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 = 0.0089935, antiderivative size = 29, normalized size of antiderivative = 1., 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 266
Rule 43
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*}
Mathematica [A] time = 0.0082711, 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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Maple [A] time = 0.002, size = 20, normalized size = 0.7 \begin{align*} -3\, \left ( 1+\sqrt [4]{x} \right ) ^{4/3}+{\frac{12}{7} \left ( 1+\sqrt [4]{x} \right ) ^{{\frac{7}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.935212, size = 26, normalized size = 0.9 \begin{align*} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.78556, size = 69, normalized size = 2.38 \begin{align*} \frac{3}{7} \,{\left (4 \, \sqrt{x} + x^{\frac{1}{4}} - 3\right )}{\left (x^{\frac{1}{4}} + 1\right )}^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.32971, size = 134, normalized size = 4.62 \begin{align*} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.049, size = 26, normalized size = 0.9 \begin{align*} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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