JEE Mains · Maths · STD 12 - 7.1 indefinite integral
\(\int {\frac{{\sin \,\frac{{5x}}{2}}}{{\sin \,\frac{x}{2}}}} dx\) is equal to (where \(c\) is a constant of integration).
- A \(x + 2\,\sin \,x + 2\,\sin \,2x + c\)
- B \(2x + \,\sin \,x + 2\,\sin \,2x + c\)
- C \(x + 2\,\sin \,x + \,\sin \,2x + c\)
- D \(2x + \,\sin \,x + \,\sin \,2x + c\)
Answer & Solution
Correct Answer
(C) \(x + 2\,\sin \,x + \,\sin \,2x + c\)
Step-by-step Solution
Detailed explanation
\(\int \frac{\sin \frac{5 x}{2}}{\sin \frac{x}{2}} d \) \(x=\int \frac{2 \sin \frac{5 x}{2} \cos \frac{x}{2}}{2 \sin \frac{x}{2} \cos \frac{x}{2}} d x\) \(=\int \frac{\sin 3 x+\sin 2 x}{\sin x} d x\) \(=\int \frac{3 \sin x-4 \sin ^{3} x+2 \sin x \cos x}{\sin x} d x\)…
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