Optimal. Leaf size=29 \[ -3 \left (1+\sqrt [4]{x}\right )^{4/3}+\frac {12}{7} \left (1+\sqrt [4]{x}\right )^{7/3} \]
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Rubi [A]
time = 0.01, antiderivative size = 29, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {272, 45}
\begin {gather*} \frac {12}{7} \left (\sqrt [4]{x}+1\right )^{7/3}-3 \left (\sqrt [4]{x}+1\right )^{4/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 272
Rubi steps
\begin {align*} \int \frac {\sqrt [3]{1+\sqrt [4]{x}}}{\sqrt {x}} \, dx &=4 \text {Subst}\left (\int x \sqrt [3]{1+x} \, dx,x,\sqrt [4]{x}\right )\\ &=4 \text {Subst}\left (\int \left (-\sqrt [3]{1+x}+(1+x)^{4/3}\right ) \, dx,x,\sqrt [4]{x}\right )\\ &=-3 \left (1+\sqrt [4]{x}\right )^{4/3}+\frac {12}{7} \left (1+\sqrt [4]{x}\right )^{7/3}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 24, normalized size = 0.83 \begin {gather*} \frac {3}{7} \left (1+\sqrt [4]{x}\right )^{4/3} \left (-3+4 \sqrt [4]{x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 20, normalized size = 0.69
method | result | size |
meijerg | \(2 \sqrt {x}\, \hypergeom \left (\left [-\frac {1}{3}, 2\right ], \left [3\right ], -x^{\frac {1}{4}}\right )\) | \(17\) |
derivativedivides | \(-3 \left (1+x^{\frac {1}{4}}\right )^{\frac {4}{3}}+\frac {12 \left (1+x^{\frac {1}{4}}\right )^{\frac {7}{3}}}{7}\) | \(20\) |
default | \(-3 \left (1+x^{\frac {1}{4}}\right )^{\frac {4}{3}}+\frac {12 \left (1+x^{\frac {1}{4}}\right )^{\frac {7}{3}}}{7}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.45, size = 19, normalized size = 0.66 \begin {gather*} \frac {12}{7} \, {\left (x^{\frac {1}{4}} + 1\right )}^{\frac {7}{3}} - 3 \, {\left (x^{\frac {1}{4}} + 1\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 19, normalized size = 0.66 \begin {gather*} \frac {3}{7} \, {\left (4 \, \sqrt {x} + x^{\frac {1}{4}} - 3\right )} {\left (x^{\frac {1}{4}} + 1\right )}^{\frac {1}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 134 vs.
\(2 (24) = 48\).
time = 0.65, size = 134, normalized size = 4.62 \begin {gather*} \frac {12 x^{\frac {7}{4}} \sqrt [3]{\sqrt [4]{x} + 1}}{7 x^{\frac {5}{4}} + 7 x} - \frac {6 x^{\frac {5}{4}} \sqrt [3]{\sqrt [4]{x} + 1}}{7 x^{\frac {5}{4}} + 7 x} + \frac {9 x^{\frac {5}{4}}}{7 x^{\frac {5}{4}} + 7 x} + \frac {15 x^{\frac {3}{2}} \sqrt [3]{\sqrt [4]{x} + 1}}{7 x^{\frac {5}{4}} + 7 x} - \frac {9 x \sqrt [3]{\sqrt [4]{x} + 1}}{7 x^{\frac {5}{4}} + 7 x} + \frac {9 x}{7 x^{\frac {5}{4}} + 7 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.46, size = 19, normalized size = 0.66 \begin {gather*} \frac {12}{7} \, {\left (x^{\frac {1}{4}} + 1\right )}^{\frac {7}{3}} - 3 \, {\left (x^{\frac {1}{4}} + 1\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.54, size = 16, normalized size = 0.55 \begin {gather*} \frac {3\,{\left (x^{1/4}+1\right )}^{4/3}\,\left (4\,x^{1/4}-3\right )}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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