Question

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

Answer 1

`\displaystyle\int(\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=(\ln|y|)/(b-a)+C`

`\displaystyle\int(\mathrm dx)/(a+b-(a-b)x)=(\ln|a+b-(a-b)x|)/(b-a)+C`