Question

Evaluate: \[ \int \frac{\sin4x}{\sin x}\,dx \]

• A. \(4(3\sin x+3\sin3x)+C\)
• B. \(\frac43(2\sin^3x+3\sin x)+C\)
• C. \(4(3\sin x-3\sin x)+C\)
• D. \(\frac43(3\sin x-2\sin^3x)+C\)

Hint:

Whenever \(\sin nx\) appears divided by \(\sin x\), first use multiple-angle identities. This often converts the problem into a simple polynomial integral after substitution.

Answer 1

The Correct Option is D