Optimal. Leaf size=24 \[ -3 e^x-e^{x^3}+2 x+\log (2)-\log \left (x^2\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 20, normalized size of antiderivative = 0.83, number of steps used = 8, number of rules used = 4, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.160, Rules used = {14, 2209, 2194, 43} \begin {gather*} -e^{x^3}+2 x-3 e^x-2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 43
Rule 2194
Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-3 e^{x^3} x^2-\frac {2-2 x+3 e^x x}{x}\right ) \, dx\\ &=-\left (3 \int e^{x^3} x^2 \, dx\right )-\int \frac {2-2 x+3 e^x x}{x} \, dx\\ &=-e^{x^3}-\int \left (3 e^x-\frac {2 (-1+x)}{x}\right ) \, dx\\ &=-e^{x^3}+2 \int \frac {-1+x}{x} \, dx-3 \int e^x \, dx\\ &=-3 e^x-e^{x^3}+2 \int \left (1-\frac {1}{x}\right ) \, dx\\ &=-3 e^x-e^{x^3}+2 x-2 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 0.83 \begin {gather*} -3 e^x-e^{x^3}+2 x-2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.74, size = 18, normalized size = 0.75 \begin {gather*} 2 \, x - e^{\left (x^{3}\right )} - 3 \, e^{x} - 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 18, normalized size = 0.75 \begin {gather*} 2 \, x - e^{\left (x^{3}\right )} - 3 \, e^{x} - 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 19, normalized size = 0.79
method | result | size |
default | \(2 x -2 \ln \relax (x )-{\mathrm e}^{x^{3}}-3 \,{\mathrm e}^{x}\) | \(19\) |
norman | \(2 x -2 \ln \relax (x )-{\mathrm e}^{x^{3}}-3 \,{\mathrm e}^{x}\) | \(19\) |
risch | \(2 x -2 \ln \relax (x )-{\mathrm e}^{x^{3}}-3 \,{\mathrm e}^{x}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 18, normalized size = 0.75 \begin {gather*} 2 \, x - e^{\left (x^{3}\right )} - 3 \, e^{x} - 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 18, normalized size = 0.75 \begin {gather*} 2\,x-{\mathrm {e}}^{x^3}-3\,{\mathrm {e}}^x-2\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 17, normalized size = 0.71 \begin {gather*} 2 x - 3 e^{x} - e^{x^{3}} - 2 \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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