Optimal. Leaf size=29 \[ e^{\frac {e^{5 \left (2+e^3+\left (-e^5+x^2\right )^2\right )}}{2 x}} \]
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Rubi [F]
time = 2.65, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {\exp \left (10+5 e^3+5 e^{10}+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right ) \left (-1-20 e^5 x^2+20 x^4\right )}{2 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \frac {\exp \left (10+5 e^3+5 e^{10}+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right ) \left (-1-20 e^5 x^2+20 x^4\right )}{x^2} \, dx\\ &=\frac {1}{2} \int \frac {\exp \left (10 \left (1+\frac {1}{2} e^3 \left (1+e^7\right )\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right ) \left (-1-20 e^5 x^2+20 x^4\right )}{x^2} \, dx\\ &=\frac {1}{2} \int \left (-20 \exp \left (5+10 \left (1+\frac {1}{2} e^3 \left (1+e^7\right )\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right )-\frac {\exp \left (10 \left (1+\frac {1}{2} e^3 \left (1+e^7\right )\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right )}{x^2}+20 \exp \left (10 \left (1+\frac {1}{2} e^3 \left (1+e^7\right )\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right ) x^2\right ) \, dx\\ &=-\left (\frac {1}{2} \int \frac {\exp \left (10 \left (1+\frac {1}{2} e^3 \left (1+e^7\right )\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right )}{x^2} \, dx\right )-10 \int \exp \left (5+10 \left (1+\frac {1}{2} e^3 \left (1+e^7\right )\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right ) \, dx+10 \int \exp \left (10 \left (1+\frac {1}{2} e^3 \left (1+e^7\right )\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right ) x^2 \, dx\\ &=-\left (\frac {1}{2} \int \frac {\exp \left (10 \left (1+\frac {1}{2} e^3 \left (1+e^7\right )\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right )}{x^2} \, dx\right )-10 \int \exp \left (5 \left (3+e^3+e^{10}\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right ) \, dx+10 \int \exp \left (10 \left (1+\frac {1}{2} e^3 \left (1+e^7\right )\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right ) x^2 \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.44, size = 32, normalized size = 1.10 \begin {gather*} e^{\frac {e^{5 \left (2+e^3+e^{10}-2 e^5 x^2+x^4\right )}}{2 x}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.28, size = 30, normalized size = 1.03
method | result | size |
risch | \({\mathrm e}^{\frac {{\mathrm e}^{5 \,{\mathrm e}^{10}-10 x^{2} {\mathrm e}^{5}+5 \,{\mathrm e}^{3}+5 x^{4}+10}}{2 x}}\) | \(30\) |
norman | \({\mathrm e}^{\frac {{\mathrm e}^{5 \,{\mathrm e}^{10}-10 x^{2} {\mathrm e}^{5}+5 \,{\mathrm e}^{3}+5 x^{4}+10}}{2 x}}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.57, size = 29, normalized size = 1.00 \begin {gather*} e^{\left (\frac {e^{\left (5 \, x^{4} - 10 \, x^{2} e^{5} + 5 \, e^{10} + 5 \, e^{3} + 10\right )}}{2 \, x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 77 vs.
\(2 (25) = 50\).
time = 0.38, size = 77, normalized size = 2.66 \begin {gather*} e^{\left (-5 \, x^{4} + 10 \, x^{2} e^{5} + \frac {10 \, x^{5} - 20 \, x^{3} e^{5} + 10 \, x e^{10} + 10 \, x e^{3} + 20 \, x + e^{\left (5 \, x^{4} - 10 \, x^{2} e^{5} + 5 \, e^{10} + 5 \, e^{3} + 10\right )}}{2 \, x} - 5 \, e^{10} - 5 \, e^{3} - 10\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.15, size = 31, normalized size = 1.07 \begin {gather*} e^{\frac {e^{5 x^{4} - 10 x^{2} e^{5} + 10 + 5 e^{3} + 5 e^{10}}}{2 x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.77, size = 32, normalized size = 1.10 \begin {gather*} {\mathrm {e}}^{\frac {{\mathrm {e}}^{-10\,x^2\,{\mathrm {e}}^5}\,{\mathrm {e}}^{5\,{\mathrm {e}}^3}\,{\mathrm {e}}^{5\,{\mathrm {e}}^{10}}\,{\mathrm {e}}^{10}\,{\mathrm {e}}^{5\,x^4}}{2\,x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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