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anonymous
 5 years ago
evaluate the integral 5/(n(n+9)) from 1 to infinity. Please Help
anonymous
 5 years ago
evaluate the integral 5/(n(n+9)) from 1 to infinity. Please Help

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0maybe partial fractions, but I need help on that part too...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0First, you should break up the 5/(n(n + 9)) into two separate fractions. A/n + B/(n + 9) = 5/(n(n+9)) > A(n + 9) + Bn = 5 Let n = 0 to find A = 5/9 and n = 9 to find B = 5/9. You should find that 5/(n(n + 9)) = 5/(9n)  5(9(n + 9)). You should be wanting to integrate this: \[\lim_{b \rightarrow \infty}\int\limits_{1}^{b}[5/(9n)5/(9(n + 9))]dn\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Awww yeah, thats how it's done

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Just use some u substitution and your done!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Other than the limit, just use log rules to combine them and it should work out

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Factor out a 5/9 to make the calculations somewhat easier: \[(5/9)\int\limits_{1}^{b}[1/n1/(n+9)]dn\] \[(5/9)[\ln n\ln n+9]_{1}^{b}\] \[(5/9)[\ln b\ln b+9\ln1+\ln10]\] \[(5/9)\ln[10b/(b+9)]\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Take the limit as b approaches infinity of the last thing, I got (5/9)*ln10

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I think it's e^ of that answer. I don't think you can use L'hospitals rule inside logs, can you?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I didn't use L'Hopital's rule. I divided the top and the bottom of the fraction by b.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah... it's just (5/9)ln10

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank you so much, that was so hard for me!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Try wolframalpha.com for these things, if you just want a solution, by the way.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=integrate%205%2F(n(n%2B9))%20from%201%20to%20infinity&t=macw01
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