INTEGRALS CONTAINING THE SQUARE ROOT OF ax2+bx+c

1.
$\displaystyle \int\displaystyle \frac{dx}{\displaystyle \sqrt{ax^{\displaystyle...
...2ax+b}{\displaystyle \sqrt{4ac-b^{\displaystyle2}}}\right)
\end{array} \right.$

2.
$\displaystyle \int\displaystyle \frac{x\,dx}{\displaystyle \sqrt{ax^{\displayst...
...tyle \int\displaystyle \frac{dx}{\displaystyle \sqrt{ax^{\displaystyle2}+bx+c}}$

3.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle2}\,dx}{\displaystyle \sq...
...tyle \int\displaystyle \frac{dx}{\displaystyle \sqrt{ax^{\displaystyle2}+bx+c}}$

4.
$\displaystyle \int\displaystyle \frac{dx}{x\displaystyle \sqrt{ax^{\displaystyl...
...ht\vert\displaystyle \sqrt{4ac-b^{\displaystyle2}}}\right)
\end{array} \right.$

5.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}\displaystyle \sqrt...
...yle \int\displaystyle \frac{dx}{x\displaystyle \sqrt{ax^{\displaystyle2}+bx+c}}$

6.
$\displaystyle \int\displaystyle \sqrt{ax^{\displaystyle2}+bx+c}\,dx=\displaysty...
...tyle \int\displaystyle \frac{dx}{\displaystyle \sqrt{ax^{\displaystyle2}+bx+c}}$

7.
$\displaystyle
\begin{array}{lclcl}
\displaystyle \int x\displaystyle \sqrt{ax^{...
...splaystyle \frac{dx}{\displaystyle \sqrt{ax^{\displaystyle2}+bx+c}}
\end{array}$

8.
$\displaystyle \int x^{\displaystyle2}\displaystyle \sqrt{ax^{\displaystyle2}+bx...
...playstyle2}}\displaystyle \int\displaystyle \sqrt{ax^{\displaystyle2}+bx+c}\,dx$

9.
$\displaystyle \int\displaystyle \frac{\displaystyle \sqrt{ax^{\displaystyle2}+b...
...yle \int\displaystyle \frac{dx}{x\displaystyle \sqrt{ax^{\displaystyle2}+bx+c}}$

10.
$\displaystyle \int\displaystyle \frac{\displaystyle \sqrt{ax^{\displaystyle2}+b...
...tyle \int\displaystyle \frac{dx}{\displaystyle \sqrt{ax^{\displaystyle2}+bx+c}}$

11.
$\displaystyle \int\displaystyle \frac{dx}{(ax^{\displaystyle2}+bx+c)^{\displays...
...ax+b)}{(4ac-b^{\displaystyle2})\,\displaystyle \sqrt{ax^{\displaystyle2}+bx+c}}$

12.
$\displaystyle \int\displaystyle \frac{x\,dx}{(ax^{\displaystyle2}+bx+c)^{\displ...
...x+2c)}{(b^{\displaystyle2}-4ac)\,\displaystyle \sqrt{ax^{\displaystyle2}+bx+c}}$

13.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle2}\,dx}{(ax^{\displaystyl...
...tyle \int\displaystyle \frac{dx}{\displaystyle \sqrt{ax^{\displaystyle2}+bx+c}}$

14.
$\begin{array}{lcl}
\displaystyle \int\displaystyle \frac{dx}{x(ax^{\displaystyl...
...isplaystyle \frac{dx}{(ax^{\displaystyle2}+bx+c)^{\displaystyle3/2}}\end{array}$

15.
$\displaystyle
\begin{array}{lcccl}
\displaystyle \int\displaystyle \frac{dx}{x^...
...playstyle \frac{dx}{x\displaystyle \sqrt{ax^{\displaystyle2}+bx+c}}
\end{array}$

16.
$\displaystyle
\begin{array}{lcl}
\displaystyle \int(ax^{\displaystyle2}+bx+c)^{...
...playstyle \int(ax^{\displaystyle2}+bx+c)^{\displaystyle n-1/2}\,dx
\end{array}$

17.
$\begin{array}{llll}
\displaystyle \int x(ax^{\displaystyle2}+bx+c)^{\displaysty...
...splaystyle \int(ax^{\displaystyle2}+bx+c)^{\displaystyle n+1/2}\,dx
\end{array}$

18.
$\displaystyle
\begin{array}{lcl}
\displaystyle \int\displaystyle \frac{dx}{(ax^...
...aystyle \frac{dx}{(ax^{\displaystyle2}+bx+c)^{\displaystyle n-1/2}}
\end{array}$

19.
$\displaystyle
\begin{array}{ll}
\displaystyle \int\displaystyle \frac{dx}{x(ax^...
...aystyle \frac{dx}{(ax^{\displaystyle2}+bx+c)^{\displaystyle n+1/2}}
\end{array}$

[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