Use differentiation to verify the integration formulas

[ranger1716]

ok, so my problem goes like this:

I have that the integral of dx/((cx+a)(dx+b))=1/(ad-bc)lnabs((dx+b)/cx+a)) + C
I have to use differentiation to verify the integration formulas.

So far I've gotten to:

D(1/(ad-bc)lnabs((dx+b)/cx+a)))=(1/ad-bc)((cx=a)/(dx+b)) => (cx+a)/((ad-bc)(dx+b))

where do I go from here to get back to the original integration formula?

 

[Fermat]

You differentiation is at fault.

if you have F = ln{f(x)/g(x)}, then

F = lnf(x) - lng(x)

dF/dx = f'/f - g'/g

where f' = df/dx, g' = dg/dx