Question

\[\int {3y \over (5y^2 + 4)^2} dy\]

Answer 1

\[u = 5y^2 + 4 \]

Answer 2

\[du = 10ydy \]

Answer 3

\[ydy = {1 \over 10}du \]

Answer 4

So then substituting:\[ \int{3y \over u^2}dy\]Next, take 3 out:\[3\int{y \over u^2} dy \]Substituting for \(ydy\) next:\[3\int u^{-2} {1 \over 10}du \]

Answer 5

Taking 1/10 out:\[{3 \over 10}\int u^{-2} du \]

Answer 6

\[{3 \over 10} \times {u^{-1} \over -1}+c \]?

Answer 7

Well done

Answer 8

Thanks, and then:\[{-3 \over 10} u^{-1} + c \]

Answer 9

Substituting back for \(u\).\[{-3 \over 10}\left(5y^2 + 4 \right)^{-1} + c \]

Answer 10

Does that become\[{-3 \over 10\left(5y^2 + 4 \right)^{}} \]?

Answer 11

+ c

Answer 12

yes

Answer 13

Thank you guys for taking time just for me!

Answer 14

anytime parth