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 = 0.02, antiderivative size = 27, normalized size of antiderivative = 1.00, 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 43
Rule 266
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*}
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Mathematica [A] time = 0.01, 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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IntegrateAlgebraic [A] time = 0.01, size = 20, normalized size = 0.74 \[ \frac {15 x^2-1}{750 \left (5 x^2-2\right )^6} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.24, size = 43, normalized size = 1.59 \[ \frac {15 \, x^{2} - 1}{750 \, {\left (15625 \, x^{12} - 37500 \, x^{10} + 37500 \, x^{8} - 20000 \, x^{6} + 6000 \, x^{4} - 960 \, x^{2} + 64\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.10, size = 18, normalized size = 0.67 \[ \frac {15 \, x^{2} - 1}{750 \, {\left (5 \, x^{2} - 2\right )}^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.29, size = 19, normalized size = 0.70
method | result | size |
gosper | \(\frac {15 x^{2}-1}{750 \left (5 x^{2}-2\right )^{6}}\) | \(19\) |
risch | \(\frac {\frac {x^{2}}{50}-\frac {1}{750}}{\left (5 x^{2}-2\right )^{6}}\) | \(19\) |
default | \(\frac {1}{150 \left (5 x^{2}-2\right )^{6}}+\frac {1}{250 \left (5 x^{2}-2\right )^{5}}\) | \(24\) |
norman | \(\frac {-\frac {25}{32} x^{10}-\frac {5}{12} x^{6}+\frac {1}{8} x^{4}+\frac {25}{32} x^{8}+\frac {125}{384} x^{12}}{\left (5 x^{2}-2\right )^{6}}\) | \(37\) |
meijerg | \(\frac {x^{4} \left (\frac {625}{16} x^{8}-\frac {375}{4} x^{6}+\frac {375}{4} x^{4}-50 x^{2}+15\right )}{7680 \left (1-\frac {5 x^{2}}{2}\right )^{6}}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.64, size = 43, normalized size = 1.59 \[ \frac {15 \, x^{2} - 1}{750 \, {\left (15625 \, x^{12} - 37500 \, x^{10} + 37500 \, x^{8} - 20000 \, x^{6} + 6000 \, x^{4} - 960 \, x^{2} + 64\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 18, normalized size = 0.67 \[ \frac {15\,x^2-1}{750\,{\left (5\,x^2-2\right )}^6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 39, normalized size = 1.44 \[ - \frac {1 - 15 x^{2}}{11718750 x^{12} - 28125000 x^{10} + 28125000 x^{8} - 15000000 x^{6} + 4500000 x^{4} - 720000 x^{2} + 48000} \]
Verification of antiderivative is not currently implemented for this CAS.
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