Optimal. Leaf size=23 \[ 5+e^{-25+e^{x^3}-5 x^2 \left (-5+x^2\right )} x \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(62\) vs. \(2(23)=46\).
time = 0.19, antiderivative size = 62, normalized size of antiderivative = 2.70, number of steps
used = 1, number of rules used = 1, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {2326}
\begin {gather*} \frac {e^{-5 x^4+e^{x^3}+25 x^2-25} \left (-20 x^4+3 e^{x^3} x^3+50 x^2\right )}{-20 x^3+3 e^{x^3} x^2+50 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{-25+e^{x^3}+25 x^2-5 x^4} \left (50 x^2+3 e^{x^3} x^3-20 x^4\right )}{50 x+3 e^{x^3} x^2-20 x^3}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.10, size = 22, normalized size = 0.96 \begin {gather*} e^{e^{x^3}-5 \left (5-5 x^2+x^4\right )} x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.33, size = 20, normalized size = 0.87
method | result | size |
risch | \(x \,{\mathrm e}^{-25+{\mathrm e}^{x^{3}}-5 x^{4}+25 x^{2}}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 19, normalized size = 0.83 \begin {gather*} x e^{\left (-5 \, x^{4} + 25 \, x^{2} + e^{\left (x^{3}\right )} - 25\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.52, size = 19, normalized size = 0.83 \begin {gather*} e^{\left (-5 \, x^{4} + 25 \, x^{2} + e^{\left (x^{3}\right )} + \log \left (x\right ) - 25\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.36, size = 19, normalized size = 0.83 \begin {gather*} x e^{- 5 x^{4} + 25 x^{2} + e^{x^{3}} - 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 19, normalized size = 0.83 \begin {gather*} e^{\left (-5 \, x^{4} + 25 \, x^{2} + e^{\left (x^{3}\right )} + \log \left (x\right ) - 25\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.87, size = 21, normalized size = 0.91 \begin {gather*} x\,{\mathrm {e}}^{-25}\,{\mathrm {e}}^{-5\,x^4}\,{\mathrm {e}}^{25\,x^2}\,{\mathrm {e}}^{{\mathrm {e}}^{x^3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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