INTEGRALS CONTAINING THE SQUARE ROOT OF ax+b AND px+q

1.

$\displaystyle \int\displaystyle \frac{px+q}{\displaystyle \sqrt{ax+b}}\,dx=\displaystyle \frac{2(apx+3aq-2bp)}{3a^{\displaystyle2 }}\displaystyle \sqrt{ax+b}$

2.
$\displaystyle \int\displaystyle \frac{dx}{(px+q)\displaystyle \sqrt{ax+b}}=\lef...
...1}\displaystyle \sqrt{\displaystyle \frac{p(ax+b)}{aq-bp}}
\end{array} \right.$

3.
$\displaystyle \int\displaystyle \frac{\displaystyle \sqrt{ax+b}}{px+q}\,dx=\lef...
...1}\displaystyle \sqrt{\displaystyle \frac{p(ax+b)}{aq-bp}}
\end{array} \right.$

4.
$\displaystyle \int(px+q)^{\displaystyle n}\displaystyle \sqrt{ax+b}\,dx=\displa...
...int\displaystyle \frac{(px+q)^{\displaystyle n}}{\displaystyle \sqrt{ax+b}}\,dx$

5.
$\displaystyle \int\displaystyle \frac{(px+q)^{\displaystyle n}}{\displaystyle \...
...t\displaystyle \frac{(px+q)^{\displaystyle
n-1}\,dx}{\displaystyle \sqrt{ax+b}}$

6.
$\displaystyle \int\displaystyle \frac{\displaystyle \sqrt{ax+b}}{(px+q)^{\displ...
...int\displaystyle \frac{dx}{(px+q)^{\displaystyle n-1}\displaystyle \sqrt{ax+b}}$

7.
$\displaystyle
\begin{array}{l}
\displaystyle \int\displaystyle \frac{dx}{(px+q...
...frac{dx}{(px+q)^{\displaystyle
n-1}\displaystyle \sqrt{ax+b}}\right.\end{array}$

[Tables]

S.O.S MATHematics home page

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

Copyright 1999-2017 MathMedics, LLC. All rights reserved.
Contact us
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
users online during the last hour