Optimal. Leaf size=12 \[ -2+x+x^{\left .\frac {5}{3}\right /x} \]
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Rubi [F] time = 0.09, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {3 x^2+x^{\left .\frac {5}{3}\right /x} (5-5 \log (x))}{3 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \frac {3 x^2+x^{\left .\frac {5}{3}\right /x} (5-5 \log (x))}{x^2} \, dx\\ &=\frac {1}{3} \int \left (3-5 x^{-2+\frac {5}{3 x}} (-1+\log (x))\right ) \, dx\\ &=x-\frac {5}{3} \int x^{-2+\frac {5}{3 x}} (-1+\log (x)) \, dx\\ &=x-\frac {5}{3} \int \left (-x^{-2+\frac {5}{3 x}}+x^{-2+\frac {5}{3 x}} \log (x)\right ) \, dx\\ &=x+\frac {5}{3} \int x^{-2+\frac {5}{3 x}} \, dx-\frac {5}{3} \int x^{-2+\frac {5}{3 x}} \log (x) \, dx\\ &=x+\frac {5}{3} \int x^{-2+\frac {5}{3 x}} \, dx+\frac {5}{3} \int \frac {\int x^{-2+\frac {5}{3 x}} \, dx}{x} \, dx-\frac {1}{3} (5 \log (x)) \int x^{-2+\frac {5}{3 x}} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 11, normalized size = 0.92 \begin {gather*} x+x^{\left .\frac {5}{3}\right /x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 9, normalized size = 0.75 \begin {gather*} x + x^{\frac {5}{3 \, x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 9, normalized size = 0.75 \begin {gather*} x + x^{\frac {5}{3 \, x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 10, normalized size = 0.83
method | result | size |
risch | \(x +x^{\frac {5}{3 x}}\) | \(10\) |
default | \(x +{\mathrm e}^{\frac {5 \ln \relax (x )}{3 x}}\) | \(11\) |
norman | \(\frac {x^{2}+x \,{\mathrm e}^{\frac {5 \ln \relax (x )}{3 x}}}{x}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 9, normalized size = 0.75 \begin {gather*} x + x^{\frac {5}{3 \, x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.48, size = 9, normalized size = 0.75 \begin {gather*} x+x^{\frac {5}{3\,x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.30, size = 10, normalized size = 0.83 \begin {gather*} x + e^{\frac {5 \log {\relax (x )}}{3 x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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