Integration in fraction

[Evil]

Hi,

Please explain how Should I integrate this function

z'=\[\frac{1}{x}\left[ {\frac{{ - 2\, + 5z}}{{2 + z}}\, - \,z} \right]\]

Thanks.

 

[Steven G]

Hi,

Please explain how Should I integrate this function

z'=\[\frac{1}{x}\left[ {\frac{{ - 2\, + 5z}}{{2 + z}}\, - \,z} \right]\]

Thanks.

with respect to z, x, j,,,?
I suspect it is wrt z. I would do the division (-2+5z)/(2+z). What have you tried????

 

[Evil]

with respect to z, x, j,,,?
I suspect it is wrt z. I would do the division (-2+5z)/(2+z). What have you tried????

I tried saperable method But I am stuck here

dz / dx = 1/x [-2 + 5z / 2 + z]

BUT here I am stuck, how I should simplify it to get integral ????

 

[Evil]

with respect to z, x, j,,,?
I suspect it is wrt z. I would do the division (-2+5z)/(2+z). What have you tried????

There is an example related to this:

I am attaching. please explain how this step 4 is coming because there is no 3 and -4 in above expression ?

 

[Steven G]

I tried saperable method But I am stuck here

dz / dx = 1/x [-2 + 5z / 2 + z]

BUT here I am stuck, how I should simplify it to get integral ????

Ah, z'=dz/dx. You need to tell us all this.
You can't separate it? That is not good at all. Here is a hint: If dz/dx=a/b then bdz=adx or dz/a=dx/b. Now integrate both sides.

 

[Steven G]

There is an example related to this:

I am attaching. please explain how this step 4 is coming because there is no 3 and -4 in above expression ?

Separate and do the long division as mentioned before.

 

[Evil]

Separate and do the long division as mentioned before.

Got it.