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integration

paulmdrdo

Active member
May 13, 2013
386
how would you integrate

1. $\displaystyle \int \left(\frac{x}{y}\right) d\left(\frac{x}{y}\right)$

2. $\displaystyle \int \frac{d(xy)}{(xy)^3}$

if the two is just in this form I could easily answer it

$\displaystyle \int d\left(\frac{x}{y}\right)=(\frac{x}{y})$

$\displaystyle \int d(xy)=(xy)$

but I don't know how to treat $\frac{x}{y}$ in 1 and the $(xy)^3$ in 2.

please help!
 

mente oscura

Well-known member
Nov 29, 2013
172
how would you integrate

1. $\displaystyle \int \left(\frac{x}{y}\right) d\left(\frac{x}{y}\right)$

2. $\displaystyle \int \frac{d(xy)}{(xy)^3}$

if the two is just in this form I could easily answer it

$\displaystyle \int d\left(\frac{x}{y}\right)=(\frac{x}{y})$

$\displaystyle \int d(xy)=(xy)$

but I don't know how to treat $\frac{x}{y}$ in 1 and the $(xy)^3$ in 2.

please help!
Hello.

[tex]1) \ u=\dfrac{x}{y}[/tex]

[tex]\displaystyle \int u \ d(u)=u= \dfrac{x}{y}[/tex]

[tex]2) \ u=(xy)[/tex]

[tex]\displaystyle \int \dfrac{d(u)}{u^3}=?[/tex]

Can you follow?

Regards.
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Hello.

[tex]1) \ u=\dfrac{x}{y}[/tex]

[tex]\displaystyle \int u \ d(u)=u= \dfrac{x}{y}[/tex]
What we want here is:

\(\displaystyle \int u\,du=\frac{1}{2}u^2+C\)
 

mente oscura

Well-known member
Nov 29, 2013
172
What we want here is:

\(\displaystyle \int u\,du=\frac{1}{2}u^2+C\)
Right. I I'm wrong.

I wrote:

[tex]\int u\,du[/tex]

And I thought in:

[tex]\int \,du[/tex]

(Headbang)(Headbang)(Headbang)

I'm sorry.

Regards.
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Hey, we all make mistakes...I know I have made my share! (Emo)