x) \cos (x)}{\sin (x)} d x$

Step 1.2

Multiply $3$ by $2$ .

$\int \frac{6 \sin (x) \cos (x)}{\sin (x)} d x$

Step 2

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

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Step 2.1

Cancel the common factor.

$\int \frac{6 \sin (x) \cos (x)}{\sin (x)} d x$

Step 2.2

Divide $6 \cos (x)$ by $1$ .

$\int 6 \cos (x) d x$

Step 3

Since $6$ is constant with respect to $x$ , move $6$ out of the integral.

$6 \int \cos (x) d x$

Step 4

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

$6 (\sin (x) + C)$

Step 5

Simplify.

$6 \sin (x) + C$