Optimal. Leaf size=46 \[ -\frac{x^2}{250}-\frac{6}{625 \left (2-5 x^2\right )}+\frac{2}{625 \left (2-5 x^2\right )^2}-\frac{3}{625} \log \left (2-5 x^2\right ) \]
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Rubi [A] time = 0.0299033, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ -\frac{x^2}{250}-\frac{6}{625 \left (2-5 x^2\right )}+\frac{2}{625 \left (2-5 x^2\right )^2}-\frac{3}{625} \log \left (2-5 x^2\right ) \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{x^7}{\left (2-5 x^2\right )^3} \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int \frac{x^3}{(2-5 x)^3} \, dx,x,x^2\right )\\ &=\frac{1}{2} \operatorname{Subst}\left (\int \left (-\frac{1}{125}-\frac{8}{125 (-2+5 x)^3}-\frac{12}{125 (-2+5 x)^2}-\frac{6}{125 (-2+5 x)}\right ) \, dx,x,x^2\right )\\ &=-\frac{x^2}{250}+\frac{2}{625 \left (2-5 x^2\right )^2}-\frac{6}{625 \left (2-5 x^2\right )}-\frac{3}{625} \log \left (2-5 x^2\right )\\ \end{align*}
Mathematica [A] time = 0.0134481, size = 44, normalized size = 0.96 \[ -\frac{125 x^6-150 x^4+6 \left (2-5 x^2\right )^2 \log \left (5 x^2-2\right )+12}{1250 \left (2-5 x^2\right )^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 39, normalized size = 0.9 \begin{align*} -{\frac{{x}^{2}}{250}}+{\frac{2}{625\, \left ( 5\,{x}^{2}-2 \right ) ^{2}}}-{\frac{3\,\ln \left ( 5\,{x}^{2}-2 \right ) }{625}}+{\frac{6}{3125\,{x}^{2}-1250}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.92504, size = 53, normalized size = 1.15 \begin{align*} -\frac{1}{250} \, x^{2} + \frac{2 \,{\left (3 \, x^{2} - 1\right )}}{125 \,{\left (25 \, x^{4} - 20 \, x^{2} + 4\right )}} - \frac{3}{625} \, \log \left (5 \, x^{2} - 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.70484, size = 143, normalized size = 3.11 \begin{align*} -\frac{125 \, x^{6} - 100 \, x^{4} - 40 \, x^{2} + 6 \,{\left (25 \, x^{4} - 20 \, x^{2} + 4\right )} \log \left (5 \, x^{2} - 2\right ) + 20}{1250 \,{\left (25 \, x^{4} - 20 \, x^{2} + 4\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.121358, size = 34, normalized size = 0.74 \begin{align*} - \frac{x^{2}}{250} + \frac{6 x^{2} - 2}{3125 x^{4} - 2500 x^{2} + 500} - \frac{3 \log{\left (5 x^{2} - 2 \right )}}{625} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07179, size = 54, normalized size = 1.17 \begin{align*} -\frac{1}{250} \, x^{2} + \frac{225 \, x^{4} - 120 \, x^{2} + 16}{1250 \,{\left (5 \, x^{2} - 2\right )}^{2}} - \frac{3}{625} \, \log \left ({\left | 5 \, x^{2} - 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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