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Question

Evaluate sin2xsin4x+cos4xdx

A
tan1(1/2tan2x).
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B
tan1(tan2x)+C.
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C
x
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D
tan1(2tan2x).
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Solution

The correct option is B tan1(tan2x)+C.
I=sin2xsin4x+cos4xdx=2sinxcosxsin4x+cos4xdx.
Divide NandD by cos4x.
I=2tanxsec2xdx1+tan4x
Substitute tan2x=t.2tanxsec2xdx=dt

I=dt1+t2=tan1t=tan1(tan2x)+C

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