Question

Evaluate the indefinite integral.
(3x)/(x^2+4)

Answer 1

Let \(u=x^2+4\). What is \(dx\) equal to?

Answer 2

dx= du/ (x^2+4)?

Answer 3

\[u=x^2+4\]
\[du=2xdx\]
\[dx=\frac{du}{2x}\]

Answer 4

oh yeah, i totally forgot that you have to take the derivative first.
kay what's next?

Answer 5

\[u=x^2+4\]
\[\frac{du}{dx}=2x\]
\[du=2xdx\]
is another way to look at it

Answer 6

plug that into the equation now

Answer 7

\[\int \frac{3x}{x^2+4}\frac{du}{2x}\]

Answer 8

but \[x^2+4=u\]
\[\int\frac{3x}{u}\frac{du}{2x}\]

Answer 9

now you shoudl be able to get something with u only and something smiple to solve

Answer 10

so you take du/2x out right, cuz it's a constant or something like that?

Answer 11

not quite you cant take variables out , but if you look the x's cancel and you're left with
\[\int \frac{3}{2}\frac{1}{u}du\]

Answer 12

constants you can pull out so you're left with a pretty simple integral

\[\int \frac{du}{u}\]

Answer 13

ok so then what do you plug in?

Answer 14

what do you mean? indefinite integrals don't have upper nad lower limits

Answer 15

like don't you have to integrate u? then plug it in?

Answer 16

yes so you integrated it correct?

Answer 17

?

Answer 18

um x^3/3+4x?

Answer 19

or u^2/2?

Answer 20

and what happens to du?

Answer 21

Do you know the integral of 1/x? \[\int\limits_{}^{} \frac{ 1 }{ x}dx = \ln \left| x \right|\]

Here we have \[\int\limits \frac{1}{u} du = ?\]

Answer 22

yeah...

Answer 23

So then what's the integral of \[\int\limits\limits \frac{1}{u} du = ? \]

Answer 24

Given you know that \[\int\limits\limits_{}^{} \frac{ 1 }{ x}dx = \ln \left| x \right| \]

Answer 25

Oh don't forget the 3/2 out front...\[\frac{3}{2} \int\limits \frac{1}{u}du \]

Answer 26

I don't think you comprehend the point of a substitution.