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 (4 x - 3) d x

e^{x}, x = 2

y = \frac{4 81 + x - 3}{x}

y^{^{'}} + 8 y + 6 x = 0

y = 4 x - 9

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