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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