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Integration - Ex1c.tex
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\documentclass[10pt]{article} \usepackage{amssymb,amsmath} \begin{document} \begin{align*} \text{Ex 1 c)}\\ &\int\frac{dx}{1-\sin x}\\ =&\int\frac{\frac{2}{1+t^2}\:dt}{1-\frac{2t}{1+t^2}}\\ =&\int\frac{2\:dt}{1+t^2-2t}\\ =&\int\frac{2\:dt}{\left(1-t\right)^2}\\ =&-\frac{2}{1-t}+C\\ =&\frac{2}{\tan \frac{x}{2}-1}+C\\ \end{align*} \end{document}