Final answer to the problem
Step-by-step Solution
Specify the solving method
Find the integral
Learn how to solve problems step by step online.
$\int\cos\left(\theta\right)\cot\left(\theta\right)\left(\sec\left(\theta\right)-2\tan\left(\theta\right)\right)dt$
Learn how to solve problems step by step online. Integrate the function cos(t)cot(t)(sec(t)-2tan(t)). Find the integral. Rewrite the integrand \cos\left(\theta\right)\cot\left(\theta\right)\left(\sec\left(\theta\right)-2\tan\left(\theta\right)\right) in expanded form. Expand the integral \int\left(\cot\left(\theta\right)-2\cos\left(\theta\right)\right)dt into 2 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\cot\left(\theta\right)dt 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 \theta by setting the substitution.