Evaluate the integral using the substitution rule. (Use C for the constant of integration.)

Integration of 2y/((2+3y^2)^3) dy

Question

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

anonymous · Answer

$$\int\limits \frac{2y}{(2+3y^2)^3}  dy$$
$$ u=2+3y^2$$
$$\frac{du}{dy}=6y \Rightarrow  dy=\frac{du}{6y}$$
$$\Rightarrow \int\limits \frac{2y}{(u)^3} \frac{du}{6y}$$You can do the rest

anonymous · Answer

arent' the variables supposed to be the same?

anonymous · Answer

i'm not getting the answer. i thought it would be 6y/(3(2+3y^2)^3) +C

anonymous · Answer

It cancels to$$\frac{1}{3}\int\limits\frac{du}{u^3}=\frac{1}{3}\frac{1}{-4u^4}$$

anonymous · Answer

oh i forgot to integrate. i just got so confused on the substitution. oops! :) thanks a bunch!

anonymous · Answer

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)

anonymous · Answer

Sorry about that- I half misread it as $$u^3$$, not $$\frac{1}{u^3}$$. You're right