INTEGRALS CONTAINING THE SQUARE ROOT OF a2-x2

1.
$\displaystyle \int\displaystyle \frac{dx}{\displaystyle \sqrt{a^{\displaystyle2}-x^{\displaystyle2}}}=\sin^{\displaystyle-1}\displaystyle \frac{x}{a}$

2.
$\displaystyle \int\displaystyle \frac{x\,dx}{\displaystyle \sqrt{a^{\displaysty... ...^{\displaystyle2}}}=-\displaystyle \sqrt{a^{\displaystyle2}-x^{\displaystyle2}}$

3.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle2}\,dx}{\displaystyle \sq... ...yle \frac{a^{\displaystyle2}}{2}\sin^{\displaystyle-1}\displaystyle \frac{x}{a}$

4.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle3}\,dx}{\displaystyle \sq... ...-\;a^{\displaystyle2}\displaystyle \sqrt{a^{\displaystyle2}-x^{\displaystyle2}}$

5.
$\displaystyle \int\displaystyle \frac{dx}{x\displaystyle \sqrt{a^{\displaystyle... ...e \frac{a+\displaystyle \sqrt{a^{\displaystyle2}-x^{\displaystyle2}}}{x}\right)$

6.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}\displaystyle \sqrt... ...displaystyle \sqrt{a^{\displaystyle2}-x^{\displaystyle2}}}{a^{\displaystyle2}x}$

7.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle3}\displaystyle \sqrt... ...e \frac{a+\displaystyle \sqrt{a^{\displaystyle2}-x^{\displaystyle2}}}{x}\right)$

8.
$\displaystyle \int\displaystyle \sqrt{a^{\displaystyle2}-x^{\displaystyle2}}\,d... ...yle \frac{a^{\displaystyle2}}{2}\sin^{\displaystyle-1}\displaystyle \frac{x}{a}$

9.
$\displaystyle \int x\displaystyle \sqrt{a^{\displaystyle2}-x^{\displaystyle2}}\... ...splaystyle \frac{(a^{\displaystyle2}-x^{\displaystyle2})^{\displaystyle3/2}}{3}$

10.
$\displaystyle \int x^{\displaystyle2}\displaystyle \sqrt{a^{\displaystyle2}-x^{... ...yle \frac{a^{\displaystyle4}}{8}\sin^{\displaystyle-1}\displaystyle \frac{x}{a}$

11.
$\displaystyle \int x^{\displaystyle3}\displaystyle \sqrt{a^{\displaystyle2}-x^{... ...^{\displaystyle2}(a^{\displaystyle2}-x^{\displaystyle2})^{\displaystyle3/2}}{3}$

12.
$\displaystyle \int\displaystyle \frac{\displaystyle \sqrt{a^{\displaystyle2}-x^... ...e \frac{a+\displaystyle \sqrt{a^{\displaystyle2}-x^{\displaystyle2}}}{x}\right)$

13.
$\displaystyle \int\displaystyle \frac{\displaystyle \sqrt{a^{\displaystyle2}-x^... ...style2}-x^{\displaystyle2}}}{x}-\sin^{\displaystyle-1}\displaystyle \frac{x}{a}$

14.
$\displaystyle \int\displaystyle \frac{\displaystyle \sqrt{a^{\displaystyle2}-x^... ...e \frac{a+\displaystyle \sqrt{a^{\displaystyle2}-x^{\displaystyle2}}}{x}\right)$

15.
$\displaystyle \int\displaystyle \frac{dx}{(a^{\displaystyle2}-x^{\displaystyle2... ...}{a^{\displaystyle2}\displaystyle \sqrt{a^{\displaystyle2}-x^{\displaystyle2}}}$

16.
$\displaystyle \int\displaystyle \frac{x\,dx}{(a^{\displaystyle2}-x^{\displaysty... ...splaystyle \frac{1}{\displaystyle \sqrt{a^{\displaystyle2}-x^{\displaystyle2}}}$

17.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle2}\,dx}{(a^{\displaystyle... ...laystyle2}-x^{\displaystyle2}}}-\sin^{\displaystyle-1}\displaystyle \frac{x}{a}$

18.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle3}\,dx}{(a^{\displaystyle... ...a^{\displaystyle2}}{\displaystyle \sqrt{a^{\displaystyle2}-x^{\displaystyle2}}}$

19.
$\displaystyle \int\displaystyle \frac{dx}{x(a^{\displaystyle2}-x^{\displaystyle... ...e \frac{a+\displaystyle \sqrt{a^{\displaystyle2}-x^{\displaystyle2}}}{x}\right)$

20.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}(a^{\displaystyle2}... ...}{a^{\displaystyle4}\displaystyle \sqrt{a^{\displaystyle2}-x^{\displaystyle2}}}$

21.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle3}(a^{\displaystyle2}... ...e \frac{a+\displaystyle \sqrt{a^{\displaystyle2}-x^{\displaystyle2}}}{x}\right)$

22.
$\displaystyle \int(a^{\displaystyle2}-x^{\displaystyle2})^{\displaystyle3/2}\,d... ...le \frac{3}{8}a^{\displaystyle4}\sin^{\displaystyle-1}\displaystyle \frac{x}{a}$

23.
$\displaystyle \int x(a^{\displaystyle2}-x^{\displaystyle2})^{\displaystyle3/2}\... ...splaystyle \frac{(a^{\displaystyle2}-x^{\displaystyle2})^{\displaystyle3/2}}{5}$

24.
$\begin{array}{ll} \displaystyle \int x^{\displaystyle2}(a^{\displaystyle2}-x^{\... ...\displaystyle6}}{16}\sin^{\displaystyle-1}\displaystyle \frac{x}{a} \end{array}$

25.
$\displaystyle \int x^{\displaystyle3}(a^{\displaystyle2}-x^{\displaystyle2})^{\... ...^{\displaystyle2}(a^{\displaystyle2}-x^{\displaystyle2})^{\displaystyle5/2}}{5}$

26.
$\displaystyle \int\displaystyle \frac{(a^{\displaystyle2}-x^{\displaystyle2})^{... ...e \frac{a+\displaystyle \sqrt{a^{\displaystyle2}-x^{\displaystyle2}}}{x}\right)$

27.
$\displaystyle \int\displaystyle \frac{(a^{\displaystyle2}-x^{\displaystyle2})^{... ...le \frac{3}{2}a^{\displaystyle2}\sin^{\displaystyle-1}\displaystyle \frac{x}{a}$

28.
$\displaystyle \int\displaystyle \frac{(a^{\displaystyle2}-x^{\displaystyle2})^{... ...e \frac{a+\displaystyle \sqrt{a^{\displaystyle2}-x^{\displaystyle2}}}{x}\right)$

[Tables]

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