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Evaluate: int((3sinx-2)cosx)/(5-cos^2x-4...

Evaluate: `int((3sinx-2)cosx)/(5-cos^2x-4sinx)\ dx`

A

`cosx+(1)/(2)cos2x-(1)/(3)cos3x+C`

B

`cosx-(1)/(2)cos2x-(1)/(3)cos3x+C`

C

`cosx+(1)/(2)cos2x+(1)/(3)cos3x+C`

D

`cosx-(1)/(2)cos2x+(1)/(3)cos3x+C`

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int 4sinx "cos"(x)/(2)"cos"(3x)/(2)dx `
`=int 2sinx(cos2x+cosx)dx`
`=int(sin 3x-sinx+sin2x)dx`
`=cosx-(1)/(3)cos 3x-(1)/(2)cos2x+C`
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