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kimmy0394
Group Title
Evaluate the integral using the substitution rule. (Use C for the constant of integration.)
Integration of 2y/((2+3y^2)^3) dy
 one year ago
 one year ago
kimmy0394 Group Title
Evaluate the integral using the substitution rule. (Use C for the constant of integration.) Integration of 2y/((2+3y^2)^3) dy
 one year ago
 one year ago

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henpen Group TitleBest ResponseYou've already chosen the best response.2
\[\int\limits \frac{2y}{(2+3y^2)^3} dy\] \[ u=2+3y^2\] \[\frac{du}{dy}=6y \Rightarrow dy=\frac{du}{6y}\] \[\Rightarrow \int\limits \frac{2y}{(u)^3} \frac{du}{6y}\]You can do the rest
 one year ago

kimmy0394 Group TitleBest ResponseYou've already chosen the best response.1
arent' the variables supposed to be the same?
 one year ago

kimmy0394 Group TitleBest ResponseYou've already chosen the best response.1
i'm not getting the answer. i thought it would be 6y/(3(2+3y^2)^3) +C
 one year ago

henpen Group TitleBest ResponseYou've already chosen the best response.2
It cancels to\[\frac{1}{3}\int\limits\frac{du}{u^3}=\frac{1}{3}\frac{1}{4u^4}\]
 one year ago

kimmy0394 Group TitleBest ResponseYou've already chosen the best response.1
oh i forgot to integrate. i just got so confused on the substitution. oops! :) thanks a bunch!
 one year ago

kimmy0394 Group TitleBest ResponseYou've already chosen the best response.1
yeah, it was wrong. remember that 1/u^3 is the same as u^3. thus the integration of u^3 is u^2 / 2 or 1/ (2u^2)
 one year ago

henpen Group TitleBest ResponseYou've already chosen the best response.2
Sorry about that I half misread it as \[u^3\], not \[\frac{1}{u^3}\]. You're right
 one year ago
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