Optimal. Leaf size=31 \[ -4+x+\left (-e^x+4 x\right )^2+\left (\frac {3}{25 x}-x-\log (x)\right )^2 \]
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Rubi [A]
time = 0.08, antiderivative size = 50, normalized size of antiderivative = 1.61, number of steps
used = 15, number of rules used = 8, integrand size = 64, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 14, 2225,
2207, 2404, 2332, 2341, 2338} \begin {gather*} 17 x^2+\frac {9}{625 x^2}+x+8 e^x+e^{2 x}-8 e^x (x+1)+\log ^2(x)+2 x \log (x)-\frac {6 \log (x)}{25 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2207
Rule 2225
Rule 2332
Rule 2338
Rule 2341
Rule 2404
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{625} \int \frac {-18-150 x+1875 x^3+1250 e^{2 x} x^3+21250 x^4+e^x \left (-5000 x^3-5000 x^4\right )+\left (150 x+1250 x^2+1250 x^3\right ) \log (x)}{x^3} \, dx\\ &=\frac {1}{625} \int \left (1250 e^{2 x}-5000 e^x (1+x)+\frac {-18-150 x+1875 x^3+21250 x^4+150 x \log (x)+1250 x^2 \log (x)+1250 x^3 \log (x)}{x^3}\right ) \, dx\\ &=\frac {1}{625} \int \frac {-18-150 x+1875 x^3+21250 x^4+150 x \log (x)+1250 x^2 \log (x)+1250 x^3 \log (x)}{x^3} \, dx+2 \int e^{2 x} \, dx-8 \int e^x (1+x) \, dx\\ &=e^{2 x}-8 e^x (1+x)+\frac {1}{625} \int \left (\frac {-18-150 x+1875 x^3+21250 x^4}{x^3}+\frac {50 \left (3+25 x+25 x^2\right ) \log (x)}{x^2}\right ) \, dx+8 \int e^x \, dx\\ &=8 e^x+e^{2 x}-8 e^x (1+x)+\frac {1}{625} \int \frac {-18-150 x+1875 x^3+21250 x^4}{x^3} \, dx+\frac {2}{25} \int \frac {\left (3+25 x+25 x^2\right ) \log (x)}{x^2} \, dx\\ &=8 e^x+e^{2 x}-8 e^x (1+x)+\frac {1}{625} \int \left (1875-\frac {18}{x^3}-\frac {150}{x^2}+21250 x\right ) \, dx+\frac {2}{25} \int \left (25 \log (x)+\frac {3 \log (x)}{x^2}+\frac {25 \log (x)}{x}\right ) \, dx\\ &=8 e^x+e^{2 x}+\frac {9}{625 x^2}+\frac {6}{25 x}+3 x+17 x^2-8 e^x (1+x)+\frac {6}{25} \int \frac {\log (x)}{x^2} \, dx+2 \int \log (x) \, dx+2 \int \frac {\log (x)}{x} \, dx\\ &=8 e^x+e^{2 x}+\frac {9}{625 x^2}+x+17 x^2-8 e^x (1+x)-\frac {6 \log (x)}{25 x}+2 x \log (x)+\log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 43, normalized size = 1.39 \begin {gather*} e^{2 x}+\frac {9}{625 x^2}+x-8 e^x x+17 x^2-\frac {6 \log (x)}{25 x}+2 x \log (x)+\log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.20, size = 38, normalized size = 1.23
method | result | size |
default | \(-8 \,{\mathrm e}^{x} x +17 x^{2}+x +\frac {9}{625 x^{2}}+{\mathrm e}^{2 x}+2 x \ln \left (x \right )+\ln \left (x \right )^{2}-\frac {6 \ln \left (x \right )}{25 x}\) | \(38\) |
risch | \(\ln \left (x \right )^{2}+\frac {2 \left (25 x^{2}-3\right ) \ln \left (x \right )}{25 x}+\frac {10625 x^{4}-5000 \,{\mathrm e}^{x} x^{3}+625 \,{\mathrm e}^{2 x} x^{2}+625 x^{3}+9}{625 x^{2}}\) | \(53\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.37, size = 43, normalized size = 1.39 \begin {gather*} 17 \, x^{2} - 8 \, {\left (x - 1\right )} e^{x} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x - \frac {6 \, \log \left (x\right )}{25 \, x} + \frac {9}{625 \, x^{2}} + e^{\left (2 \, x\right )} - 8 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 55, normalized size = 1.77 \begin {gather*} \frac {10625 \, x^{4} - 5000 \, x^{3} e^{x} + 625 \, x^{2} \log \left (x\right )^{2} + 625 \, x^{3} + 625 \, x^{2} e^{\left (2 \, x\right )} + 50 \, {\left (25 \, x^{3} - 3 \, x\right )} \log \left (x\right ) + 9}{625 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 42, normalized size = 1.35 \begin {gather*} 17 x^{2} - 8 x e^{x} + x + e^{2 x} + \log {\left (x \right )}^{2} + \frac {\left (50 x^{2} - 6\right ) \log {\left (x \right )}}{25 x} + \frac {9}{625 x^{2}} \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 = 4.08, size = 38, normalized size = 1.23 \begin {gather*} {\mathrm {e}}^{2\,x}+{\ln \left (x\right )}^2-\frac {\frac {6\,x\,\ln \left (x\right )}{25}-\frac {9}{625}}{x^2}+x\,\left (2\,\ln \left (x\right )-8\,{\mathrm {e}}^x+1\right )+17\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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