What is the integral of 2((sin(2x))/(sin(x))) ?

The integral of 2((sin(2x))/(sin(x))) is 4sin(x)+C

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integral of 2((sin(2x))/(sin(x)))

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

4 sin (x) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int \frac{sin ( 2 x )}{sin ( x )} d x

Rewrite using trig identities

= 2 \cdot \int 2 cos (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot 2 \cdot \int cos (x) d x

Use the common integral:

\int cos (x) d x = sin (x)

= 2 \cdot 2 sin (x)

Simplify

= 4 sin (x)

Add a constant to the solution

= 4 sin (x) + C

\int (x^{2} + 1) d x

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\int 5^{2} d x

\int \frac{1}{x ( ln ^{3} ( x ) )} d x

\int \frac{x arctan ( x )}{( 1 + x ^{2} ) ^{\frac{3}{2}}} d x

What is the integral of 2((sin(2x))/(sin(x))) ?
The integral of 2((sin(2x))/(sin(x))) is 4sin(x)+C