Optimal. Leaf size=27 \[ 4+x+\frac {1}{2} e^{2 e+\frac {50}{x (x+\log (x))}} x^2 \]
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Rubi [F]
time = 3.50, 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 {x^2+2 x \log (x)+\log ^2(x)+e^{\frac {2 \left (25+e x^2+e x \log (x)\right )}{x^2+x \log (x)}} \left (-25-50 x+x^3+\left (-25+2 x^2\right ) \log (x)+x \log ^2(x)\right )}{x^2+2 x \log (x)+\log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x^2+2 x \log (x)+\log ^2(x)+e^{\frac {2 \left (25+e x^2+e x \log (x)\right )}{x^2+x \log (x)}} \left (-25-50 x+x^3+\left (-25+2 x^2\right ) \log (x)+x \log ^2(x)\right )}{(x+\log (x))^2} \, dx\\ &=\int \left (1+\frac {e^{\frac {2 \left (25+e x^2\right )}{x (x+\log (x))}} x^{\frac {2 e}{x+\log (x)}} \left (-25-50 x+x^3-25 \log (x)+2 x^2 \log (x)+x \log ^2(x)\right )}{(x+\log (x))^2}\right ) \, dx\\ &=x+\int \frac {e^{\frac {2 \left (25+e x^2\right )}{x (x+\log (x))}} x^{\frac {2 e}{x+\log (x)}} \left (-25-50 x+x^3-25 \log (x)+2 x^2 \log (x)+x \log ^2(x)\right )}{(x+\log (x))^2} \, dx\\ &=x+\int \left (e^{\frac {2 \left (25+e x^2\right )}{x (x+\log (x))}} x^{1+\frac {2 e}{x+\log (x)}}-\frac {25 e^{\frac {2 \left (25+e x^2\right )}{x (x+\log (x))}} x^{\frac {2 e}{x+\log (x)}} (1+x)}{(x+\log (x))^2}-\frac {25 e^{\frac {2 \left (25+e x^2\right )}{x (x+\log (x))}} x^{\frac {2 e}{x+\log (x)}}}{x+\log (x)}\right ) \, dx\\ &=x-25 \int \frac {e^{\frac {2 \left (25+e x^2\right )}{x (x+\log (x))}} x^{\frac {2 e}{x+\log (x)}} (1+x)}{(x+\log (x))^2} \, dx-25 \int \frac {e^{\frac {2 \left (25+e x^2\right )}{x (x+\log (x))}} x^{\frac {2 e}{x+\log (x)}}}{x+\log (x)} \, dx+\int e^{\frac {2 \left (25+e x^2\right )}{x (x+\log (x))}} x^{1+\frac {2 e}{x+\log (x)}} \, dx\\ &=x-25 \int \frac {e^{\frac {2 \left (25+e x^2\right )}{x (x+\log (x))}} x^{\frac {2 e}{x+\log (x)}}}{x+\log (x)} \, dx-25 \int \left (\frac {e^{\frac {2 \left (25+e x^2\right )}{x (x+\log (x))}} x^{\frac {2 e}{x+\log (x)}}}{(x+\log (x))^2}+\frac {e^{\frac {2 \left (25+e x^2\right )}{x (x+\log (x))}} x^{1+\frac {2 e}{x+\log (x)}}}{(x+\log (x))^2}\right ) \, dx+\int e^{\frac {2 \left (25+e x^2\right )}{x (x+\log (x))}} x^{1+\frac {2 e}{x+\log (x)}} \, dx\\ &=x-25 \int \frac {e^{\frac {2 \left (25+e x^2\right )}{x (x+\log (x))}} x^{\frac {2 e}{x+\log (x)}}}{(x+\log (x))^2} \, dx-25 \int \frac {e^{\frac {2 \left (25+e x^2\right )}{x (x+\log (x))}} x^{1+\frac {2 e}{x+\log (x)}}}{(x+\log (x))^2} \, dx-25 \int \frac {e^{\frac {2 \left (25+e x^2\right )}{x (x+\log (x))}} x^{\frac {2 e}{x+\log (x)}}}{x+\log (x)} \, dx+\int e^{\frac {2 \left (25+e x^2\right )}{x (x+\log (x))}} x^{1+\frac {2 e}{x+\log (x)}} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 2.15, size = 26, normalized size = 0.96 \begin {gather*} x+\frac {1}{2} e^{2 e+\frac {50}{x (x+\log (x))}} x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 2.65, size = 34, normalized size = 1.26
method | result | size |
risch | \(x +\frac {x^{2} {\mathrm e}^{\frac {2 x \,{\mathrm e} \ln \left (x \right )+2 x^{2} {\mathrm e}+50}{\left (x +\ln \left (x \right )\right ) x}}}{2}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 34, normalized size = 1.26 \begin {gather*} \frac {1}{2} \, x^{2} e^{\left (\frac {2 \, {\left (x^{2} e + x e \log \left (x\right ) + 25\right )}}{x^{2} + x \log \left (x\right )}\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.56, size = 34, normalized size = 1.26 \begin {gather*} \frac {1}{2} \, x^{2} e^{\left (\frac {2 \, {\left (x^{2} e + x e \log \left (x\right ) + 25\right )}}{x^{2} + x \log \left (x\right )}\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.76, size = 55, normalized size = 2.04 \begin {gather*} x+\frac {x^{\frac {2\,x\,\mathrm {e}}{x\,\ln \left (x\right )+x^2}}\,x^2\,{\mathrm {e}}^{\frac {50}{x\,\ln \left (x\right )+x^2}}\,{\mathrm {e}}^{\frac {2\,x^2\,\mathrm {e}}{x\,\ln \left (x\right )+x^2}}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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