INTEGRALS CONTAINING "x4+a4" or "x4-a4"

1.

$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle4}+a^{\displaystyle4}... ...laystyle \frac{ax\displaystyle \sqrt{2}}{x^{\displaystyle2}-a^{\displaystyle2}}$

2.
$\displaystyle \int\displaystyle \frac{x\,dx}{x^{\displaystyle4}+a^{\displaystyl... ...an^{\displaystyle-1}\displaystyle \frac{x^{\displaystyle2}}{a^{\displaystyle2}}$

3.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle2}\,dx}{x^{\displaystyle4... ...laystyle \frac{ax\displaystyle \sqrt{2}}{x^{\displaystyle2}-a^{\displaystyle2}}$

4.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle3}\,dx}{x^{\displaystyle4... ...}=\displaystyle \frac{1}{4}ln\left(x^{\displaystyle4}+a^{\displaystyle4}\right)$

5.
$\displaystyle \int\displaystyle \frac{dx}{x\left(x^{\displaystyle4}+a^{\display... ...aystyle \frac{x^{\displaystyle4}}{x^{\displaystyle4}+a^{\displaystyle4}}\right)$

6.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}\left(x^{\displayst... ...laystyle \frac{ax\displaystyle \sqrt{2}}{x^{\displaystyle2}-a^{\displaystyle2}}$

7.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle3}\left(x^{\displayst... ...an^{\displaystyle-1}\displaystyle \frac{x^{\displaystyle2}}{a^{\displaystyle2}}$

8.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle4}-a^{\displaystyle4}... ...le \frac{1}{2a^{\displaystyle3}}\tan^{\displaystyle-1}\displaystyle \frac{x}{a}$

9.
$\displaystyle \int\displaystyle \frac{x\,dx}{x^{\displaystyle4}-a^{\displaystyl... ...isplaystyle2}-a^{\displaystyle2}}{x^{\displaystyle2}+a^{\displaystyle2}}\right)$

10.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle2}\,dx}{x^{\displaystyle4... ...)\,+\,\displaystyle \frac{1}{2a}\tan^{\displaystyle-1}\displaystyle \frac{x}{a}$

11.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle3}\,dx}{x^{\displaystyle4... ...=\displaystyle \frac{1}{4}\ln\left(x^{\displaystyle4}+a^{\displaystyle4}\right)$

12.
$\displaystyle \int\displaystyle \frac{dx}{x\left(x^{\displaystyle4}-a^{\display... ...aystyle \frac{x^{\displaystyle4}-a^{\displaystyle4}}{x^{\displaystyle4}}\right)$

13.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}\left(x^{\displayst... ...le \frac{1}{2a^{\displaystyle5}}\tan^{\displaystyle-1}\displaystyle \frac{x}{a}$

14.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle3}\left(x^{\displayst... ...a^{\displaystyle4}x^2 }+ \frac{1}{4a^6} \ln\left(\frac{x^2-a^2}{x^2+a^2}\right)$

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