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Evaluate: int1/(1+3sin^2x+8cos^2x)\ dx...

Evaluate: `int1/(1+3sin^2x+8cos^2x)\ dx`

Text Solution

Verified by Experts

I=`int1/(1+3sin^2x+8cos^2x)\ dx`
I=`int1/(sin^2x+cos^2x+3sin^2x+8cos^2x)\ dx`
I=`int1/(4sin^2x+9cos^2x)\ dx`
I=`int (sec^2x) /(4tan^2x+9)\ dx`
let `tanx=t`
`sec^2xdx=dt`
so,
I=`int (dt) /(4t^2+3^2)\ dx`
...
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