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Evaluate: int(sin2x)/(sqrt(cos^4x-sin^2x...

Evaluate: `int(sin2x)/(sqrt(cos^4x-sin^2x+2))\ dx`

Text Solution

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I=`int(sin2x)/(sqrt(cos^4x-sin^2x+2))\ dx`
I=`int(sin2x)/((sqrt(cos^4x)-cos^2x+2))\ dx`
I=`int(sin2x)/(sqrt(cos^4x+cos^2x+2))\ dx`
let `cos^2x=t`
`⇒2cosx(−sinx)dx=dt`
`⇒sin2x.dx=−dt`
Substituting these values in the given integration we get-
`I=-int (dt)/sqrt(t^2+t+1)`
...
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