Optimal. Leaf size=22 \[ 11-e^2-e^x-4 x \left (-\frac {1}{5}+x^2\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.73, number of steps
used = 3, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 2225}
\begin {gather*} -4 x^3+\frac {4 x}{5}-e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \left (4-5 e^x-60 x^2\right ) \, dx\\ &=\frac {4 x}{5}-4 x^3-\int e^x \, dx\\ &=-e^x+\frac {4 x}{5}-4 x^3\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 16, normalized size = 0.73 \begin {gather*} -e^x+\frac {4 x}{5}-4 x^3 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 14, normalized size = 0.64
method | result | size |
default | \(\frac {4 x}{5}-4 x^{3}-{\mathrm e}^{x}\) | \(14\) |
norman | \(\frac {4 x}{5}-4 x^{3}-{\mathrm e}^{x}\) | \(14\) |
risch | \(\frac {4 x}{5}-4 x^{3}-{\mathrm e}^{x}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 13, normalized size = 0.59 \begin {gather*} -4 \, x^{3} + \frac {4}{5} \, x - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 13, normalized size = 0.59 \begin {gather*} -4 \, x^{3} + \frac {4}{5} \, 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 = 12, normalized size = 0.55 \begin {gather*} - 4 x^{3} + \frac {4 x}{5} - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 13, normalized size = 0.59 \begin {gather*} -4 \, x^{3} + \frac {4}{5} \, x - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.46, size = 13, normalized size = 0.59 \begin {gather*} \frac {4\,x}{5}-{\mathrm {e}}^x-4\,x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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