Mathematics: Integrate: log(ax+b)/(ax+b) dx

Integrate: log(ax+b)/(ax+b) dx - id10052494, taylorbean315

Ответ:

gracie2492

14.02.2022

$\frac{1}{2a} \bigg[log(ax + b) \bigg]^{2} + c$

Step-by-step explanation:

$\int \frac{log(ax + b)}{(ax + b)} dx \\ \\ let \: log(ax + b) = t \\ \\ \frac{1}{(ax + b)} .a \: dx = dt \\ \\ \frac{1}{(ax + b)} \: dx = \frac{1}{a} dt \\ \\ \therefore \: \int \frac{log(ax + b)}{(ax + b)} dx = \int t. \frac{1}{a} dt \\ \\ = \frac{1}{a} \int t. dt \\ \\ = \frac{1}{a} \times \frac{ {t}^{2} }{2} + c \\ \\ = \frac{1}{2a} \bigg[log(ax + b) \bigg]^{2} + c \\ \\ \purple{ \bold{\therefore \: \int \frac{log(ax + b)}{(ax + b)} dx = \frac{1}{2a} \bigg[log(ax + b) \bigg]^{2} + c}}$

0,0(0 оценок)

Ответ:

kimryan520

17.03.2021

Mathematics

Step-by-step explanation:

0,0(0 оценок)

Integrate: log(ax+b)/(ax+b) dx

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question