Exercise
$\int cscx\left(1+cot^2x\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the trigonometric integral int(csc(x)(1+cot(x)^2))dx. Simplify the expression. Rewrite the trigonometric function \csc\left(x\right)^{3} as the product of two lower exponents. We can solve the integral \int\csc\left(x\right)^2\csc\left(x\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du.
Solve the trigonometric integral int(csc(x)(1+cot(x)^2))dx
Final answer to the exercise
$-\frac{1}{2}\cot\left(x\right)\csc\left(x\right)-\frac{1}{2}\ln\left|\csc\left(x\right)+\cot\left(x\right)\right|+C_0$