Optimal. Leaf size=19 \[ \log \left (\frac {1}{2} e^{16 \left (e^x-3 x\right )^2} x\right ) \]
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Rubi [A]
time = 0.03, antiderivative size = 28, normalized size of antiderivative = 1.47, number of steps
used = 7, number of rules used = 3, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.094, Rules used = {14, 2225, 2207}
\begin {gather*} 144 x^2+96 e^x+16 e^{2 x}-96 e^x (x+1)+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2207
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (32 e^{2 x}-96 e^x (1+x)+\frac {1+288 x^2}{x}\right ) \, dx\\ &=32 \int e^{2 x} \, dx-96 \int e^x (1+x) \, dx+\int \frac {1+288 x^2}{x} \, dx\\ &=16 e^{2 x}-96 e^x (1+x)+96 \int e^x \, dx+\int \left (\frac {1}{x}+288 x\right ) \, dx\\ &=96 e^x+16 e^{2 x}+144 x^2-96 e^x (1+x)+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 21, normalized size = 1.11 \begin {gather*} 16 e^{2 x}-96 e^x x+144 x^2+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 20, normalized size = 1.05
method | result | size |
default | \(\ln \left (x \right )+144 x^{2}+16 \,{\mathrm e}^{2 x}-96 \,{\mathrm e}^{x} x\) | \(20\) |
norman | \(\ln \left (x \right )+144 x^{2}+16 \,{\mathrm e}^{2 x}-96 \,{\mathrm e}^{x} x\) | \(20\) |
risch | \(\ln \left (x \right )+144 x^{2}+16 \,{\mathrm e}^{2 x}-96 \,{\mathrm e}^{x} x\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 25, normalized size = 1.32 \begin {gather*} 144 \, x^{2} - 96 \, {\left (x - 1\right )} e^{x} + 16 \, e^{\left (2 \, x\right )} - 96 \, e^{x} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 19, normalized size = 1.00 \begin {gather*} 144 \, x^{2} - 96 \, x e^{x} + 16 \, e^{\left (2 \, x\right )} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 20, normalized size = 1.05 \begin {gather*} 144 x^{2} - 96 x e^{x} + 16 e^{2 x} + \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 19, normalized size = 1.00 \begin {gather*} 144 \, x^{2} - 96 \, x e^{x} + 16 \, e^{\left (2 \, x\right )} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 19, normalized size = 1.00 \begin {gather*} 16\,{\mathrm {e}}^{2\,x}+\ln \left (x\right )-96\,x\,{\mathrm {e}}^x+144\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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