$\int\frac{1}{\sin\left(x\right)-1}dx$
$\int\frac{dx}{1-\sin\left(x\right)}$
$\int\frac{1}{sin\left(x\right)-1}dx$
$\int\frac{1}{2-cos\left(x\right)}dx$
$\int\frac{dx}{\sin\left(x\right)+\cos\left(x\right)}$
$\int\frac{1}{1-\sin x}dx$
$\int\frac{dx}{cosx-1}$
Integrals that contain trigonometric functions and their powers.
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