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Question

Question: \(\int_{}^{}\frac{\sin 3x}{\sin x}\)dx =...

∫sin⁡3xsin⁡x\int_{}^{}\frac{\sin 3x}{\sin x}dx =

A

x + sin2x + cq

B

3x + sin 2x + c

C

3x + sin2x + c

D

None of these

Answer

x + sin2x + cq

Explanation

Solution

= ∫3sin⁡x–4sin⁡3xsin⁡x\int_{}^{}\frac{3\sin x–4\sin^{3}x}{\sin x}dx

xdx = 3x –2 ∫(1–cos⁡2x)\int_{}^{}{(1–\cos 2x)}dx +c

= 3x – 2x + sin2x + c = x + sin2x + c