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ΟΛΟΚΛΗΡΩΜΑΤΑ ΠΟΥ ΠΕΡΙΕΧΟΥΝ ΤΟ x²+ a²

1.: $\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}+a^{\displaystyle2}}=\displaystyle \frac{1}{a}\tan^{\displaystyle-1}\displaystyle \frac{x}{a}$
2.: $\displaystyle \int\displaystyle \frac{x\,dx}{x^{\displaystyle2}+a^{\displaystyle2}}=\displaystyle \frac{1}{2}\ln(x^{\displaystyle2}+a^{\displaystyle2})$
3.: $\displaystyle \int\displaystyle \frac{x^{\displaystyle2}\,dx}{x^{\displaystyle2}+a^{\displaystyle2}}=x-a\tan^{\displaystyle-1}\displaystyle \frac{x}{a}$
4.: $\displaystyle \int\displaystyle \frac{x^{\displaystyle3}\,dx}{x^{\displaystyle2... ...laystyle \frac{a^{\displaystyle2}}{2}\ln(x^{\displaystyle2}+a^{\displaystyle2})$
5.: $\displaystyle \int\displaystyle \frac{dx}{x(x^{\displaystyle2}+a^{\displaystyle... ...aystyle \frac{x^{\displaystyle2}}{x^{\displaystyle2}+a^{\displaystyle2}}\right)$
6.: $\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}(x^{\displaystyle2}... ...yle \frac{1}{a^{\displaystyle3}}\tan^{\displaystyle-1}\displaystyle \frac{x}{a}$
7.: $\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle3}(x^{\displaystyle2}... ...aystyle \frac{x^{\displaystyle2}}{x^{\displaystyle2}+a^{\displaystyle2}}\right)$
8.: $\displaystyle \int\displaystyle \frac{dx}{(x^{\displaystyle2}+a^{\displaystyle2... ...le \frac{1}{2a^{\displaystyle3}}\tan^{\displaystyle-1}\displaystyle \frac{x}{a}$
9.: $\displaystyle \int\displaystyle \frac{x\,dx}{(x^{\displaystyle2}+a^{\displaysty... ...splaystyle2}}=\displaystyle \frac{-1}{2(x^{\displaystyle2}+a^{\displaystyle2})}$
10.: $\displaystyle \int\displaystyle \frac{x^{\displaystyle2}\,dx}{(x^{\displaystyle... ...e2})}+\displaystyle \frac{1}{2a}\tan^{\displaystyle-1}\displaystyle \frac{x}{a}$
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.: $\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}(x^{\displaystyle2}... ...le \frac{3}{2a^{\displaystyle5}}\tan^{\displaystyle-1}\displaystyle \frac{x}{a}$
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.: $\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle m}(x^{\displaystyle2... ...x^{\displaystyle m-2}(x^{\displaystyle2}+a^{\displaystyle2})^{\displaystyle n}}$