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Question

dx4 sin2x+5 cos2x=

A
15tan1(2 tan x5)+c
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B
15tan1(tan x5)+c
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C
125tan1(2 tan x5)+c
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D
None of these
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Solution

The correct option is C 125tan1(2 tan x5)+c
dx4 sin2x+5 cos2x=sec2x dx4 tan2x+5=14sec2x dxtan2x+54
Put tan x=tsec2x dx=dt, then it reduces to
14dtt2+(52)2=245tan1(2t5)+c=125tan1(2 tan x5)+c

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