Question

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

Answer 1

Answer:

$\int\limits {\frac{10}{x^2-25} } \,dx=\ln |\frac{x-5}{x+5}|+C$

Step-by-step explanation:

We want to find the indefinite integral

$\int\limits {\frac{10}{x^2-25} } \, dx$

We can rewrite this in  the form: $10\int\limits {\frac{dx}{x^2-5^2} } \,$

This will allow us to use tables of integration.

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

$\int\limits {\frac{du}{u^2-a^2} } \,=\frac{1}{2a}\ln |\frac{u-a}{u+a}|+C$

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

$10*\int\limits {\frac{dx}{x^2-5^2} } \,=10*\frac{1}{2*5}\ln |\frac{x-5}{x+5}|+C$

We simplify to get:

$10*\int\limits {\frac{dx}{x^2-5^2} } \,=\ln |\frac{x-5}{x+5}|+C$