Optimal. Leaf size=22 \[ \log \left (-4+e^5-e^x-\frac {4}{e^{10} x^2}+3 x\right ) \]
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Rubi [F] time = 1.17, 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 {-8-3 e^{10} x^3+e^{10+x} x^3}{4 x-e^{15} x^3+e^{10+x} x^3+e^{10} \left (4 x^3-3 x^4\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\frac {-8-4 x-e^{10} \left (7-e^5\right ) x^3+3 e^{10} x^4}{x \left (4+e^{10+x} x^2+4 e^{10} \left (1-\frac {e^5}{4}\right ) x^2-3 e^{10} x^3\right )}\right ) \, dx\\ &=x+\int \frac {-8-4 x-e^{10} \left (7-e^5\right ) x^3+3 e^{10} x^4}{x \left (4+e^{10+x} x^2+4 e^{10} \left (1-\frac {e^5}{4}\right ) x^2-3 e^{10} x^3\right )} \, dx\\ &=x+\int \left (\frac {e^{10} \left (-7+e^5\right ) x^2}{4+e^{10+x} x^2+4 e^{10} \left (1-\frac {e^5}{4}\right ) x^2-3 e^{10} x^3}+\frac {3 e^{10} x^3}{4+e^{10+x} x^2+4 e^{10} \left (1-\frac {e^5}{4}\right ) x^2-3 e^{10} x^3}+\frac {4}{-4-e^{10+x} x^2-4 e^{10} \left (1-\frac {e^5}{4}\right ) x^2+3 e^{10} x^3}+\frac {8}{x \left (-4-e^{10+x} x^2-4 e^{10} \left (1-\frac {e^5}{4}\right ) x^2+3 e^{10} x^3\right )}\right ) \, dx\\ &=x+4 \int \frac {1}{-4-e^{10+x} x^2-4 e^{10} \left (1-\frac {e^5}{4}\right ) x^2+3 e^{10} x^3} \, dx+8 \int \frac {1}{x \left (-4-e^{10+x} x^2-4 e^{10} \left (1-\frac {e^5}{4}\right ) x^2+3 e^{10} x^3\right )} \, dx+\left (3 e^{10}\right ) \int \frac {x^3}{4+e^{10+x} x^2+4 e^{10} \left (1-\frac {e^5}{4}\right ) x^2-3 e^{10} x^3} \, dx-\left (e^{10} \left (7-e^5\right )\right ) \int \frac {x^2}{4+e^{10+x} x^2+4 e^{10} \left (1-\frac {e^5}{4}\right ) x^2-3 e^{10} x^3} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.39, size = 37, normalized size = 1.68 \begin {gather*} -2 \log (x)+\log \left (4-e^{15} x^2+e^{10+x} x^2+e^{10} (4-3 x) x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 37, normalized size = 1.68 \begin {gather*} \log \left (-\frac {x^{2} e^{15} - x^{2} e^{\left (x + 10\right )} + {\left (3 \, x^{3} - 4 \, x^{2}\right )} e^{10} - 4}{x^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 37, normalized size = 1.68 \begin {gather*} \log \left (-3 \, x^{3} e^{10} - x^{2} e^{15} + 4 \, x^{2} e^{10} + x^{2} e^{\left (x + 10\right )} + 4\right ) - 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.18, size = 34, normalized size = 1.55
method | result | size |
risch | \(\ln \left ({\mathrm e}^{x}-\frac {\left (x^{2} {\mathrm e}^{15}+3 x^{3} {\mathrm e}^{10}-4 x^{2} {\mathrm e}^{10}-4\right ) {\mathrm e}^{-10}}{x^{2}}\right )\) | \(34\) |
norman | \(-2 \ln \relax (x )+\ln \left (x^{2} {\mathrm e}^{15}-x^{2} {\mathrm e}^{10} {\mathrm e}^{x}+3 x^{3} {\mathrm e}^{10}-4 x^{2} {\mathrm e}^{10}-4\right )\) | \(46\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 37, normalized size = 1.68 \begin {gather*} \log \left (-\frac {{\left (3 \, x^{3} e^{10} + x^{2} {\left (e^{15} - 4 \, e^{10}\right )} - x^{2} e^{\left (x + 10\right )} - 4\right )} e^{\left (-10\right )}}{x^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 8.19, size = 33, normalized size = 1.50 \begin {gather*} \ln \left (\frac {x^2\,{\mathrm {e}}^5}{3}-\frac {x^2\,{\mathrm {e}}^x}{3}-\frac {4\,{\mathrm {e}}^{-10}}{3}-\frac {4\,x^2}{3}+x^3\right )-2\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.24, size = 36, normalized size = 1.64 \begin {gather*} \log {\left (e^{x} + \frac {- 3 x^{3} e^{10} - x^{2} e^{15} + 4 x^{2} e^{10} + 4}{x^{2} e^{10}} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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