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ggrree
 2 years ago
Best ResponseYou've already chosen the best response.0I was able to separate the integrand into partial fractions but then I get stuck.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2\[\int\limits_{0}^{9}\frac{dx}{x^26+5}\]

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2Is it really suppose to be x^26+5 and not x^26x+5?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2\[\frac{1}{x^21} \text{ since } 6+5=1\] \[\frac{1}{(x1)(x+1)}=\frac{A}{x1}+\frac{B}{x+1}\]

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2\[\frac{1}{(x1)(x+1)}=\frac{A(x+1)+B(x1)}{(x1)(x+1)}\] => 1=x(A+B)+(AB) A+B=0 ; AB=1

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2Can you do the test now?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2And by the way this is an improper integral meaning the function is not continuous on [0,9]

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2You will have to break up the integral

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2\[\int\limits_{0}^{1}\frac{dx}{x^21} +\int\limits_{1}^{9}\frac{dx}{x^21}\]

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2See if both parts converge if so then take the sum in you are done if not then the area/net area is divergent

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2lol I meant rest above not test

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2@ggrree any questions?

apoorvk
 2 years ago
Best ResponseYou've already chosen the best response.1i think we have a standard formula as well for integrals of this type rather than use partial fractions every time: \[\int\limits(1/(x^2a^2))dx =(1/2a)\ln((xa)/(x+a)) + k\]

ggrree
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah, I think I got it. I think... I think it diverges. is that right?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2you are right! @ggrree does not converge :)
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