I have to find the reduction formula for the following :


I took this integral from wikipedia. By using parts this is what I got.


The answer is in this link in reduction formula table: https://en.m.wikipedia.org/wiki/Integration_by_reduction_formulae

Any help is appreciated. Thanks in advance.


Hint: Perform integration-by-parts suggested below

$$I_n= \int\frac{(px+q)^n}{\sqrt{ax+b}}dx =\frac{1}{a(n+\frac12)} \int \left( \frac{px+q}{ax+b}\right)^n d\left( (ax+b)^{n+\frac12}\right) $$

  • $\begingroup$ Thank you so much. This helped me solve it. $\endgroup$
    – Natasha J
    Apr 10 at 15:49

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