# Thread: How to integrate 1/(y^2+3y) dy?

1. ## How to integrate 1/(y^2+3y) dy?

1
---------- dy
y^2 + 3y

2. Originally Posted by orange890
1
---------- dy
y^2 + 3y

How do you find:

$
\int \frac{1}{y^2+3y} \ dy
$
?

You resolve the integrand into partial fractions, which can then be integrated
by inspection.

$
\frac{1}{y^2+3y}=\frac{1}{y(y+3)}=\frac{A}{y}+ \frac{B}{y+3}
$

With a bit of manipulation you will find:

$
\frac{1}{y^2+3y}=\frac{1}{3}\left\{ \frac{1}{y}- \frac{1}{y+3} \right\}
$
.

You should now be able to find the integral yourself from this point.

RonL

3. Originally Posted by CaptainBlack
With a bit of manipulation you will find:

$
\frac{1}{y^2+3y}=\frac{1}{3}\left\{ \frac{-1}{y}+ \frac{1}{y+3} \right\}
$
.
I believe the signs should be switched, so:

$
\frac{1}{y^2+3y}=\frac{1}{3}\left\{ \frac{1}{y}+ \frac{-1}{y+3} \right\}
$

4. Originally Posted by TD!
I believe the signs should be switched, so:

$
\frac{1}{y^2+3y}=\frac{1}{3}\left\{ \frac{1}{y}+ \frac{-1}{y+3} \right\}
$
So it does

RonL

5. Don't be angry, be happy. Making mistakes is a sign of being (only?) human

6. Originally Posted by TD!
Don't be angry, be happy. Making mistakes is a sign of being (only?) human
Hey, I once had a Mechanics prof who would take 15 points off for missing a "-" sign. (Yes, it WAS out of a 100 point exam.) The bad news was that his lectures contained just those sorts of errors. (We were all happy to get B's in that class!)

-Dan

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