Basic Integration (math)

Question

how can you integrate the integral of (ax+b)/(cx+d) dx ?

Answer 1

First separate the fraction into 2 parts: ax/(cx+d) + b/(cx+d)

The term with b in the numerator integrates as a ln(cx+d) ... some details omitted there!

For the term with ax in the numerator divide ax by (cx+d) by long division to get

ax/(cx+d) = (a/c) + [ad/(c²x + dc)

The first term integrates as ax/c and the second term integrates as a ln(c²x + dc)...again some details omitted.

Answer 2

=ax/cx+d + b/cx+d

use u = cx+d to solve