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Question

If sec6xdx=15tan5x+Atan3x+tanx+c, then A is equal to

A
13
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B
23
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C
13
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D
23
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Solution

The correct option is B 23
sec6xdx
=sec4x.sec2xdx
=(1+tan2x)2sec2x.dx
=(1+tan4x+2tan2x)sec2x.dx
=sec2xdx+tan4xsec2x.dx+2tan2xsec2x.dx
Put tanx=t, so sec2xdx=dt
=dt+t4dt+2t2dt
=t+t55+2t33+c
=tanx+tan5x5+23tan3x+c.
So, A=23

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