Solve the trigonometric integral $\int2\left(1+\cos\left(x\right)\right)\sin\left(x\right)dx$

Find the integral

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

Find the integral

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

Find the integral

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

Find the integral

$\int\frac{dx}{1+sinx+cosx}$

Find the integral

$\int\arccsc\left(x\right)dx$

Find the integral

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

Find the integral

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