Optimal. Leaf size=26 \[ \frac {3 x^{2/3}}{2}+\frac {10}{11} \sqrt {x} \sqrt [5]{x^3} \]
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Rubi [A]
time = 0.00, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {14, 15, 30}
\begin {gather*} \frac {3 x^{2/3}}{2}+\frac {10}{11} \sqrt [5]{x^3} \sqrt {x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {\sqrt [6]{x}+\sqrt [5]{x^3}}{\sqrt {x}} \, dx &=\int \left (\frac {1}{\sqrt [3]{x}}+\frac {\sqrt [5]{x^3}}{\sqrt {x}}\right ) \, dx\\ &=\frac {3 x^{2/3}}{2}+\int \frac {\sqrt [5]{x^3}}{\sqrt {x}} \, dx\\ &=\frac {3 x^{2/3}}{2}+\frac {\sqrt [5]{x^3} \int \sqrt [10]{x} \, dx}{x^{3/5}}\\ &=\frac {3 x^{2/3}}{2}+\frac {10}{11} \sqrt {x} \sqrt [5]{x^3}\\ \end {align*}
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Mathematica [A]
time = 7.08, size = 26, normalized size = 1.00 \begin {gather*} \frac {3 x^{2/3}}{2}+\frac {10}{11} \sqrt {x} \sqrt [5]{x^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 17, normalized size = 0.65
method | result | size |
default | \(\frac {3 x^{\frac {2}{3}}}{2}+\frac {10 \left (x^{3}\right )^{\frac {1}{5}} \sqrt {x}}{11}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 16, normalized size = 0.62 \begin {gather*} \frac {10}{11} \, {\left (x^{3}\right )}^{\frac {1}{5}} \sqrt {x} + \frac {3}{2} \, x^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 16, normalized size = 0.62 \begin {gather*} \frac {10}{11} \, {\left (x^{3}\right )}^{\frac {1}{5}} \sqrt {x} + \frac {3}{2} \, x^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: SystemError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 5.06, size = 11, normalized size = 0.42 \begin {gather*} \frac {10}{11} \, x^{\frac {11}{10}} + \frac {3}{2} \, x^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.54, size = 16, normalized size = 0.62 \begin {gather*} \frac {10\,\sqrt {x}\,{\left (x^3\right )}^{1/5}}{11}+\frac {3\,x^{2/3}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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