44. $int\frac{sin 2x}{sin x}dx$

Explanation:

Step1: Use double - angle formula

Recall that $\sin 2x = 2\sin x\cos x$. So the integral $\int\frac{\sin 2x}{\sin x}dx=\int\frac{2\sin x\cos x}{\sin x}dx$.

Step2: Simplify the integrand

Cancel out the $\sin x$ terms in the integrand. We get $\int 2\cos xdx$.

Step3: Integrate

The antiderivative of $\cos x$ is $\sin x$. So $\int 2\cos xdx = 2\int\cos xdx=2\sin x + C$.

Answer:

$2\sin x + C$