Calculate $\int\frac{\ln^2(a+bx)}{x^n}dx$

Asked Dec 31 '20 at 16:47

Active Dec 31 '20 at 17:07

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I know the solve the integral $$\int\frac{\ln(a+bx)}{x^n}dx$$ by the integration by parts method. I'm interested to solve the given integral $$\int\frac{\ln^2(a+bx)}{x^n}dx$$ by the parts method Thanks for help.

edited Dec 31 '20 at 17:07

Cooperation

asked Dec 31 '20 at 16:47

Madrit Zhaku

1

It's amazing to me how much easier it is if you replace $ \ln(a+bx)$ with $\ln(x)$ in both of the above. WolframAlpha says the answer involves the hypergeometric function, which I know nothing about. – Adam Rubinson Dec 31 '20 at 17:38

Calculate $\int\frac{\ln^2(a+bx)}{x^n}dx$

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