Evaluate: `int(sinx+cosx)/(9+16sin2x)\ dx`

Explanation

`int frac{sin x+cos x}{9+16 sin 2 x} d x`

Put `sin x-cos x=t`

`(cos x+sin x) d x=d t`

Consider,

`(sin x-cos x)^{2}=t^{2}`

`sin ^{2} x+cos ^{2} x-2 sin x cos x=t^{2}`

`(1-sin 2 x)=t^{2}` `1-t^{2}=sin 2 x`

`int frac{d t}{9+16(1-t^{2})}`

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