Final Answer
$-\frac{1}{2}\cot\left(x\right)\csc\left(x\right)-\frac{1}{2}\ln\left(\csc\left(x\right)+\cot\left(x\right)\right)+C_0$
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Step-by-step Solution
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1
Rewrite the trigonometric function $\csc\left(x\right)^3$ as the product of two lower exponents
$\int\csc\left(x\right)^2\csc\left(x\right)dx$
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$\int\csc\left(x\right)^2\csc\left(x\right)dx$
Learn how to solve integral calculus problems step by step online. Solve the trigonometric integral int(csc(x)^3)dx. 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 u and calculate du. Now, identify dv and calculate v.
Final Answer
$-\frac{1}{2}\cot\left(x\right)\csc\left(x\right)-\frac{1}{2}\ln\left(\csc\left(x\right)+\cot\left(x\right)\right)+C_0$