(1 point)\nfind the general indefinite integral $int\frac{sin 2x}{cos x}dx.$\nanswer

Explanation:

Step1: Use double - angle formula

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

Step2: Simplify the integrand

Cancel out $\cos x$ in the numerator and denominator. We get $\int 2\sin xdx$.

Step3: Integrate

The integral of $\sin x$ is $-\cos x$. So $\int 2\sin xdx = 2(-\cos x)+C=- 2\cos x + C$.

Answer:

$-2\cos x + C$