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Question

If In=tannxdx then
I0+I1+2(I2+I3+....+I8)+I9+I10 equals

A
1+8n=1tannxn
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B
9n=1tannxn
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C
n=2tannxn+1
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D
9n=1tannxn+1
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Solution

The correct option is B 9n=1tannxn
In=tannxdx=tann2x(sec2x1)dx
In=tann2xsec2xdxtann2xdx
In2+In=tann2xsec2xdx=tann1xn1(n2)
Putting n=2,3,4,...10&adding we get
I0+I1+2(I2+I3+I4+...+I8)+I9+I10=9n=1tannxn

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