What is the integral of (7(sin(2x))/(sin(x))) ?

The integral of (7(sin(2x))/(sin(x))) is 14sin(x)+C

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integral of (7(sin(2x))/(sin(x)))

\int (7 \frac{sin ( 2 x )}{sin ( x )}) d x

14 sin (x) + C

Solution steps

\int 7 \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

= 7 \cdot \int \frac{sin ( 2 x )}{sin ( x )} d x

Rewrite using trig identities

= 7 \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

= 7 \cdot 2 \cdot \int cos (x) d x

Use the common integral:

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

= 7 \cdot 2 sin (x)

Simplify

= 14 sin (x)

Add a constant to the solution

= 14 sin (x) + C

\int_{- 5}^{5} \frac{1}{2} (2 5^{2} - x^{4}) d x

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

\int (3 x^{2} + 14 x) (x^{3} + 7 x^{2} + 1) d x

g (t) = \frac{1}{t ^{2} - 2}

(5 x^{2} - 3 x + 2)^{7}

What is the integral of (7(sin(2x))/(sin(x))) ?
The integral of (7(sin(2x))/(sin(x))) is 14sin(x)+C