Optimal. Leaf size=26 \[ -\frac {e^{-x^3}}{3}-\frac {1}{3} e^{-x^3} x^3 \]
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Rubi [A]
time = 0.02, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {2243, 2240}
\begin {gather*} -\frac {1}{3} e^{-x^3} x^3-\frac {e^{-x^3}}{3} \end {gather*}
Antiderivative was successfully verified.
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Rule 2240
Rule 2243
Rubi steps
\begin {align*} \int e^{-x^3} x^5 \, dx &=-\frac {1}{3} e^{-x^3} x^3+\int e^{-x^3} x^2 \, dx\\ &=-\frac {e^{-x^3}}{3}-\frac {1}{3} e^{-x^3} x^3\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 16, normalized size = 0.62 \begin {gather*} -\frac {1}{3} e^{-x^3} \left (1+x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 21, normalized size = 0.81
method | result | size |
gosper | \(-\frac {\left (x^{3}+1\right ) {\mathrm e}^{-x^{3}}}{3}\) | \(14\) |
norman | \(\left (-\frac {x^{3}}{3}-\frac {1}{3}\right ) {\mathrm e}^{-x^{3}}\) | \(15\) |
risch | \(\left (-\frac {x^{3}}{3}-\frac {1}{3}\right ) {\mathrm e}^{-x^{3}}\) | \(15\) |
meijerg | \(\frac {1}{3}-\frac {\left (2 x^{3}+2\right ) {\mathrm e}^{-x^{3}}}{6}\) | \(18\) |
derivativedivides | \(-\frac {{\mathrm e}^{-x^{3}}}{3}-\frac {x^{3} {\mathrm e}^{-x^{3}}}{3}\) | \(21\) |
default | \(-\frac {{\mathrm e}^{-x^{3}}}{3}-\frac {x^{3} {\mathrm e}^{-x^{3}}}{3}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.69, size = 13, normalized size = 0.50 \begin {gather*} -\frac {1}{3} \, {\left (x^{3} + 1\right )} e^{\left (-x^{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.46, size = 13, normalized size = 0.50 \begin {gather*} -\frac {1}{3} \, {\left (x^{3} + 1\right )} e^{\left (-x^{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 12, normalized size = 0.46 \begin {gather*} \frac {\left (- x^{3} - 1\right ) e^{- x^{3}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.41, size = 13, normalized size = 0.50 \begin {gather*} -\frac {1}{3} \, {\left (x^{3} + 1\right )} e^{\left (-x^{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 13, normalized size = 0.50 \begin {gather*} -\frac {{\mathrm {e}}^{-x^3}\,\left (x^3+1\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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