What is the integral of (sin(2t))/(sin(t)) ?

The integral of (sin(2t))/(sin(t)) is 2sin(t)+C

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integral of (sin(2t))/(sin(t))

\int \frac{sin ( 2 t )}{sin ( t )} d t

2 sin (t) + C

Solution steps

\int \frac{sin ( 2 t )}{sin ( t )} d t

Rewrite using trig identities

= \int 2 cos (t) d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int cos (t) d t

Use the common integral:

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

= 2 sin (t)

Add a constant to the solution

= 2 sin (t) + C

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