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Question

dx4sin2x+5cos2x=?

A
15tan1(2tanx5)+c
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B
15tan1(tanx5)+c
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C
125tan1(2tanx5)+c
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D
None of these
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Solution

The correct option is B 125tan1(2tanx5)+c
Let I=dx4sin2x+5cos2x
I=dx×14cos2xtan2x+54I=14sec2xdxtan2x+54
Let tanx=zsec2xdx=dz
I=14dzz2+54I=14×154tan1(z54)+CI=125tan1(2z5)+C
and as z=tanx
I=125tan1(2tanx5)+C

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