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int sin(2x)/(acos^2x+bsin^2x) dx=...

`int sin(2x)/(acos^2x+bsin^2x) dx=`

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`"Let I " = int ("sin 2x ")/(a" cos"^(2) x+b " sin"^(2) x)" dx "`
`" and a "cos"^(2) x+b "sin"^(2) x=t`
`rArr " " a.2 " cos x (-sin x) + b.2 sin x. cos x " = (dt)/(dx)`
`rArr " ""sin 2x (b -a) dx =dt "`
`rArr " " " sin 2x. dx "= (dt)/(b-a)`
`:. I = int (dt)/((b-a).t)`
` =(1)/(b-a) ."log " |t|+c`
` =(1)/(b-a) "log " | acos"^(2)x +b " sin"^(2) x| +c.`
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