Optimal. Leaf size=29 \[ -5+e^{-4+x}-x-x \left (4-\log \left (\frac {e^{2 x^2}}{16}\right )\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 23, normalized size of antiderivative = 0.79, number of steps used = 5, number of rules used = 4, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {2194, 2548, 12, 30} \begin {gather*} x \log \left (\frac {e^{2 x^2}}{16}\right )-5 x+e^{x-4} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rule 2194
Rule 2548
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-5 x+\frac {4 x^3}{3}+\int e^{-4+x} \, dx+\int \log \left (\frac {e^{2 x^2}}{16}\right ) \, dx\\ &=e^{-4+x}-5 x+\frac {4 x^3}{3}+x \log \left (\frac {e^{2 x^2}}{16}\right )-\int 4 x^2 \, dx\\ &=e^{-4+x}-5 x+\frac {4 x^3}{3}+x \log \left (\frac {e^{2 x^2}}{16}\right )-4 \int x^2 \, dx\\ &=e^{-4+x}-5 x+x \log \left (\frac {e^{2 x^2}}{16}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 34, normalized size = 1.17 \begin {gather*} e^{-4+x}-5 x+2 x^3+x \left (-2 x^2+\log \left (\frac {e^{2 x^2}}{16}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.91, size = 18, normalized size = 0.62 \begin {gather*} 2 \, x^{3} - 4 \, x \log \relax (2) - 5 \, x + e^{\left (x - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 18, normalized size = 0.62 \begin {gather*} 2 \, x^{3} - 4 \, x \log \relax (2) - 5 \, x + e^{\left (x - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 20, normalized size = 0.69
method | result | size |
default | \(-5 x +{\mathrm e}^{x -4}+x \ln \left (\frac {{\mathrm e}^{2 x^{2}}}{16}\right )\) | \(20\) |
risch | \(2 x \ln \left ({\mathrm e}^{x^{2}}\right )-\frac {i \pi \mathrm {csgn}\left (i {\mathrm e}^{x^{2}}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{2 x^{2}}\right ) x}{2}+i \pi \,\mathrm {csgn}\left (i {\mathrm e}^{x^{2}}\right ) \mathrm {csgn}\left (i {\mathrm e}^{2 x^{2}}\right )^{2} x -\frac {i \pi \mathrm {csgn}\left (i {\mathrm e}^{2 x^{2}}\right )^{3} x}{2}-4 x \ln \relax (2)+{\mathrm e}^{x -4}-5 x\) | \(89\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 19, normalized size = 0.66 \begin {gather*} x \log \left (\frac {1}{16} \, e^{\left (2 \, x^{2}\right )}\right ) - 5 \, x + e^{\left (x - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 17, normalized size = 0.59 \begin {gather*} {\mathrm {e}}^{x-4}-x\,\left (\ln \left (16\right )+5\right )+2\,x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.27, size = 19, normalized size = 0.66 \begin {gather*} 2 x^{3} + x \left (-5 - 4 \log {\relax (2 )}\right ) + e^{x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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