Integral of Cosecant function

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$\int \csc\left(6x+9\right)\; dx$

**Answer**

$\int \csc\left(6x+9\right)\; dx$

Substitute $u=6x+9$. So, $du =6\; dx$

Or, $\frac{1}{6}\; du = dx$

And, $\int \csc\left(6x+9\right)\; dx = \frac{1}{6}\int \csc u \;du$

$=-\frac{1}{6}\ln \left|\csc u - \cot u \right| + C$

Substituting back $u=6x+9$

$=-\frac{1}{6}\ln \left| \csc\left(6x+9\right)- \cot\left(6x+9\right)\right|+C$