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

The integral of 4(sin(2x))/(sin(x)) is 8sin(x)+C

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integral of 4(sin(2x))/(sin(x))

\int 4 \frac{sin ( 2 x )}{sin ( x )} d x

8 sin (x) + C

Solution steps

\int 4 \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

= 4 \cdot \int \frac{sin ( 2 x )}{sin ( x )} d x

Rewrite using trig identities

= 4 \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

= 4 \cdot 2 \cdot \int cos (x) d x

Use the common integral:

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

= 4 \cdot 2 sin (x)

Simplify

= 8 sin (x)

Add a constant to the solution

= 8 sin (x) + C

\frac{s - 6}{s + 2}

\int_{0}^{\frac{π}{3}} 81 sin^{2} (x) d x

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

\frac{d}{d x} (e^{- \frac{x}{2}} cos (\frac{3}{2} x))

\frac{d}{d x} (- \frac{3}{2} x^{4} cos (x))

What is the integral of 4(sin(2x))/(sin(x)) ?
The integral of 4(sin(2x))/(sin(x)) is 8sin(x)+C