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Question

dxcosx+3sinx equals

A
12logtan(x2+π12)+C
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B
13logtan(x2π12)+C
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C
logtan(x2+π6)+C
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D
12logtan(x2π6)+C
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Solution

The correct option is A 12logtan(x2+π12)+C
dxcosx+3sinx
=12dx12cosx+32sinx
=12dxcosπ3cosx+sinπ3sinx
=12dxcos(xπ3)
=12sec(xπ3)dx
=12logtan(x2π6+π4)+C
=12logtan(x2+π12)+C
Hence, option A is correct.

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