2
$\begingroup$

I have to find the reduction formula for the following :

$$\int\frac{(px+q)^n}{\sqrt{ax+b}}dx$$

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

${2a^{-1}(px+q)^{n}\sqrt{ax+b}-2pna^{-1}\int\{px+q}^{n-1}\sqrt{ax+b}dx$

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.

$\endgroup$
3
$\begingroup$

Hint: Perform integration-by-parts suggested below

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

$\endgroup$
1
  • $\begingroup$ Thank you so much. This helped me solve it. $\endgroup$
    – Natasha J
    Apr 10 at 15:49

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.