Exercise
$\int_0^{\pi}\left(\frac{1}{senx-1}\right)dx$
Step-by-step Solution
Learn how to solve weierstrass substitution problems step by step online. Integrate the function 1/(sin(x)-1) from 0 to pi. We can solve the integral \int\frac{1}{\sin\left(x\right)-1}dx by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of t by setting the substitution. Hence. Substituting in the original integral we get. Simplifying.
Integrate the function 1/(sin(x)-1) from 0 to pi
Final answer to the exercise
$\frac{2}{\tan\left(\frac{\pi }{2}\right)-1}- \frac{2}{\tan\left(\frac{0}{2}\right)-1}$