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Question

If I=sec6xdx=15tan3x+Atan3x+tanx+C then A is equal to

A
1/3
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B
2/3
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C
1/3
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D
2/3
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Solution

The correct option is B 2/3
Let I=sec6xdx
Using secmxdx=sinxsecm1xm1+m2m1sec2+mxdx
I=15tanxsec4x+45sec4xdx
=15tanxsec4x+415tanxsec2x+815sec2xdx
=15tanxsec4x+415tanxsec2x+815tanx+c
=15tanx(1+tan2x)(1+tan2x)+415tanx(1+tan2x)+815tanx+c
=15tan5x+23tan3x+tanx+c
Comparing the above equation with tan6xdx=15tan5x+Atan3x+tanxx+C

we get, A=23

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