INTEGRALS CONTAINING x3+a3

1.

$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle3}+a^{\displaystyle3}... ...qrt{3}}\tan^{\displaystyle-1}\displaystyle \frac{2x-a}{a\displaystyle \sqrt{3}}$

2.
$\displaystyle \int\displaystyle \frac{x\,dx}{x^{\displaystyle3}+a^{\displaystyl... ...qrt{3}}\tan^{\displaystyle-1}\displaystyle \frac{2x-a}{a\displaystyle \sqrt{3}}$

3.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle2}\,dx}{x^{\displaystyle3... ...laystyle3}}=\displaystyle \frac{1}{3}\ln(x^{\displaystyle3}+a^{\displaystyle3})$

4.
$\displaystyle \int\displaystyle \frac{dx}{x(x^{\displaystyle3}+a^{\displaystyle... ...aystyle \frac{x^{\displaystyle3}}{x^{\displaystyle3}+a^{\displaystyle3}}\right)$

5.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}(x^{\displaystyle3}... ...qrt{3}}\tan^{\displaystyle-1}\displaystyle \frac{2x-a}{a\displaystyle \sqrt{3}}$

6.
$\displaystyle \int\displaystyle \frac{dx}{(x^{\displaystyle3}+a^{\displaystyle3... ...qrt{3}}\tan^{\displaystyle-1}\displaystyle \frac{2x-a}{a\displaystyle \sqrt{3}}$

7.
$\displaystyle \int\displaystyle \frac{x\,dx}{(x^{\displaystyle3}+a^{\displaysty... ...qrt{3}}\tan^{\displaystyle-1}\displaystyle \frac{2x-a}{a\displaystyle \sqrt{3}}$

8.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle2}\,dx}{(x^{\displaystyle... ...splaystyle2}}=-\displaystyle \frac{1}{3(x^{\displaystyle3}+a^{\displaystyle3})}$

9.
$\displaystyle \int\displaystyle \frac{dx}{x(x^{\displaystyle3}+a^{\displaystyle... ...aystyle \frac{x^{\displaystyle3}}{x^{\displaystyle3}+a^{\displaystyle3}}\right)$

10.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}(x^{\displaystyle3}... ...playstyle \int\displaystyle \frac{x\,dx}{x^{\displaystyle3}+a^{\displaystyle3}}$

11.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle m}\,dx}{x^{\displaystyle... ...aystyle \frac{x^{\displaystyle m-3}\,dx}{x^{\displaystyle3}+a^{\displaystyle3}}$

12.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle n}(x^{\displaystyle3... ...aystyle \frac{dx}{x^{\displaystyle n-3}(x^{\displaystyle3}+a^{\displaystyle3})}$

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