What is the integral of (5(sin(2x))/(sin(x))) ?

The integral of (5(sin(2x))/(sin(x))) is 10sin(x)+C

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integral of (5(sin(2x))/(sin(x)))

\int (5 \frac{sin ( 2 x )}{sin ( x )}) d x

10 sin (x) + C

Solution steps

\int 5 \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

= 5 \cdot \int \frac{sin ( 2 x )}{sin ( x )} d x

Rewrite using trig identities

= 5 \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

= 5 \cdot 2 \cdot \int cos (x) d x

Use the common integral:

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

= 5 \cdot 2 sin (x)

Simplify

= 10 sin (x)

Add a constant to the solution

= 10 sin (x) + C

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What is the integral of (5(sin(2x))/(sin(x))) ?
The integral of (5(sin(2x))/(sin(x))) is 10sin(x)+C