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Question

If I=sin7xdx, then I equals

A
cosx+cos3xcos5x+17cos7x+C
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B
cosx+cos3x35cos5x+17cos7x+C
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C
tanxtan3x+sinx13cos3x+C
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D
cosx+cos5x13cos3x+17cos7x+C
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Solution

The correct option is B cosx+cos3x35cos5x+17cos7x+C
Let I=sin7xdx

We know that, sin2x=1cos2x

=(1cos2x)3sinxdx

Substitute cosx=tsinxdx=dt
I=(1t2)3dt

I=(13t2+3t4t6)dt
I=cosx+cos3x35cos5x+17cos7x+C

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