$$ 1.\,\int\!\! \frac{dx}{ax+b}=\frac{1}{a}\ln \vert ax+b \vert +C $$

$$ 2.\,\int\!\! (ax+b)^\mu dx=\frac{1}{a(\mu+1)}(ax+b)^{\mu+1}+C \qquad (\mu \neq -1) $$

$$ 3.\,\int\!\! \frac{x}{ax+b}dx=\frac{1}{a^2}(ax+b-b\ln\vert (x+b) \vert ) +C $$

$$ 4.\,\int\!\! \frac{x^2}{ax+b}dx=\frac{1}{a^3}\Big[\frac{1}{2}(ax+b)^2-2b(ax+b)+b^2\ln\vert ax+b\vert\Big]+C $$

$$ 5.\,\int\!\! \frac{dx}{x(ax+b)}=-\frac{1}{b}\ln \Big\vert \frac{ax+b}{x}\Big\vert +C $$

$$ 6.\,\int\!\! \frac{dx}{x^2(ax+b)}=-\frac{1}{bx}+\frac{a}{b^2}\ln\Big\vert\frac{ax+b}{x}\Big\vert+C $$

$$ 7.\,\int\!\! \frac{x}{(ax+b)^2}dx=\frac{1}{a^2}\Big(\ln \vert ax+b \vert + \frac{b}{ax+b}\Big)+C $$

$$ 8.\,\int\!\! \frac{x^2}{(ax+b)^2}dx= \frac{1}{a^3}\Big(ax+b-2b\ln\vert ax+b \vert - \frac{b^2}{ax+b}\Big ) + C $$

$$ 9.\,\int\!\! \frac{dx}{x(a+b)^2}=\frac {1}{b(ax+b)}-\frac{1}{b^2}\ln\Big\vert \frac{ax+b}{x}\Big\vert + C $$