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Question

sinxcosxsin4x+cos4xdx=

A
tan1(sinx)+c
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B
12tan1(cos2x)+c
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C
12tan1(tan2x)+c
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D
12tan1(cot2x)+c
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Solution

The correct option is B 12tan1(cos2x)+c
sin4x+cos4x=14((1cos2x)2+(1+cos2x)2)=12(1+cos22x)
sinxcosxsin4x+cos4xdx=2sinxcosxdx1+cos22x=12d(cos2x)1+(cos2x)2=12tan1(cos2x)+c

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