Question

Integral of 1/ (a+b-(a-b)x*) dx where (0

Answer 1

$\displaystyle\int\frac{\mathrm dx}{a+b-(a-b)x}=\frac1{b-a}\int\frac{\mathrm dy}y$

where $y=a+b-(a-b)x\implies \mathrm dy=(b-a)\,\mathrm dx$. Then

$\displaystyle\frac1{b-a}\int\frac{\mathrm dy}y=\frac{\ln|y|}{b-a}+C$
$\displaystyle\int\frac{\mathrm dx}{a+b-(a-b)x}=\frac{\ln|a+b-(a-b)x|}{b-a}+C$