Optimal. Leaf size=21 \[ e^3 \left (-1-e^x+x+x^2+\log \left (\frac {2}{x}\right )\right ) \]
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Rubi [A]
time = 0.02, antiderivative size = 27, normalized size of antiderivative = 1.29, number of steps
used = 5, number of rules used = 3, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.120, Rules used = {14, 2225, 77}
\begin {gather*} e^3 x^2+e^3 x-e^{x+3}-e^3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 77
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-e^{3+x}+\frac {e^3 (1+x) (-1+2 x)}{x}\right ) \, dx\\ &=e^3 \int \frac {(1+x) (-1+2 x)}{x} \, dx-\int e^{3+x} \, dx\\ &=-e^{3+x}+e^3 \int \left (1-\frac {1}{x}+2 x\right ) \, dx\\ &=-e^{3+x}+e^3 x+e^3 x^2-e^3 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 18, normalized size = 0.86 \begin {gather*} e^3 \left (-e^x+x+x^2-\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.17, size = 24, normalized size = 1.14
method | result | size |
default | \(x^{2} {\mathrm e}^{3}-\ln \left (x \right ) {\mathrm e}^{3}-{\mathrm e}^{x} {\mathrm e}^{3}+x \,{\mathrm e}^{3}\) | \(24\) |
norman | \(x^{2} {\mathrm e}^{3}-\ln \left (x \right ) {\mathrm e}^{3}-{\mathrm e}^{x} {\mathrm e}^{3}+x \,{\mathrm e}^{3}\) | \(24\) |
risch | \(x^{2} {\mathrm e}^{3}+x \,{\mathrm e}^{3}-\ln \left (x \right ) {\mathrm e}^{3}-{\mathrm e}^{3+x}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 23, normalized size = 1.10 \begin {gather*} x^{2} e^{3} + x e^{3} - e^{3} \log \left (x\right ) - e^{\left (x + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 21, normalized size = 1.00 \begin {gather*} {\left (x^{2} + x\right )} e^{3} - e^{3} \log \left (x\right ) - e^{\left (x + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 24, normalized size = 1.14 \begin {gather*} x^{2} e^{3} + x e^{3} - e^{3} e^{x} - e^{3} \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 23, normalized size = 1.10 \begin {gather*} x^{2} e^{3} + x e^{3} - e^{3} \log \left (x\right ) - e^{\left (x + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.07, size = 16, normalized size = 0.76 \begin {gather*} {\mathrm {e}}^3\,\left (x-{\mathrm {e}}^x-\ln \left (x\right )+x^2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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