Answer:
[tex]-\frac{3}{11}\ln(\cot t + \csc t)+C[/tex]
Step-by-step explanation:
We are given: [tex]\int \frac{3}{x\sqrt{121-x^2}} dx[/tex]
We will use integration by parts.
[tex]x = 11 \sin t\\dx = 11 \cos t \: dt[/tex]
[tex]\int \frac{3}{x\sqrt{121-x^2}} dx=\int \frac{3* 11 \cos t \: dt}{11 \sin t\sqrt{121-121\sin^2 t}} =\int \frac{3* 11 \cos t \: dt}{11 \sin t*11\cos t}} =\\\\= \frac{3}{11} \int \csc t = -\frac{3}{11}\ln(\cot t + \csc t)+C[/tex]
