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Evaluate: int(cos5x+cos4x)/(1-2cos3x)\ d...

Evaluate: `int(cos5x+cos4x)/(1-2cos3x)\ dx`

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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CENGAGE-INDEFINITE INTEGRATION-Single Correct Answer Type
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