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ggrree
 2 years ago
problem with integration:
http://gyazo.com/89f6c648f3cf2cf0b074b3c5ed419752
I know you're supposed to separate into partial fractions, but I get 5, 2 and 3 as the top numbers ABand C. could somebody walk me through just the separation of partial fractions?
ggrree
 2 years ago
problem with integration: http://gyazo.com/89f6c648f3cf2cf0b074b3c5ed419752 I know you're supposed to separate into partial fractions, but I get 5, 2 and 3 as the top numbers ABand C. could somebody walk me through just the separation of partial fractions?

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myname
 2 years ago
Best ResponseYou've already chosen the best response.0First, A = 5 , B= 2, C = 1 [not 3] Then,\[\int\limits(3x^2+9x+5)/(x(x+1)^2)dx= \int\limits (5/x) ( 2/(x+1)) +( 1/(x+1)^2) dx\]Now, you can use the sum and difference rule of the integration\[\int\limits\limits(3x^2+9x+5)/(x(x+1)^2)= \int\limits\limits (5/x) dx \int\limits( 2/(x+1))dx +\int\limits( 1/(x+1)^2)dx\] Next, you can use the substitution to find the antiderivatives \[\int\limits\limits\limits(3x^2+9x+5)/(x(x+1)^2) =5\ln(x)  2\ln(x+1) + (1/x+1)\]

mark_o.
 2 years ago
Best ResponseYou've already chosen the best response.1\[\int\limits_{}^{} (A/x) + \int\limits_{}^{} (B/(x+1) + \int\limits_{}^{} (C/(x+1)^2)\] w/c leads to A=5, B=2 and C=1 = 5ln x  2 ln(x+1)  (1/(x+1)) ans....
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