Question

Integration of dx/(ax+b)

Answer 1

log(ax+b)/a.................

Answer 2

Answer:

$\frac{1}{a}\ln \left|ax+b\right|+C$

Step-by-step explanation:

We have to find the integral

$\int \frac{1}{ax+b}dx$

Let ax + b = u then dx = du

Thus, the integral becomes

$=\int \frac{1}{au}du$

Take the constant out of the integral

$\frac{1}{a}\cdot \int \frac{1}{u}du$

$\mathrm{Use\:the\:common\:integral}:\quad \int \frac{1}{u}du=\ln \left(\left|u\right|\right)$

$\frac{1}{a}\ln \left|u\right|+C$

Substitute back u = ax + b

$\frac{1}{a}\ln \left|ax+b\right|+C$