Optimal. Leaf size=50 \[ \frac {x^5}{175 \left (\sqrt {10}-x^2\right )^{5/2}}+\frac {x^5}{7 \sqrt {10} \left (\sqrt {10}-x^2\right )^{7/2}} \]
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Rubi [A] time = 0.02, antiderivative size = 50, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {271, 264} \[ \frac {x^5}{5 \sqrt {10} \left (\sqrt {10}-x^2\right )^{7/2}}-\frac {x^7}{175 \left (\sqrt {10}-x^2\right )^{7/2}} \]
Antiderivative was successfully verified.
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Rule 264
Rule 271
Rubi steps
\begin {align*} \int \frac {x^4}{\left (\sqrt {10}-x^2\right )^{9/2}} \, dx &=\frac {x^5}{5 \sqrt {10} \left (\sqrt {10}-x^2\right )^{7/2}}-\frac {1}{5} \sqrt {\frac {2}{5}} \int \frac {x^6}{\left (\sqrt {10}-x^2\right )^{9/2}} \, dx\\ &=\frac {x^5}{5 \sqrt {10} \left (\sqrt {10}-x^2\right )^{7/2}}-\frac {x^7}{175 \left (\sqrt {10}-x^2\right )^{7/2}}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 35, normalized size = 0.70 \[ \frac {7 \sqrt {10} x^5-2 x^7}{350 \left (\sqrt {10}-x^2\right )^{7/2}} \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.29, size = 35, normalized size = 0.70 \[ -\frac {x^5 \left (2 x^2-7 \sqrt {10}\right )}{350 \left (\sqrt {10}-x^2\right )^{7/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.24, size = 69, normalized size = 1.38 \[ -\frac {{\left (2 \, x^{15} - 160 \, x^{11} - 2600 \, x^{7} + \sqrt {10} {\left (x^{13} - 340 \, x^{9} - 700 \, x^{5}\right )}\right )} \sqrt {-x^{2} + \sqrt {10}}}{350 \, {\left (x^{16} - 40 \, x^{12} + 600 \, x^{8} - 4000 \, x^{4} + 10000\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.80, size = 98, normalized size = 1.96 \[ -\frac {16 \, {\left (7 \, {\left (\frac {x}{\sqrt {-x^{2} + \sqrt {10}} - 10^{\frac {1}{4}}} - \frac {\sqrt {-x^{2} + \sqrt {10}} - 10^{\frac {1}{4}}}{x}\right )}^{2} + 20\right )}}{175 \, {\left (\frac {x}{\sqrt {-x^{2} + \sqrt {10}} - 10^{\frac {1}{4}}} - \frac {\sqrt {-x^{2} + \sqrt {10}} - 10^{\frac {1}{4}}}{x}\right )}^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.35, size = 28, normalized size = 0.56
method | result | size |
gosper | \(\frac {x^{5} \left (-2 x^{2}+7 \sqrt {10}\right )}{350 \left (-x^{2}+\sqrt {10}\right )^{\frac {7}{2}}}\) | \(28\) |
meijerg | \(\frac {10^{\frac {3}{4}} x^{5} \left (-\frac {\sqrt {2}\, \sqrt {5}\, x^{2}}{5}+7\right )}{35000 \left (1-\frac {\sqrt {10}\, x^{2}}{10}\right )^{\frac {7}{2}}}\) | \(34\) |
risch | \(\frac {2 x^{7}-7 \sqrt {10}\, x^{5}}{350 \left (x^{2}-\sqrt {10}\right )^{3} \sqrt {-x^{2}+\sqrt {10}}}\) | \(39\) |
trager | \(-\frac {2 \sqrt {10}\, \left (\sqrt {10}\, x^{2}-35\right ) x^{5} \sqrt {-x^{2}+\sqrt {10}}}{35 \left (\sqrt {10}\, x^{2}-10\right )^{4}}\) | \(40\) |
default | \(\frac {x^{3}}{4 \left (-x^{2}+\sqrt {10}\right )^{\frac {7}{2}}}-\frac {3 \sqrt {10}\, \left (\frac {x}{6 \left (-x^{2}+\sqrt {10}\right )^{\frac {7}{2}}}-\frac {\sqrt {10}\, \left (\frac {x \sqrt {10}}{70 \left (-x^{2}+\sqrt {10}\right )^{\frac {7}{2}}}+\frac {3 \sqrt {10}\, \left (\frac {x \sqrt {10}}{50 \left (-x^{2}+\sqrt {10}\right )^{\frac {5}{2}}}+\frac {2 \sqrt {10}\, \left (\frac {x \sqrt {10}}{30 \left (-x^{2}+\sqrt {10}\right )^{\frac {3}{2}}}+\frac {x}{15 \sqrt {-x^{2}+\sqrt {10}}}\right )}{25}\right )}{35}\right )}{6}\right )}{4}\) | \(121\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.98, size = 79, normalized size = 1.58 \[ \frac {x}{175 \, \sqrt {-x^{2} + \sqrt {10}}} + \frac {\sqrt {10} x}{350 \, {\left (-x^{2} + \sqrt {10}\right )}^{\frac {3}{2}}} + \frac {x^{3}}{4 \, {\left (-x^{2} + \sqrt {10}\right )}^{\frac {7}{2}}} + \frac {3 \, x}{140 \, {\left (-x^{2} + \sqrt {10}\right )}^{\frac {5}{2}}} - \frac {3 \, \sqrt {10} x}{28 \, {\left (-x^{2} + \sqrt {10}\right )}^{\frac {7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.02 \[ \int \frac {x^4}{{\left (\sqrt {10}-x^2\right )}^{9/2}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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