10 POINTS! Find the given integral and check your answer by differentiation. y^2/(y^3 + 4)^2 dy?



Asked on

1 Answer | Add Yours

embizze's profile pic

Posted on (Answer #1)

Find `int y^2/((y^3+4)^2)dy` :

Let `u=y^3+4,du=3y^2dy`

Then `int yy^2/((y^3+4)^2)dy=1/3int(3y^2)/((y^3+4)^2)dy`


Using the general power rule we can integrate:


`=-1/3u^(-1)+C`  substituting for u we get:

`=-1/3(y^3+4)^(-1)+C` or



Check: `d/(dy) -1/(3(y^3+4))+C=d/(dy) -1/3(y^3+4)^(-1)+C`


`=y^2/((y^3+4)^2)` as required.

We’ve answered 287,480 questions. We can answer yours, too.

Ask a question