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Evaluate: int(2sin2varphi-cosvarphi)/(6-...

Evaluate: `int(2sin2varphi-cosvarphi)/(6-cos^2varphi-4\ sinvarphi)\ dvarphi`

Text Solution

Verified by Experts

I=`int(2sin2varphi-cosvarphi)/(6-cos^2varphi-4\ sinvarphi)\ dvarphi`
I=`int(4sin2varphicos2varphi-cosvarphi)/(6-(1-sin^2varphi)^2-4\ sinvarphi)\ dvarphi`
I=`int((4sin2varphi-1)cosvarphi)/(sin^2varphi-4cosvarphi+5)\ dvarphi`
let `sinvarphi=t`
`cosvarphidphi=dt`
So,
`I=int (4t-t)dt/(t^2-4t+5)`
`I=2int (2t-4)dt/(t^2-4t+5)+7int (dt)/(t^2-4t+5)`
...
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