Optimal. Leaf size=20 \[ 4+e^6-e^{x^2}+x+(4-x) x \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.80, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2209} \begin {gather*} -x^2-e^{x^2}+5 x \end {gather*}
Antiderivative was successfully verified.
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Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=5 x-x^2-2 \int e^{x^2} x \, dx\\ &=-e^{x^2}+5 x-x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 0.80 \begin {gather*} -e^{x^2}+5 x-x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 15, normalized size = 0.75 \begin {gather*} -x^{2} + 5 \, x - e^{\left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 15, normalized size = 0.75 \begin {gather*} -x^{2} + 5 \, x - e^{\left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 16, normalized size = 0.80
method | result | size |
default | \(-x^{2}+5 x -{\mathrm e}^{x^{2}}\) | \(16\) |
norman | \(-x^{2}+5 x -{\mathrm e}^{x^{2}}\) | \(16\) |
risch | \(-x^{2}+5 x -{\mathrm e}^{x^{2}}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 15, normalized size = 0.75 \begin {gather*} -x^{2} + 5 \, x - e^{\left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 15, normalized size = 0.75 \begin {gather*} 5\,x-{\mathrm {e}}^{x^2}-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 10, normalized size = 0.50 \begin {gather*} - x^{2} + 5 x - e^{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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