Optimal. Leaf size=43 \[ \frac {x \sqrt [5]{\left (3-13 x+4 x^2\right )^5} \left (18-39 x+8 x^2\right )}{6 \left (3-13 x+4 x^2\right )} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(102\) vs. \(2(43)=86\).
time = 0.04, antiderivative size = 102, normalized size of antiderivative = 2.37, number of steps
used = 3, number of rules used = 2, integrand size = 54, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.037, Rules used = {6820, 6852}
\begin {gather*} -\frac {13 \sqrt [5]{\left (4 x^2-13 x+3\right )^5} x^2}{2 \left (4 x^2-13 x+3\right )}+\frac {3 \sqrt [5]{\left (4 x^2-13 x+3\right )^5} x}{4 x^2-13 x+3}+\frac {4 \sqrt [5]{\left (4 x^2-13 x+3\right )^5} x^3}{3 \left (4 x^2-13 x+3\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 6820
Rule 6852
Rubi steps
\begin {align*} \int \sqrt [5]{243-5265 x+47250 x^2-225810 x^3+615255 x^4-954733 x^5+820340 x^6-401440 x^7+112000 x^8-16640 x^9+1024 x^{10}} \, dx &=\int \sqrt [5]{\left (3-13 x+4 x^2\right )^5} \, dx\\ &=\frac {\sqrt [5]{\left (3-13 x+4 x^2\right )^5} \int \left (3-13 x+4 x^2\right ) \, dx}{3-13 x+4 x^2}\\ &=\frac {3 x \sqrt [5]{\left (3-13 x+4 x^2\right )^5}}{3-13 x+4 x^2}-\frac {13 x^2 \sqrt [5]{\left (3-13 x+4 x^2\right )^5}}{2 \left (3-13 x+4 x^2\right )}+\frac {4 x^3 \sqrt [5]{\left (3-13 x+4 x^2\right )^5}}{3 \left (3-13 x+4 x^2\right )}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 43, normalized size = 1.00 \begin {gather*} \frac {x \sqrt [5]{\left (3-13 x+4 x^2\right )^5} \left (18-39 x+8 x^2\right )}{6 \left (3-13 x+4 x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(77\) vs.
\(2(38)=76\).
time = 0.22, size = 78, normalized size = 1.81
method | result | size |
gosper | \(\frac {x \left (8 x^{2}-39 x +18\right ) \left (1024 x^{10}-16640 x^{9}+112000 x^{8}-401440 x^{7}+820340 x^{6}-954733 x^{5}+615255 x^{4}-225810 x^{3}+47250 x^{2}-5265 x +243\right )^{\frac {1}{5}}}{6 \left (-1+4 x \right ) \left (-3+x \right )}\) | \(78\) |
risch | \(\frac {4 \left (\left (4 x^{2}-13 x +3\right )^{5}\right )^{\frac {1}{5}} x^{3}}{3 \left (4 x^{2}-13 x +3\right )}-\frac {13 \left (\left (4 x^{2}-13 x +3\right )^{5}\right )^{\frac {1}{5}} x^{2}}{2 \left (4 x^{2}-13 x +3\right )}+\frac {3 \left (\left (4 x^{2}-13 x +3\right )^{5}\right )^{\frac {1}{5}} x}{4 x^{2}-13 x +3}\) | \(93\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 14, normalized size = 0.33 \begin {gather*} \frac {4}{3} \, x^{3} - \frac {13}{2} \, x^{2} + 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 14, normalized size = 0.33 \begin {gather*} \frac {4}{3} \, x^{3} - \frac {13}{2} \, x^{2} + 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \sqrt [5]{1024 x^{10} - 16640 x^{9} + 112000 x^{8} - 401440 x^{7} + 820340 x^{6} - 954733 x^{5} + 615255 x^{4} - 225810 x^{3} + 47250 x^{2} - 5265 x + 243}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int {\left (1024\,x^{10}-16640\,x^9+112000\,x^8-401440\,x^7+820340\,x^6-954733\,x^5+615255\,x^4-225810\,x^3+47250\,x^2-5265\,x+243\right )}^{1/5} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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