Optimal. Leaf size=29 \[ \frac {12}{7} \left (\sqrt [4]{x}+1\right )^{7/3}-3 \left (\sqrt [4]{x}+1\right )^{4/3} \]
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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 = {266, 43} \[ \frac {12}{7} \left (\sqrt [4]{x}+1\right )^{7/3}-3 \left (\sqrt [4]{x}+1\right )^{4/3} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\sqrt [3]{1+\sqrt [4]{x}}}{\sqrt {x}} \, dx &=4 \operatorname {Subst}\left (\int x \sqrt [3]{1+x} \, dx,x,\sqrt [4]{x}\right )\\ &=4 \operatorname {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 = 0.01, size = 24, normalized size = 0.83 \[ \frac {3}{7} \left (\sqrt [4]{x}+1\right )^{4/3} \left (4 \sqrt [4]{x}-3\right ) \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.03, size = 56, normalized size = 1.93 \[ \frac {12}{7} \sqrt [3]{\sqrt [4]{x}+1} \sqrt {x}+\frac {3}{7} \sqrt [3]{\sqrt [4]{x}+1} \sqrt [4]{x}-\frac {9}{7} \sqrt [3]{\sqrt [4]{x}+1} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.12, size = 19, normalized size = 0.66 \[ \frac {3}{7} \, {\left (4 \, \sqrt {x} + x^{\frac {1}{4}} - 3\right )} {\left (x^{\frac {1}{4}} + 1\right )}^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.92, size = 19, normalized size = 0.66 \[ \frac {12}{7} \, {\left (x^{\frac {1}{4}} + 1\right )}^{\frac {7}{3}} - 3 \, {\left (x^{\frac {1}{4}} + 1\right )}^{\frac {4}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.30, size = 17, normalized size = 0.59
method | result | size |
meijerg | \(2 \sqrt {x}\, \hypergeom \left (\left [-\frac {1}{3}, 2\right ], \relax [3], -x^{\frac {1}{4}}\right )\) | \(17\) |
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 = 0.49, size = 19, normalized size = 0.66 \[ \frac {12}{7} \, {\left (x^{\frac {1}{4}} + 1\right )}^{\frac {7}{3}} - 3 \, {\left (x^{\frac {1}{4}} + 1\right )}^{\frac {4}{3}} \]
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 \[ \frac {3\,{\left (x^{1/4}+1\right )}^{4/3}\,\left (4\,x^{1/4}-3\right )}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.35, size = 134, normalized size = 4.62 \[ \frac {12 x^{\frac {7}{4}} \sqrt [3]{\sqrt [4]{x} + 1}}{7 x^{\frac {5}{4}} + 7 x} - \frac {6 x^{\frac {5}{4}} \sqrt [3]{\sqrt [4]{x} + 1}}{7 x^{\frac {5}{4}} + 7 x} + \frac {9 x^{\frac {5}{4}}}{7 x^{\frac {5}{4}} + 7 x} + \frac {15 x^{\frac {3}{2}} \sqrt [3]{\sqrt [4]{x} + 1}}{7 x^{\frac {5}{4}} + 7 x} - \frac {9 x \sqrt [3]{\sqrt [4]{x} + 1}}{7 x^{\frac {5}{4}} + 7 x} + \frac {9 x}{7 x^{\frac {5}{4}} + 7 x} \]
Verification of antiderivative is not currently implemented for this CAS.
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