Answers: 2
![\frac{1}{2a} \bigg[log(ax + b) \bigg]^{2} + c](/tpl/images/1005/2443/5ce28.png)
![\int \frac{log(ax + b)}{(ax + b)} dx \\ \\ let \: log(ax + b) = t \\ \\ \frac{1}{(ax + b)} .a \: dx = dt \\ \\ \frac{1}{(ax + b)} \: dx = \frac{1}{a} dt \\ \\ \therefore \: \int \frac{log(ax + b)}{(ax + b)} dx = \int t. \frac{1}{a} dt \\ \\ = \frac{1}{a} \int t. dt \\ \\ = \frac{1}{a} \times \frac{ {t}^{2} }{2} + c \\ \\ = \frac{1}{2a} \bigg[log(ax + b) \bigg]^{2} + c \\ \\ \purple{ \bold{\therefore \: \int \frac{log(ax + b)}{(ax + b)} dx = \frac{1}{2a} \bigg[log(ax + b) \bigg]^{2} + c}}](/tpl/images/1005/2443/2b3ab.png)
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