What is the integral of 6(sin(2x))/(sin(x)) ?

The integral of 6(sin(2x))/(sin(x)) is 12sin(x)+C

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integral of 6(sin(2x))/(sin(x))

\int 6 \frac{sin ( 2 x )}{sin ( x )} d x

12 sin (x) + C

Solution steps

\int 6 \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

= 6 \cdot \int \frac{sin ( 2 x )}{sin ( x )} d x

Rewrite using trig identities

= 6 \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

= 6 \cdot 2 \cdot \int cos (x) d x

Use the common integral:

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

= 6 \cdot 2 sin (x)

Simplify

= 12 sin (x)

Add a constant to the solution

= 12 sin (x) + C

\int 1 + 3 x + 18 x^{2} d x

x \to 0 + lim (\frac{ln ( x ) + 1}{x})

\int (4 sin (x))^{3} d x

\frac{3 ( s + 1 )}{s ^{2} + \frac{1}{2}}

e^{- \frac{x}{2}}, 0

What is the integral of 6(sin(2x))/(sin(x)) ?
The integral of 6(sin(2x))/(sin(x)) is 12sin(x)+C