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Question

lf f(x)=cosxcos2x+cos3x to , then f(x)dx is equal to

A
tanx2+c
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B
xtanx2+c
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C
x12tanx2+c
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D
xtanx23+c
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Solution

The correct option is D xtanx2+c
f(x)=cosxcos2x+cos3x...
The function is a G.P with a common ratio of cosx.
Hence
f(x)=a1r where a is the first term and r is the common ratio.

f(x)=cosx1(cosx)

=cosx1+cosx

=1+cosx11+cosx

=111+cosx

=112cos2x2

=1sec2x22

=112(sec2x2)

Hence
f(x).dx

=(112(sec2x2))dx

=x12⎜ ⎜ ⎜tanx212⎟ ⎟ ⎟+c

=xtan(x2)+c.

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