Optimal. Leaf size=37 \[ -x+3 \left (x^2\right )^{\left .\frac {1}{5}\right /x} \left (\frac {1}{2} \left (16+2 \log \left (\frac {14}{5}\right )\right )\right )^{\left .\frac {1}{5}\right /x} \]
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Rubi [F] time = 0.29, 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 {-5 x^2+\left (8 x^2+x^2 \log \left (\frac {14}{5}\right )\right )^{\left .\frac {1}{5}\right /x} \left (6-3 \log \left (8 x^2+x^2 \log \left (\frac {14}{5}\right )\right )\right )}{5 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}{5} \int \frac {-5 x^2+\left (8 x^2+x^2 \log \left (\frac {14}{5}\right )\right )^{\left .\frac {1}{5}\right /x} \left (6-3 \log \left (8 x^2+x^2 \log \left (\frac {14}{5}\right )\right )\right )}{x^2} \, dx\\ &=\frac {1}{5} \int \left (-5-3 \left (x^2\right )^{-1+\frac {1}{5 x}} \left (8+\log \left (\frac {14}{5}\right )\right )^{\left .\frac {1}{5}\right /x} \left (-2+\log \left (x^2 \left (8+\log \left (\frac {14}{5}\right )\right )\right )\right )\right ) \, dx\\ &=-x-\frac {3}{5} \int \left (x^2\right )^{-1+\frac {1}{5 x}} \left (8+\log \left (\frac {14}{5}\right )\right )^{\left .\frac {1}{5}\right /x} \left (-2+\log \left (x^2 \left (8+\log \left (\frac {14}{5}\right )\right )\right )\right ) \, dx\\ &=-x-\frac {3}{5} \int \left (-2 \left (x^2\right )^{-1+\frac {1}{5 x}} \left (8+\log \left (\frac {14}{5}\right )\right )^{\left .\frac {1}{5}\right /x}+\left (x^2\right )^{-1+\frac {1}{5 x}} \left (8+\log \left (\frac {14}{5}\right )\right )^{\left .\frac {1}{5}\right /x} \log \left (x^2 \left (8+\log \left (\frac {14}{5}\right )\right )\right )\right ) \, dx\\ &=-x-\frac {3}{5} \int \left (x^2\right )^{-1+\frac {1}{5 x}} \left (8+\log \left (\frac {14}{5}\right )\right )^{\left .\frac {1}{5}\right /x} \log \left (x^2 \left (8+\log \left (\frac {14}{5}\right )\right )\right ) \, dx+\frac {6}{5} \int \left (x^2\right )^{-1+\frac {1}{5 x}} \left (8+\log \left (\frac {14}{5}\right )\right )^{\left .\frac {1}{5}\right /x} \, dx\\ &=-x+\frac {3}{5} \int \frac {2 \int \left (x^2\right )^{-1+\frac {1}{5 x}} \left (8+\log \left (\frac {14}{5}\right )\right )^{\left .\frac {1}{5}\right /x} \, dx}{x} \, dx+\frac {6}{5} \int \left (x^2\right )^{-1+\frac {1}{5 x}} \left (8+\log \left (\frac {14}{5}\right )\right )^{\left .\frac {1}{5}\right /x} \, dx-\frac {1}{5} \left (3 \log \left (x^2 \left (8+\log \left (\frac {14}{5}\right )\right )\right )\right ) \int \left (x^2\right )^{-1+\frac {1}{5 x}} \left (8+\log \left (\frac {14}{5}\right )\right )^{\left .\frac {1}{5}\right /x} \, dx\\ &=-x+\frac {6}{5} \int \left (x^2\right )^{-1+\frac {1}{5 x}} \left (8+\log \left (\frac {14}{5}\right )\right )^{\left .\frac {1}{5}\right /x} \, dx+\frac {6}{5} \int \frac {\int \left (x^2\right )^{-1+\frac {1}{5 x}} \left (8+\log \left (\frac {14}{5}\right )\right )^{\left .\frac {1}{5}\right /x} \, dx}{x} \, dx-\frac {1}{5} \left (3 \log \left (x^2 \left (8+\log \left (\frac {14}{5}\right )\right )\right )\right ) \int \left (x^2\right )^{-1+\frac {1}{5 x}} \left (8+\log \left (\frac {14}{5}\right )\right )^{\left .\frac {1}{5}\right /x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.28, size = 31, normalized size = 0.84 \begin {gather*} -x+3 \left (x^2\right )^{\left .\frac {1}{5}\right /x} \left (8+\log \left (\frac {14}{5}\right )\right )^{\left .\frac {1}{5}\right /x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.48, size = 24, normalized size = 0.65 \begin {gather*} 3 \, {\left (x^{2} \log \left (\frac {14}{5}\right ) + 8 \, x^{2}\right )}^{\frac {1}{5 \, x}} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {5 \, x^{2} + 3 \, {\left (x^{2} \log \left (\frac {14}{5}\right ) + 8 \, x^{2}\right )}^{\frac {1}{5 \, x}} {\left (\log \left (x^{2} \log \left (\frac {14}{5}\right ) + 8 \, x^{2}\right ) - 2\right )}}{5 \, x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.16, size = 26, normalized size = 0.70
method | result | size |
default | \(-x +3 \,{\mathrm e}^{\frac {\ln \left (x^{2} \ln \left (\frac {14}{5}\right )+8 x^{2}\right )}{5 x}}\) | \(26\) |
risch | \(-x +3 \left (x^{2} \left (\ln \relax (2)+\ln \relax (7)-\ln \relax (5)\right )+8 x^{2}\right )^{\frac {1}{5 x}}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 31, normalized size = 0.84 \begin {gather*} -x + 3 \, e^{\left (\frac {2 \, \log \relax (x)}{5 \, x} + \frac {\log \left (\log \relax (7) - \log \relax (5) + \log \relax (2) + 8\right )}{5 \, x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.99, size = 31, normalized size = 0.84 \begin {gather*} 3\,{\left (x^2\,\ln \left (14\right )-x^2\,\ln \relax (5)+8\,x^2\right )}^{\frac {1}{5\,x}}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.33, size = 22, normalized size = 0.59 \begin {gather*} - x + 3 e^{\frac {\log {\left (x^{2} \log {\left (\frac {14}{5} \right )} + 8 x^{2} \right )}}{5 x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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