What is the integral of 8(sin(2x))/(sin(x)) ?

The integral of 8(sin(2x))/(sin(x)) is 16sin(x)+C

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integral of 8(sin(2x))/(sin(x))

\int 8 \frac{sin ( 2 x )}{sin ( x )} d x

16 sin (x) + C

Solution steps

\int 8 \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

= 8 \cdot \int \frac{sin ( 2 x )}{sin ( x )} d x

Rewrite using trig identities

= 8 \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

= 8 \cdot 2 \cdot \int cos (x) d x

Use the common integral:

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

= 8 \cdot 2 sin (x)

Simplify

= 16 sin (x)

Add a constant to the solution

= 16 sin (x) + C

\int_{0}^{1} (4 x - 4 x) d x

\frac{d y}{d x} + 12 y = 8

\frac{d}{d x} (\frac{sin ( x ^{2} )}{ln ( 2 x + 8 )})

(1 + x)^{3}

What is the integral of 8(sin(2x))/(sin(x)) ?
The integral of 8(sin(2x))/(sin(x)) is 16sin(x)+C