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Question

The integral π/3π/6sec2/3x cosec4/3x dx is equal to :

A
35/331/3
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B
34/331/3
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C
35/632/3
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D
37/635/6
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Solution

The correct option is D 37/635/6
Given,
I=π/3π/6sec2/3x cosec4/3xdx
=π/3π/6sec2xtan4/3xdx
Let tanx=tsec2xdx=dt
I=dtt4/3
=3(t1/3)
=(3(tanx)13)π/3π/6
=3(31/6131/6)
=37/635/6

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