Optimal. Leaf size=27 \[ \frac{1}{150 \left (2-5 x^2\right )^6}-\frac{1}{250 \left (2-5 x^2\right )^5} \]
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Rubi [A] time = 0.0191322, antiderivative size = 27, 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} \[ \frac{1}{150 \left (2-5 x^2\right )^6}-\frac{1}{250 \left (2-5 x^2\right )^5} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{x^3}{\left (2-5 x^2\right )^7} \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int \frac{x}{(2-5 x)^7} \, dx,x,x^2\right )\\ &=\frac{1}{2} \operatorname{Subst}\left (\int \left (-\frac{2}{5 (-2+5 x)^7}-\frac{1}{5 (-2+5 x)^6}\right ) \, dx,x,x^2\right )\\ &=\frac{1}{150 \left (2-5 x^2\right )^6}-\frac{1}{250 \left (2-5 x^2\right )^5}\\ \end{align*}
Mathematica [A] time = 0.0074893, size = 20, normalized size = 0.74 \[ \frac{15 x^2-1}{750 \left (2-5 x^2\right )^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 24, normalized size = 0.9 \begin{align*}{\frac{1}{150\, \left ( 5\,{x}^{2}-2 \right ) ^{6}}}+{\frac{1}{250\, \left ( 5\,{x}^{2}-2 \right ) ^{5}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.934018, size = 58, normalized size = 2.15 \begin{align*} \frac{15 \, x^{2} - 1}{750 \,{\left (15625 \, x^{12} - 37500 \, x^{10} + 37500 \, x^{8} - 20000 \, x^{6} + 6000 \, x^{4} - 960 \, x^{2} + 64\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.74723, size = 130, normalized size = 4.81 \begin{align*} \frac{15 \, x^{2} - 1}{750 \,{\left (15625 \, x^{12} - 37500 \, x^{10} + 37500 \, x^{8} - 20000 \, x^{6} + 6000 \, x^{4} - 960 \, x^{2} + 64\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.18098, size = 37, normalized size = 1.37 \begin{align*} \frac{15 x^{2} - 1}{11718750 x^{12} - 28125000 x^{10} + 28125000 x^{8} - 15000000 x^{6} + 4500000 x^{4} - 720000 x^{2} + 48000} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05182, size = 24, normalized size = 0.89 \begin{align*} \frac{15 \, x^{2} - 1}{750 \,{\left (5 \, x^{2} - 2\right )}^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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