`intdx/(sinx+secx)`

Explanation

`int frac{1}{sin x+sec x} d x`

`int frac{1}{sin x+frac{1}{cos x}} d x`

`int frac{cos x}{sin x cos x+1} d x`

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

`int frac{(sin x+cos x)-(sin x-cos x)}{2+2 sin x cos x} d x`

`int frac{sin x+cos x}{2+2 sin x cos x} d x-int frac{sin x-cos x}{2+2 sin x cos x} d x`

`int frac{sin x+cos x}{3-(sin x-cos x)^{2}} d x-int frac{sin x-cos x}{1+(sin x+cos x)^{2}} d x`

`I_{1}=int frac{sin x+cos x}{3-(sin x-cos x)^{2}} d x`

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