Question

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

∫3/x√121-x^2 dx.

Answer 1

`-(3)/(11)\ln(\cot t + \csc t)+C`

Explanation:

We are given:
`\int (3)/(x√(121-x^2)) dx`

We will use integration by parts.

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

`\int (3)/(x√(121-x^2)) dx=\int (3* 11 \cos t \: dt)/(11 \sin t√(121-121\sin^2 t)) =\int (3* 11 \cos t \: dt)/(11 \sin t*11\cos t)} =\\\\= (3)/(11) \int \csc t = -(3)/(11)\ln(\cot t + \csc t)+C`