I am a student and just learning about integrals. **Could you please explain to me how the highlighted part of the equation was derived?**
I can't quite understand how was the c/a term brought of the integral and how 1 integral just became a product of 2 other ones.
Thank you in advance!
There is no product of two integrals there. What the author is claiming is that, since we always have$$\frac{cx+d}{ax+b}=\frac ca+\frac{d-\frac{bc}a}{ax+b},$$then$$\int\frac{cx+d}{ax+b}\,\mathrm dx$$is the sum of$$\int\frac ca\,\mathrm dx\quad\text{with}\quad\int\frac{d-\frac{bc}a}{ax+b}\,\mathrm dx.$$That is, it is the sum of$$\frac ca\int\mathrm dx\quad\text{with}\quad\left(d-\frac{bc}a\right)\int\frac{\mathrm dx}{ax+b}.$$