Optimal. Leaf size=24 \[ -e^x+x^2 \left (e^4+x+\frac {\frac {4}{3}+x}{x^2}\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 17, normalized size of antiderivative = 0.71, number of steps
used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {2225}
\begin {gather*} x^3+e^4 x^2+x-e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+e^4 x^2+x^3-\int e^x \, dx\\ &=-e^x+x+e^4 x^2+x^3\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 17, normalized size = 0.71 \begin {gather*} -e^x+x+e^4 x^2+x^3 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.24, size = 18, normalized size = 0.75
method | result | size |
risch | \(x^{3}+x +x^{2} {\mathrm e}^{4}-{\mathrm e}^{x}\) | \(16\) |
default | \(x^{3}+x +x^{2} {\mathrm e}^{4}-{\mathrm e}^{x}\) | \(18\) |
norman | \(x^{3}+x +x^{2} {\mathrm e}^{4}-{\mathrm e}^{x}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 15, normalized size = 0.62 \begin {gather*} x^{3} + x^{2} e^{4} + x - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 15, normalized size = 0.62 \begin {gather*} x^{3} + x^{2} e^{4} + x - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 14, normalized size = 0.58 \begin {gather*} x^{3} + x^{2} e^{4} + x - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 15, normalized size = 0.62 \begin {gather*} x^{3} + x^{2} e^{4} + x - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 15, normalized size = 0.62 \begin {gather*} x-{\mathrm {e}}^x+x^2\,{\mathrm {e}}^4+x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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