Question

Use the table of integrals, or a computer or calculator with symbolic integration capabilities, to find the indefinite integral.

Answer 1

Answer:

$-\frac{3}{11}\ln(\cot t + \csc t)+C$

Step-by-step explanation:

We are given:  $\int \frac{3}{x\sqrt{121-x^2}} dx$

We will use integration by parts.

$x = 11 \sin t\\dx = 11 \cos t \: dt$

$\int \frac{3}{x\sqrt{121-x^2}} dx=\int \frac{3* 11 \cos t \: dt}{11 \sin t\sqrt{121-121\sin^2 t}} =\int \frac{3* 11 \cos t \: dt}{11 \sin t*11\cos t}} =\\\\= \frac{3}{11} \int \csc t = -\frac{3}{11}\ln(\cot t + \csc t)+C$