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Question

The value of dx1+3cos2x
(where C is integration constant)

A
tan1(tanx2)+C
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B
12tan1(tanx2)+C
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C
tan1(tanx3)+C
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D
13tan1(tanx3)+C
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Solution

The correct option is B 12tan1(tanx2)+C
Multiplying Numerator and Denominator of the given integral by sec2x, we get
I=sec2x dxsec2x+3I=sec2x dxtan2x+4
Put tanx=t
sec2x dx=dtI=dtt2+22I=12tan1t2+C[1x2+a2dx=1atan1(xa)+C]I=12tan1(tanx2)+C

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