Optimal. Leaf size=30 \[ x^3+\frac {\log (4)+\frac {-e^x+x (4+x)+x \log (x)}{x}}{x} \]
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Rubi [A] time = 0.06, antiderivative size = 25, normalized size of antiderivative = 0.83, number of steps used = 9, number of rules used = 4, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {6, 14, 2197, 2304} \begin {gather*} x^3-\frac {e^x}{x^2}+\frac {4}{x}+\frac {\log (4 x)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 14
Rule 2197
Rule 2304
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^x (2-x)+3 x^5+x (-3-\log (4))-x \log (x)}{x^3} \, dx\\ &=\int \left (-\frac {e^x (-2+x)}{x^3}+\frac {-3+3 x^4-\log (4 x)}{x^2}\right ) \, dx\\ &=-\int \frac {e^x (-2+x)}{x^3} \, dx+\int \frac {-3+3 x^4-\log (4 x)}{x^2} \, dx\\ &=-\frac {e^x}{x^2}+\int \left (\frac {3 \left (-1+x^4\right )}{x^2}-\frac {\log (4 x)}{x^2}\right ) \, dx\\ &=-\frac {e^x}{x^2}+3 \int \frac {-1+x^4}{x^2} \, dx-\int \frac {\log (4 x)}{x^2} \, dx\\ &=-\frac {e^x}{x^2}+\frac {1}{x}+\frac {\log (4 x)}{x}+3 \int \left (-\frac {1}{x^2}+x^2\right ) \, dx\\ &=-\frac {e^x}{x^2}+\frac {4}{x}+x^3+\frac {\log (4 x)}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 22, normalized size = 0.73 \begin {gather*} \frac {-e^x+4 x+x^5+x \log (4 x)}{x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 24, normalized size = 0.80 \begin {gather*} \frac {x^{5} + 2 \, x \log \relax (2) + x \log \relax (x) + 4 \, x - e^{x}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 24, normalized size = 0.80 \begin {gather*} \frac {x^{5} + 2 \, x \log \relax (2) + x \log \relax (x) + 4 \, x - e^{x}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 28, normalized size = 0.93
method | result | size |
risch | \(\frac {\ln \relax (x )}{x}+\frac {x^{5}+2 x \ln \relax (2)+4 x -{\mathrm e}^{x}}{x^{2}}\) | \(28\) |
default | \(x^{3}+\frac {2 \ln \relax (2)}{x}+\frac {4}{x}+\frac {\ln \relax (x )}{x}-\frac {{\mathrm e}^{x}}{x^{2}}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.47, size = 36, normalized size = 1.20 \begin {gather*} x^{3} + \frac {2 \, \log \relax (2)}{x} + \frac {\log \relax (x)}{x} + \frac {4}{x} - \Gamma \left (-1, -x\right ) - 2 \, \Gamma \left (-2, -x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.00, size = 21, normalized size = 0.70 \begin {gather*} x^3-\frac {{\mathrm {e}}^x-x\,\left (\ln \left (4\,x\right )+4\right )}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.31, size = 22, normalized size = 0.73 \begin {gather*} x^{3} + \frac {\log {\relax (x )}}{x} + \frac {2 \log {\relax (2 )} + 4}{x} - \frac {e^{x}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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