Solve the trigonometric integral $\int\frac{1}{1+\sin\left(x\right)+\cos\left(x\right)}dx$

Find the integral

$\int\frac{1}{1-sin\left(x\right)}dx$

Find the integral

$\int\frac{dx}{1-sin\left(x\right)}$

Find the integral

$\int\frac{1}{1-sinx}dx$

Find the integral

$\int\frac{1}{cosx-1}dx$

Find the integral

$\int\frac{1}{cos\left(x\right)-1}dx$

Find the integral

$\int\frac{1}{\sin\left(x\right)-\cos\left(x\right)}dx$

Find the integral

$\int\frac{dx}{1-\cos x+\sin x}$