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$x^2+a^2$ içeren integraller- 1.
- $\int \frac{dx}{x^{2}+a^{2}}=\frac{1}{a}\tan^{-1} \frac{x}{a}$
- 2.
- $\int \frac{x\,dx}{x^{2}+a^{2}}=\frac{1}{2}\ln(x^{2}+a^{2})$
- 3.
- $\int \frac{x^{2}\,dx}{x^{2}+a^{2}}=x-a\tan^{-1} \frac{x}{a}$
- 4.
- $\int \frac{x^{3}\,dx}{x^{2}+a^{2}}= \frac{x^{2}}{2}- \frac{a^{2}}{2}\ln(x^{2}+a^{2})$
- 5.
- $\int \frac{dx}{x(x^{2}+a^{2})}= \frac{1}{2a^{2}}\ln\left( \frac{x^{2}}{x^{2}+a^{2}}\right)$
- 6.
- $\int \frac{dx}{x^{2}(x^{2}+a^{2})}=- \frac{1}{a^{2}x}- \frac{1}{a^{3}}\tan^{-1} \frac{x}{a}$
- 7.
- $\int \frac{dx}{x^{3}(x^{2}+a^{2})}=- \frac{1}{2a^{2}x^{2}}- \frac{1}{2a^{4}}\ln\left( \frac{x^{2}}{x^{2}+a^{2}}\right)$
- 8.
- $\int \frac{dx}{(x^{2}+a^{2})^{2}}=\frac{x}{2a^{2}(x^{2}+a^{2})}+ \frac{1}{2a^{3}}\tan^{-1} \frac{x}{a}$
- 9.
- $\int \frac{x\,dx}{(x^{2}+a^{2})^{2}}= \frac{-1}{2(x^{2}+a^{2})}$
- 10.
- $\int \frac{x^{2}\,dx}{(x^{2}+a^{2})^{2}}= \frac{-x}{2(x^{2}+a^{2})}+\frac{1}{2a}\tan^{-1} \frac{x}{a}$
- 11.
- $\int \frac{x^{3}\,dx}{(x^{2}+a^{2})^{2}}= \frac{a^{2}}{2(x^{2}+a^{2})}+ \frac{1}{2}\ln(x^{2}+a^{2})$
- 12.
- $\int\frac{dx}{x(x^{2}+a^{2})^{2}}=\frac{1}{2a^{2}(x^{2}+a^{2})}+\frac{1}{2a^{4}}\ln\left( \frac{x^{2}}{x^{2}+a^{2}}\right)$
- 13.
- $\int \frac{dx}{x^{2}(x^{2}+a^{2})^{2}}=- \frac{1}{a^{4}x}-\frac{x}{2a^{4}(x^{2}+a^{2})}-\frac{3}{2a^{5}}\tan^{-1}\frac{x}{a}$
- 14.
- $\int\frac{dx}{x^{3}(x^{2}+a^{2})^{2}}=-\frac{1}{2a^{4}x^{2}}-\frac{1}{2a^{4}(x^{2}+a^{2})}- \frac{1}{a^{6}}\ln\left( \frac{x^{2}}{x^{2}+a^{2}}\right)$
- 15.
- $\int\frac{dx}{(x^{2}+a^{2})^{ n}}= \frac{x}{2(n-1)a^{2}(x^{2}+a^{2})^{n-1}}+\frac{2n-3}{(2n-2)a^{2}} \int \frac{dx}{(x^{2}+a^{2})^{n-1}}$
- 16.
- $\int\frac{x\,dx}{(x^{2}+a^{2})^{n}}=\frac{-1}{2(n-1)(x^{2}+a^{2})^{n-1}}$
- 17.
- $\int\frac{dx}{x(x^{2}+a^{2})^{n}}=\frac{1}{2(n-1)a^{2}(x^{2}+a^{2})^{n-1}}+\frac{1}{a^{2}}\int\frac{dx}{x(x^{2}+a^{2})^{n-1}}$
- 18.
- $\int\frac{x^{m}\,dx}{(x^{2}+a^{2})^{n}}=\int\frac{x^{m-2}\,dx}{(x^{2}+a^{2})^{n-1}}-a^{2} \int\frac{x^{m-2}\,dx}{(x^{2}+a^{2})^{n}}$
- 19.
- $\int\frac{dx}{x^{m}(x^{2}+a^{2})^{n}}=\frac{1}{a^{2}}\int\frac{dx}{x^{m}(x^{2}+a^{2})^{n-1}}- \frac{1}{a^{2}}\int\frac{dx}{x^{m-2}(x^{2}+a^{2})^{n}}$
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