Need help with an Integral Homework Question

[juice34]

Homework Statement

I am having trouble finding the right solution to this integral it is of the form int(1/x)dx=lnx+c but apparently I am doing it wrong because of the other factors in the denominator
integral(dx/[(k1+k2)x-k2*y]

Homework Equations

The Attempt at a Solution

i get (1/(k1+k2))(ln(x/xi))-(x-xi)/k2*y but apparently the answer is
(1/(k2+k2))ln[((k1+k2)x-k2*xi)/((k1+k2)xi-k2*xi)]
so what am i doing wrong

 

[juice34]

please note that i evalued the integrals for both from xi to x also

 

[Mark44]

Is this your integral?
\int_{x_i}^x \frac{dt}{(k_1 + k_2)t - k_2 y}

It's unusual to have a variable as a limit of integration that is also the dummy variable of the integrand, so I switched the dummy variable to t.

To do this integral, use u = (k_1 + k_2)t - k_2*y. Then du = (k_1 + k_2)dt. Can you finish this?

 

[juice34]

Thank you mark I understand now, you are a great help!

 

[Mark44]

Aw, shucks!