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int(cos5x+cos4x)/(1-2cos3x)dx " is equal...

` int(cos5x+cos4x)/(1-2cos3x)dx " is equal to "`

A

`-((sin2x)/(2)+cosx)+C`

B

`-((sin2x)/(2)+cosx)+C`

C

`-((cos2x)/(2)+cosx)+C`

D

`-((sin2x)/(2)+sinx)+C`

Text Solution

Verified by Experts

The correct Answer is:
D

`int(cos5x+cos4x)/(1-2cos3x)dx`
`=int(2cos.(9x)/(2)cos.(x)/(2)dx)/(1-2(2cos^(2)((3x)/(2))-1))`
`=int(2cos.(x)/(2)(4cos^(3),(3x)/(2)-3cos.(3x)/(2)))/(3-4cos^(2).(3x)/(2))dx`
`=-int2cos.(3x)/(2)cos.(x)/(2)dx=-intcos2xdx-int cosxdx`
`=-((sin2x)/(2)+sinx)+C`
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Knowledge Check

  • (cos 6x + 6 cos 4x + 15 cos 2x + 10)/(cos 5x + 5 cos 3x + 10 cos x ) is equal to

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    C
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