Lore For Math

${\displaystyle \underset{‾}{\int \frac{dx}{ax+b}=\frac{1}{a}\ln \mid ax+b\mid +C\mathrm{.}}}$

${\displaystyle 1}$

${\displaystyle \int \frac{dx}{ax+b}}$

${\displaystyle letu=ax+b,du=adx,dx=\frac{du}{a},}$

${\displaystyle =\int \frac{1}{u}\frac{du}{a}}$

${\displaystyle =\frac{1}{a}\int \frac{du}{u}}$

${\displaystyle =\frac{1}{a}\ln \mid u\mid +C}$

${\displaystyle =\frac{1}{a}\ln \mid ax+b\mid +C\mathrm{.}}$