If $$I=$$∫$$sin$$⁡$$2x(3+4cos$$⁡$$x)3dx$$, then I equals

Correct option is 23+8cos⁡x16(3+4cos⁡x)2+C

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$If I = \int \frac{\sin 2 x}{(3 + 4 \cos x)^{3}} d x, then I equals$

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3cos⁡x+8(3+4cos⁡x)2+C

3+8cos⁡x16(3+4cos⁡x)2+C

3+cos⁡x(3+4cos⁡x)2+C

3−8cos⁡x16(3+4cos⁡x)2+C

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detailed solution

Correct option is B

Write I=∫2sin⁡xcos⁡x(3+4cos⁡x)3dx and put 3+4cos⁡x=t, so that −4sin⁡xdx=dt and I=−18∫(t−3)t3dt=181t−321t2+C =2t−316t2=8cos⁡x+316(3+4cos⁡x)2+C

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If I=∫sin⁡2x(3+4cos⁡x)3dx, then I equals

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$If I = \int \frac{\sin 2 x}{(3 + 4 \cos x)^{3}} d x, then I equals$