INTEGRALS CONTAINING x²+a²

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INTEGRALS CONTAINING x²+a²

1.: $displaystyle intdisplaystyle rac{dx}{x^{displaystyle2}+a^{displaystyle2}}=displaystyle rac{1}{a} an^{displaystyle-1}displaystyle rac{x}{a}$
2.: $displaystyle intdisplaystyle rac{x,dx}{x^{displaystyle2}+a^{displaystyle2}}=displaystyle rac{1}{2}ln(x^{displaystyle2}+a^{displaystyle2})$
3.: $displaystyle intdisplaystyle rac{x^{displaystyle2},dx}{x^{displaystyle2}+a^{displaystyle2}}=x-a an^{displaystyle-1}displaystyle rac{x}{a}$
4.: $displaystyle intdisplaystyle rac{x^{displaystyle3},dx}{x^{displaystyle2... ...laystyle rac{a^{displaystyle2}}{2}ln(x^{displaystyle2}+a^{displaystyle2})$
5.: $displaystyle intdisplaystyle rac{dx}{x(x^{displaystyle2}+a^{displaystyle... ...aystyle rac{x^{displaystyle2}}{x^{displaystyle2}+a^{displaystyle2}} ight)$
6.: $displaystyle intdisplaystyle rac{dx}{x^{displaystyle2}(x^{displaystyle2}... ...yle rac{1}{a^{displaystyle3}} an^{displaystyle-1}displaystyle rac{x}{a}$
7.: $displaystyle intdisplaystyle rac{dx}{x^{displaystyle3}(x^{displaystyle2}... ...aystyle rac{x^{displaystyle2}}{x^{displaystyle2}+a^{displaystyle2}} ight)$
8.: $displaystyle intdisplaystyle rac{dx}{(x^{displaystyle2}+a^{displaystyle2... ...le rac{1}{2a^{displaystyle3}} an^{displaystyle-1}displaystyle rac{x}{a}$
9.: $displaystyle intdisplaystyle rac{x,dx}{(x^{displaystyle2}+a^{displaysty... ...splaystyle2}}=displaystyle rac{-1}{2(x^{displaystyle2}+a^{displaystyle2})}$
10.: $displaystyle intdisplaystyle rac{x^{displaystyle2},dx}{(x^{displaystyle... ...e2})}+displaystyle rac{1}{2a} an^{displaystyle-1}displaystyle rac{x}{a}$
11.: $displaystyle intdisplaystyle rac{x^{displaystyle3},dx}{(x^{displaystyle... ...aystyle2})}+displaystyle rac{1}{2}ln(x^{displaystyle2}+a^{displaystyle2})$
12.: $displaystyle intdisplaystyle rac{dx}{x(x^{displaystyle2}+a^{displaystyle... ...aystyle rac{x^{displaystyle2}}{x^{displaystyle2}+a^{displaystyle2}} ight)$
13.: $displaystyle intdisplaystyle rac{dx}{x^{displaystyle2}(x^{displaystyle2}... ...le rac{3}{2a^{displaystyle5}} an^{displaystyle-1}displaystyle rac{x}{a}$
14.: $displaystyle intdisplaystyle rac{dx}{x^{displaystyle3}(x^{displaystyle2}... ...aystyle rac{x^{displaystyle2}}{x^{displaystyle2}+a^{displaystyle2}} ight)$
15.: $displaystyle intdisplaystyle rac{dx}{(x^{displaystyle2}+a^{displaystyle2... ...laystyle rac{dx}{(x^{displaystyle2}+a^{displaystyle2})^{displaystyle n-1}}$
16.: $displaystyle intdisplaystyle rac{x,dx}{(x^{displaystyle2}+a^{displaysty... ...le rac{-1}{2(n-1)(x^{displaystyle2}+a^{displaystyle2})^{displaystyle n-1}}$
17.: $displaystyle intdisplaystyle rac{dx}{x(x^{displaystyle2}+a^{displaystyle... ...aystyle rac{dx}{x(x^{displaystyle2}+a^{displaystyle2})^{displaystyle n-1}}$
18.: $displaystyle intdisplaystyle rac{x^{displaystyle m},dx}{(x^{displaystyl... ...splaystyle m-2},dx}{(x^{displaystyle2}+a^{displaystyle2})^{displaystyle n}}$
19.: $displaystyle intdisplaystyle rac{dx}{x^{displaystyle m}(x^{displaystyle2... ...x^{displaystyle m-2}(x^{displaystyle2}+a^{displaystyle2})^{displaystyle n}}$

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INTEGRALS CONTAINING x2+a2

INTEGRALS CONTAINING x²+a²