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Evaluate: int1/(4cos^2x+9sin^2x)dx...

Evaluate: `int1/(4cos^2x+9sin^2x)dx`

Text Solution

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`int(1/cos^2x)/(4+(9sin^2x)/(cos^2x))dx`
Let`t=tanx`
`dt=secc^2xdx`
`intsec^2x/(4+9tan^2x)dx`
`intdt/(4+9t^2)`
`1/9*int(dt)/(4/9+t^2)`
`1/9*3/2*tan^(-1)(t/(2/3))+c`
`1/6*tan^(-1)((3t)/2)+c`
...
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