Final Answer
$-\ln\left(\csc\left(x\right)+\cot\left(x\right)\right)+C_0$
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Step-by-step Solution
Problem to solve:
$\int\csc\left(x\right)dx$
Specify the solving method
1
The integral of $\csc(x)$ is $-\ln(\csc(x)+\cot(x))$
$-\ln\left(\csc\left(x\right)+\cot\left(x\right)\right)$
2
As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$
$-\ln\left(\csc\left(x\right)+\cot\left(x\right)\right)+C_0$
Final Answer
$-\ln\left(\csc\left(x\right)+\cot\left(x\right)\right)+C_0$