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

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