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

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henpen
 2 years ago
Best 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

kimmy0394
 2 years ago
Best ResponseYou've already chosen the best response.1arent' the variables supposed to be the same?

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

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

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

kimmy0394
 2 years ago
Best ResponseYou've already chosen the best response.1yeah, 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)

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