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

\frac{d}{d x} (1 + 2 x - 1 - 4 x)

\int \frac{1}{x x ^{2} + 9} d x

\int \frac{4}{( x + 1 )} d x

\frac{d ^{2} y}{d t ^{2}} + 5 \frac{d y}{d t} + 6 y = 3 cos (2 t)

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

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