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Question

tan1{(1cos2x1+cos2x)}dx,0<x<π2 is equal to

A
x22+C
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B
x33+C
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C
x22+C
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D
x44+C
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Solution

The correct option is A x22+C
tan1{(1cos2x1+cos2x)}dx=tan1{(2sin2x2cos2x)}dx
{1cos2x=2sin2x,1+cos2x=2cos2x}
tan1(|tanx|)dx
{x is in first quadrant ,hence |tanx|=tanx}
tan1(tanx)dx=x dx=x22+C

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