Integral of exponential function

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$\int \left(\csc^211x\right)\;e^{\cot11x} \; dx$

**Answer**

$\int \left(\csc^211x\right)\;e^{\cot11x} \; dx$

Substitute $u= \cot11x$. So, $du =-11\csc^211x\; dx$

And, $-\frac{1}{11}\; du = {\csc}^2 11x\; dx$

Then $\int \left(\csc^211x\right)\;e^{\cot11x} \; dx$

$=-\frac{1}{11}\int e^{u} \; du$

$=-\frac{1}{11}e^u + C $

Substituting back $u= \tan 11x$

$=-\frac{1}{11}e^{\cot 11x} + C$