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Evaluate: int1/(4sin^2x+5cos^2x)\ dx...

Evaluate: `int1/(4sin^2x+5cos^2x)\ dx`

Text Solution

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`int1/(4sin^2x+5cos^2x)\ dx`
`=int(sec^2x)/(4tan^2x+5)\ dx`
`tanx=t` and `sec^2xdx=dt`
`=int frac{dt}{4t^2+5}`
`=1/4 int frac{dt}{t^2+5/4}`
`=1/4 1/(sqrt 5/2)tan^(-1)(t/frac{sqrt 5}{2})+C`
`=1/(2sqrt 5)tan^(-1)( (2tanx)/sqrt 5)+C`
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