csc(x) = cos(x) / (cos(x)^2)

u = sin(x)

du = cos(x)dx

now using the trigonometric identity sin^2(x) + cos^2(x) = 1

we arrive at the following equivalent integral

du/(1-u^2)

which can be written as:

0.5*[1/(1-u) + 1/(1+u)]du

integrating we get:

0.5*[ln(1+u) - ln(1-u)] = 0.5*ln[(1+u)/(1-u)]