Answer:
[tex]\int\limits {\frac{10}{x^2-25} } \,dx=\ln |\frac{x-5}{x+5}|+C[/tex]
Step-by-step explanation:
We want to find the indefinite integral
[tex]\int\limits {\frac{10}{x^2-25} } \, dx[/tex]
We can rewrite this in the form: [tex]10\int\limits {\frac{dx}{x^2-5^2} } \,[/tex]
This will allow us to use tables of integration.
We use formula 31 from the table of integration shown in the attachment.
[tex]\int\limits {\frac{du}{u^2-a^2} } \,=\frac{1}{2a}\ln |\frac{u-a}{u+a}|+C[/tex]
We let [tex]u=x,a=5[/tex],then
[tex]10*\int\limits {\frac{dx}{x^2-5^2} } \,=10*\frac{1}{2*5}\ln |\frac{x-5}{x+5}|+C[/tex]
We simplify to get:
[tex]10*\int\limits {\frac{dx}{x^2-5^2} } \,=\ln |\frac{x-5}{x+5}|+C[/tex]
