Optimal. Leaf size=24 \[ 1+e^x+x+x \left (1+\frac {e^3 x}{5}\right )+\frac {\log (x)}{x^2} \]
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Rubi [A] time = 0.04, antiderivative size = 23, normalized size of antiderivative = 0.96, number of steps used = 9, number of rules used = 4, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {12, 14, 2194, 2304} \begin {gather*} \frac {e^3 x^2}{5}+\frac {\log (x)}{x^2}+2 x+e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2194
Rule 2304
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {5+10 x^3+5 e^x x^3+2 e^3 x^4-10 \log (x)}{x^3} \, dx\\ &=\frac {1}{5} \int \left (5 e^x+\frac {5+10 x^3+2 e^3 x^4-10 \log (x)}{x^3}\right ) \, dx\\ &=\frac {1}{5} \int \frac {5+10 x^3+2 e^3 x^4-10 \log (x)}{x^3} \, dx+\int e^x \, dx\\ &=e^x+\frac {1}{5} \int \left (\frac {5+10 x^3+2 e^3 x^4}{x^3}-\frac {10 \log (x)}{x^3}\right ) \, dx\\ &=e^x+\frac {1}{5} \int \frac {5+10 x^3+2 e^3 x^4}{x^3} \, dx-2 \int \frac {\log (x)}{x^3} \, dx\\ &=e^x+\frac {1}{2 x^2}+\frac {\log (x)}{x^2}+\frac {1}{5} \int \left (10+\frac {5}{x^3}+2 e^3 x\right ) \, dx\\ &=e^x+2 x+\frac {e^3 x^2}{5}+\frac {\log (x)}{x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 23, normalized size = 0.96 \begin {gather*} e^x+2 x+\frac {e^3 x^2}{5}+\frac {\log (x)}{x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 28, normalized size = 1.17 \begin {gather*} \frac {x^{4} e^{3} + 10 \, x^{3} + 5 \, x^{2} e^{x} + 5 \, \log \relax (x)}{5 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 28, normalized size = 1.17 \begin {gather*} \frac {x^{4} e^{3} + 10 \, x^{3} + 5 \, x^{2} e^{x} + 5 \, \log \relax (x)}{5 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 20, normalized size = 0.83
method | result | size |
default | \(2 x +\frac {x^{2} {\mathrm e}^{3}}{5}+\frac {\ln \relax (x )}{x^{2}}+{\mathrm e}^{x}\) | \(20\) |
risch | \(2 x +\frac {x^{2} {\mathrm e}^{3}}{5}+\frac {\ln \relax (x )}{x^{2}}+{\mathrm e}^{x}\) | \(20\) |
norman | \(\frac {{\mathrm e}^{x} x^{2}+2 x^{3}+\frac {x^{4} {\mathrm e}^{3}}{5}+\ln \relax (x )}{x^{2}}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 19, normalized size = 0.79 \begin {gather*} \frac {1}{5} \, x^{2} e^{3} + 2 \, x + \frac {\log \relax (x)}{x^{2}} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.49, size = 19, normalized size = 0.79 \begin {gather*} 2\,x+{\mathrm {e}}^x+\frac {\ln \relax (x)}{x^2}+\frac {x^2\,{\mathrm {e}}^3}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.28, size = 20, normalized size = 0.83 \begin {gather*} \frac {x^{2} e^{3}}{5} + 2 x + e^{x} + \frac {\log {\relax (x )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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