ΟΛΟΚΛΗΡΩΜΑΤΑ ΠΟΥ ΠΕΡΙΕΧΟΥΝ ΤΟ x2    -  a2    

Υποθέτουμε ότι  x2 > a2:

1.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}-a^{\displaystyle2}}=\displaystyle \frac{1}{2a}\ln\left(\displaystyle \frac{x-a}{x+a}\right)\;\;$ ή $\;\;-\displaystyle \frac{1}{a}$coth $^{\displaystyle-1}\displaystyle \frac{x}{a}$
2.
$\displaystyle \int\displaystyle \frac{x\,dx}{x^{\displaystyle2}-a^{\displaystyle2}}=\displaystyle \frac{1}{2}\ln(x^{\displaystyle2}-a^{\displaystyle2})$
3.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle2}\,dx}{x^{\displaystyle2...
...yle2}}=x+\displaystyle \frac{a}{2}\ln\left(\displaystyle \frac{x-a}{x+a}\right)$
4.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle3}\,dx}{x^{\displaystyle2...
...laystyle \frac{a^{\displaystyle2}}{2}\ln(x^{\displaystyle2}-a^{\displaystyle2})$
5.
$\displaystyle \int\displaystyle \frac{dx}{x(x^{\displaystyle2}-a^{\displaystyle...
...aystyle \frac{x^{\displaystyle2}-a^{\displaystyle2}}{x^{\displaystyle2}}\right)$
6.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}(x^{\displaystyle2}...
...tyle \frac{1}{2a^{\displaystyle3}}\ln\left(\displaystyle \frac{x-a}{x+a}\right)$
7.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle3}(x^{\displaystyle2}...
...aystyle \frac{x^{\displaystyle2}}{x^{\displaystyle2}-a^{\displaystyle2}}\right)$
8.
$\displaystyle \int\displaystyle \frac{dx}{(x^{\displaystyle2}-a^{\displaystyle2...
...tyle \frac{1}{4a^{\displaystyle3}}\ln\left(\displaystyle \frac{x-a}{x+a}\right)$
9.
$\displaystyle \int\displaystyle \frac{x\,dx}{(x^{\displaystyle2}-a^{\displaysty...
...splaystyle2}}=\displaystyle \frac{-1}{2(x^{\displaystyle2}-a^{\displaystyle2})}$
10.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle2}\,dx}{(x^{\displaystyle...
...yle2})}+\displaystyle \frac{1}{4a}\ln\left(\displaystyle \frac{x-a}{x+a}\right)$
11.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle3}\,dx}{(x^{\displaystyle...
...aystyle2})}+\displaystyle \frac{1}{2}\ln(x^{\displaystyle2}-a^{\displaystyle2})$
12.
$\displaystyle \int\displaystyle \frac{dx}{x(x^{\displaystyle2}-a^{\displaystyle...
...aystyle \frac{x^{\displaystyle2}}{x^{\displaystyle2}-a^{\displaystyle2}}\right)$
13.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}(x^{\displaystyle2}...
...tyle \frac{3}{4a^{\displaystyle5}}\ln\left(\displaystyle \frac{x-a}{x+a}\right)$
14.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle3}(x^{\displaystyle2}...
...aystyle \frac{x^{\displaystyle2}}{x^{\displaystyle2}-a^{\displaystyle2}}\right)$
15.
$\displaystyle \int\displaystyle \frac{dx}{(x^{\displaystyle2}-a^{\displaystyle2...
...laystyle \frac{dx}{(x^{\displaystyle2}-a^{\displaystyle2})^{\displaystyle n-1}}$
16.
$\displaystyle \int\displaystyle \frac{x\,dx}{(x^{\displaystyle2}-a^{\displaysty...
...le \frac{-1}{2(n-1)(x^{\displaystyle2}-a^{\displaystyle2})^{\displaystyle n-1}}$
17.
$\displaystyle \int\displaystyle \frac{dx}{x(x^{\displaystyle2}-a^{\displaystyle...
...aystyle \frac{dx}{x(x^{\displaystyle2}-a^{\displaystyle2})^{\displaystyle n-1}}$
18.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle m}\,dx}{(x^{\displaystyl...
...splaystyle m-2}\,dx}{(x^{\displaystyle2}-a^{\displaystyle2})^{\displaystyle n}}$
19.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle m}(x^{\displaystyle2...
...x^{\displaystyle m}(x^{\displaystyle2}-a^{\displaystyle2})^{\displaystyle n-1}}$

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