Optimal. Leaf size=46 \[ \frac{x^2}{2}+\frac{75}{2 \left (5-x^2\right )}-\frac{125}{4 \left (5-x^2\right )^2}+\frac{15}{2} \log \left (5-x^2\right ) \]
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Rubi [A] time = 0.0237345, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {266, 43} \[ \frac{x^2}{2}+\frac{75}{2 \left (5-x^2\right )}-\frac{125}{4 \left (5-x^2\right )^2}+\frac{15}{2} \log \left (5-x^2\right ) \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{x^7}{\left (-5+x^2\right )^3} \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int \frac{x^3}{(-5+x)^3} \, dx,x,x^2\right )\\ &=\frac{1}{2} \operatorname{Subst}\left (\int \left (1+\frac{125}{(-5+x)^3}+\frac{75}{(-5+x)^2}+\frac{15}{-5+x}\right ) \, dx,x,x^2\right )\\ &=\frac{x^2}{2}-\frac{125}{4 \left (5-x^2\right )^2}+\frac{75}{2 \left (5-x^2\right )}+\frac{15}{2} \log \left (5-x^2\right )\\ \end{align*}
Mathematica [A] time = 0.0127481, size = 36, normalized size = 0.78 \[ \frac{1}{4} \left (2 x^2-\frac{150}{x^2-5}-\frac{125}{\left (x^2-5\right )^2}+30 \log \left (x^2-5\right )\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 33, normalized size = 0.7 \begin{align*}{\frac{{x}^{2}}{2}}-{\frac{75}{2\,{x}^{2}-10}}+{\frac{15\,\ln \left ({x}^{2}-5 \right ) }{2}}-{\frac{125}{4\, \left ({x}^{2}-5 \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.947302, size = 47, normalized size = 1.02 \begin{align*} \frac{1}{2} \, x^{2} - \frac{25 \,{\left (6 \, x^{2} - 25\right )}}{4 \,{\left (x^{4} - 10 \, x^{2} + 25\right )}} + \frac{15}{2} \, \log \left (x^{2} - 5\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.86473, size = 130, normalized size = 2.83 \begin{align*} \frac{2 \, x^{6} - 20 \, x^{4} - 100 \, x^{2} + 30 \,{\left (x^{4} - 10 \, x^{2} + 25\right )} \log \left (x^{2} - 5\right ) + 625}{4 \,{\left (x^{4} - 10 \, x^{2} + 25\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.111764, size = 32, normalized size = 0.7 \begin{align*} \frac{x^{2}}{2} - \frac{150 x^{2} - 625}{4 x^{4} - 40 x^{2} + 100} + \frac{15 \log{\left (x^{2} - 5 \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05348, size = 49, normalized size = 1.07 \begin{align*} \frac{1}{2} \, x^{2} - \frac{5 \,{\left (9 \, x^{4} - 60 \, x^{2} + 100\right )}}{4 \,{\left (x^{2} - 5\right )}^{2}} + \frac{15}{2} \, \log \left ({\left | x^{2} - 5 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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