Exercise
$\int\left(\frac{1}{\sec^2\left(x\right)-1}\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the trigonometric integral int(1/(sec(x)^2-1))dx. We can solve the integral \int\frac{1}{\sec\left(x\right)^2-1}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.
Solve the trigonometric integral int(1/(sec(x)^2-1))dx
Final answer to the exercise
$\frac{1}{2}\tan\left(\frac{x}{2}\right)-x+\frac{1}{-2\tan\left(\frac{x}{2}\right)}+C_0$