Solving Separable ODEs: How to Integrate with Functions of t?

[dgamma3]

I understand how to integrate this: ∫y²dy.

I don't understand how to integrate this:
di(t)/dt = i(t)p(t)
intergrate((di(t)/dt/i(t))*dt = p(t)dt) (see this image: http://i.imgur.com/OdKI309.png)

how do you perform the intergral on the left, seeing as as it not dt, but di(t)?

thanks

 

[Mark44]

I understand how to integrate this: ∫y²dy.

I don't understand how to integrate this:
di(t)/dt = i(t)p(t)
intergrate((di(t)/dt/i(t))*dt = p(t)dt) (see this image: http://i.imgur.com/OdKI309.png)

how do you perform the intergral on the left, seeing as as it not dt, but di(t)?

thanks

Can you do this integration? $\int \frac{du}{u}?$

BTW, there are no such words in English as "intergrate" and "intergral."

 

[dgamma3]

Can you do this integration? $\int \frac{du}{u}?$

BTW, there are no such words in English as "intergrate" and "intergral."

Yes I can do that.

But I do not understand how do integrate (what word do I use?)
∫di(t)/i(t)

 

[Mark44]

Yes I can do that.

But I do not understand how do integrate (what word do I use?)
∫di(t)/i(t)

This is essentially the same as what I wrote.
$\int \frac{du}{u}$ is the same as $\int \frac{du(t)}{u(t)}$. The only difference is that in the second integral, it is made explicit that u is a function of t.

 

[dgamma3]

This is essentially the same as what I wrote.
$\int \frac{du}{u}$ is the same as $\int \frac{du(t)}{u(t)}$. The only difference is that in the second integral, it is made explicit that u is a function of t.

Thank you Mark!