Optimal. Leaf size=24 \[ \left (-e^5+x\right )^{\frac {20}{-x+\frac {\log ^4(7)}{x}}} \]
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Rubi [F]
time = 1.74, 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 {\left (-e^5+x\right )^{\frac {20 x}{-x^2+\log ^4(7)}} \left (20 x^3-20 x \log ^4(7)+\left (20 e^5 x^2-20 x^3+\left (20 e^5-20 x\right ) \log ^4(7)\right ) \log \left (-e^5+x\right )\right )}{e^5 x^4-x^5+\left (-2 e^5 x^2+2 x^3\right ) \log ^4(7)+\left (e^5-x\right ) \log ^8(7)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {20 \left (-e^5+x\right )^{-1+\frac {20 x}{-x^2+\log ^4(7)}} \left (-x^3+x \log ^4(7)-\left (e^5-x\right ) \left (x^2+\log ^4(7)\right ) \log \left (-e^5+x\right )\right )}{\left (x^2-\log ^4(7)\right )^2} \, dx\\ &=20 \int \frac {\left (-e^5+x\right )^{-1+\frac {20 x}{-x^2+\log ^4(7)}} \left (-x^3+x \log ^4(7)-\left (e^5-x\right ) \left (x^2+\log ^4(7)\right ) \log \left (-e^5+x\right )\right )}{\left (x^2-\log ^4(7)\right )^2} \, dx\\ &=20 \int \left (-\frac {x \left (-e^5+x\right )^{-1+\frac {20 x}{-x^2+\log ^4(7)}}}{x^2-\log ^4(7)}+\frac {\left (-e^5+x\right )^{\frac {20 x}{-x^2+\log ^4(7)}} \left (x^2+\log ^4(7)\right ) \log \left (-e^5+x\right )}{\left (x^2-\log ^4(7)\right )^2}\right ) \, dx\\ &=-\left (20 \int \frac {x \left (-e^5+x\right )^{-1+\frac {20 x}{-x^2+\log ^4(7)}}}{x^2-\log ^4(7)} \, dx\right )+20 \int \frac {\left (-e^5+x\right )^{\frac {20 x}{-x^2+\log ^4(7)}} \left (x^2+\log ^4(7)\right ) \log \left (-e^5+x\right )}{\left (x^2-\log ^4(7)\right )^2} \, dx\\ &=-\left (20 \int \left (\frac {\left (-e^5+x\right )^{-1+\frac {20 x}{-x^2+\log ^4(7)}}}{2 \left (x-\log ^2(7)\right )}+\frac {\left (-e^5+x\right )^{-1+\frac {20 x}{-x^2+\log ^4(7)}}}{2 \left (x+\log ^2(7)\right )}\right ) \, dx\right )+20 \int \left (\frac {\left (-e^5+x\right )^{\frac {20 x}{-x^2+\log ^4(7)}} \log \left (-e^5+x\right )}{2 \left (x-\log ^2(7)\right )^2}+\frac {\left (-e^5+x\right )^{\frac {20 x}{-x^2+\log ^4(7)}} \log \left (-e^5+x\right )}{2 \left (x+\log ^2(7)\right )^2}\right ) \, dx\\ &=-\left (10 \int \frac {\left (-e^5+x\right )^{-1+\frac {20 x}{-x^2+\log ^4(7)}}}{x-\log ^2(7)} \, dx\right )-10 \int \frac {\left (-e^5+x\right )^{-1+\frac {20 x}{-x^2+\log ^4(7)}}}{x+\log ^2(7)} \, dx+10 \int \frac {\left (-e^5+x\right )^{\frac {20 x}{-x^2+\log ^4(7)}} \log \left (-e^5+x\right )}{\left (x-\log ^2(7)\right )^2} \, dx+10 \int \frac {\left (-e^5+x\right )^{\frac {20 x}{-x^2+\log ^4(7)}} \log \left (-e^5+x\right )}{\left (x+\log ^2(7)\right )^2} \, dx\\ &=\frac {\left (-e^5+x\right )^{-\frac {20 x}{x^2-\log ^4(7)}} \, _2F_1\left (1,-\frac {20 x}{x^2-\log ^4(7)};1-\frac {20 x}{x^2-\log ^4(7)};\frac {e^5-x}{e^5-\log ^2(7)}\right ) \left (x^2-\log ^4(7)\right )}{2 x \left (e^5-\log ^2(7)\right )}+\frac {\left (-e^5+x\right )^{-\frac {20 x}{x^2-\log ^4(7)}} \, _2F_1\left (1,-\frac {20 x}{x^2-\log ^4(7)};1-\frac {20 x}{x^2-\log ^4(7)};\frac {e^5-x}{e^5+\log ^2(7)}\right ) \left (x^2-\log ^4(7)\right )}{2 x \left (e^5+\log ^2(7)\right )}+10 \int \frac {\left (-e^5+x\right )^{\frac {20 x}{-x^2+\log ^4(7)}} \log \left (-e^5+x\right )}{\left (x-\log ^2(7)\right )^2} \, dx+10 \int \frac {\left (-e^5+x\right )^{\frac {20 x}{-x^2+\log ^4(7)}} \log \left (-e^5+x\right )}{\left (x+\log ^2(7)\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.10, size = 23, normalized size = 0.96 \begin {gather*} \left (-e^5+x\right )^{-\frac {20 x}{x^2-\log ^4(7)}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.79, size = 25, normalized size = 1.04
method | result | size |
risch | \(\left (-{\mathrm e}^{5}+x \right )^{\frac {20 x}{\ln \left (7\right )^{4}-x^{2}}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.63, size = 38, normalized size = 1.58 \begin {gather*} e^{\left (-\frac {10 \, \log \left (x - e^{5}\right )}{\log \left (7\right )^{2} + x} + \frac {10 \, \log \left (x - e^{5}\right )}{\log \left (7\right )^{2} - x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 22, normalized size = 0.92 \begin {gather*} {\left (x - e^{5}\right )}^{\frac {20 \, x}{\log \left (7\right )^{4} - x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.26, size = 19, normalized size = 0.79 \begin {gather*} e^{\frac {20 x \log {\left (x - e^{5} \right )}}{- x^{2} + \log {\left (7 \right )}^{4}}} \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 = 4.98, size = 22, normalized size = 0.92 \begin {gather*} {\left (x-{\mathrm {e}}^5\right )}^{\frac {20\,x}{{\ln \left (7\right )}^4-x^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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