Question

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

∫10/x^2-25 dx.

Answer 1

`\int\limits {(10)/(x^2-25) } \,dx=\ln |(x-5)/(x+5)|+C`

Explanation:

We want to find the indefinite integral

`\int\limits {(10)/(x^2-25) } \, dx`

We can rewrite this in the form:
`10\int\limits {(dx)/(x^2-5^2) } \,`

This will allow us to use tables of integration.

We use formula 31 from the table of integration shown in the attachment.

`\int\limits {(du)/(u^2-a^2) } \,=(1)/(2a)\ln |(u-a)/(u+a)|+C`

We let
`u=x,a=5`,then

`10*\int\limits {(dx)/(x^2-5^2) } \,=10*(1)/(2*5)\ln |(x-5)/(x+5)|+C`

We simplify to get:

`10*\int\limits {(dx)/(x^2-5^2) } \,=\ln |(x-5)/(x+5)|+C`