Optimal. Leaf size=29 \[ e^{x^2}-\frac {x^2}{-x+\frac {x}{\log ^2(-30+x)}-\log (x)} \]
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Rubi [F]
time = 6.80, 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 {e^{x^2} \left (-60 x^3+2 x^4\right )-2 x^3 \log (-30+x)+\left (30 x^2-x^3+e^{x^2} \left (120 x^3-4 x^4\right )\right ) \log ^2(-30+x)+\left (30 x-31 x^2+x^3+e^{x^2} \left (-60 x^3+2 x^4\right )\right ) \log ^4(-30+x)+\left (e^{x^2} \left (120 x^2-4 x^3\right ) \log ^2(-30+x)+\left (-60 x+2 x^2+e^{x^2} \left (-120 x^2+4 x^3\right )\right ) \log ^4(-30+x)\right ) \log (x)+e^{x^2} \left (-60 x+2 x^2\right ) \log ^4(-30+x) \log ^2(x)}{-30 x^2+x^3+\left (60 x^2-2 x^3\right ) \log ^2(-30+x)+\left (-30 x^2+x^3\right ) \log ^4(-30+x)+\left (\left (60 x-2 x^2\right ) \log ^2(-30+x)+\left (-60 x+2 x^2\right ) \log ^4(-30+x)\right ) \log (x)+(-30+x) \log ^4(-30+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 \left (-2 e^{x^2} (-30+x) x^2+2 x^2 \log (-30+x)+(-30+x) x \log ^2(-30+x) \left (1+4 e^{x^2} x+4 e^{x^2} \log (x)\right )-(-30+x) \log ^4(-30+x) \left (-1+x+2 e^{x^2} x^2+\left (2+4 e^{x^2} x\right ) \log (x)+2 e^{x^2} \log ^2(x)\right )\right )}{(30-x) \left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx\\ &=\int \left (2 e^{x^2} x-\frac {2 x^3 \log (-30+x)}{(-30+x) \left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}-\frac {x^2 \log ^2(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}-\frac {x \log ^4(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}+\frac {x^2 \log ^4(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}+\frac {2 x \log ^4(-30+x) \log (x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}\right ) \, dx\\ &=2 \int e^{x^2} x \, dx-2 \int \frac {x^3 \log (-30+x)}{(-30+x) \left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx+2 \int \frac {x \log ^4(-30+x) \log (x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx-\int \frac {x^2 \log ^2(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx-\int \frac {x \log ^4(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx+\int \frac {x^2 \log ^4(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx\\ &=e^{x^2}-2 \int \frac {x^3 \log (-30+x)}{(-30+x) \left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+2 \int \frac {x \log ^4(-30+x) \log (x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x^2 \log ^2(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+\int \frac {x^2 \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx\\ &=e^{x^2}-2 \int \left (\frac {900 \log (-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}+\frac {27000 \log (-30+x)}{(-30+x) \left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}+\frac {30 x \log (-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}+\frac {x^2 \log (-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}\right ) \, dx+2 \int \left (-\frac {x^2 \log ^2(-30+x) \left (-1+\log ^2(-30+x)\right )}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}+\frac {x \log ^2(-30+x)}{-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)}\right ) \, dx-\int \frac {x^2 \log ^2(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+\int \frac {x^2 \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx\\ &=e^{x^2}-2 \int \frac {x^2 \log (-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx-2 \int \frac {x^2 \log ^2(-30+x) \left (-1+\log ^2(-30+x)\right )}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx+2 \int \frac {x \log ^2(-30+x)}{-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)} \, dx-60 \int \frac {x \log (-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx-1800 \int \frac {\log (-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx-54000 \int \frac {\log (-30+x)}{(-30+x) \left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx-\int \frac {x^2 \log ^2(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+\int \frac {x^2 \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx\\ &=e^{x^2}-2 \int \frac {x^2 \log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-2 \int \frac {x^2 \log ^2(-30+x) \left (-1+\log ^2(-30+x)\right )}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+2 \int \frac {x \log ^2(-30+x)}{-x+\log ^2(-30+x) (x+\log (x))} \, dx-60 \int \frac {x \log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-1800 \int \frac {\log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-54000 \int \frac {\log (-30+x)}{(-30+x) \left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x^2 \log ^2(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+\int \frac {x^2 \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx\\ &=e^{x^2}-2 \int \frac {x^2 \log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+2 \int \frac {x \log ^2(-30+x)}{-x+\log ^2(-30+x) (x+\log (x))} \, dx-2 \int \left (-\frac {x^2 \log ^2(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}+\frac {x^2 \log ^4(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}\right ) \, dx-60 \int \frac {x \log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-1800 \int \frac {\log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-54000 \int \frac {\log (-30+x)}{(-30+x) \left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x^2 \log ^2(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+\int \frac {x^2 \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx\\ &=e^{x^2}+2 \int \frac {x^2 \log ^2(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx-2 \int \frac {x^2 \log ^4(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx-2 \int \frac {x^2 \log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+2 \int \frac {x \log ^2(-30+x)}{-x+\log ^2(-30+x) (x+\log (x))} \, dx-60 \int \frac {x \log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-1800 \int \frac {\log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-54000 \int \frac {\log (-30+x)}{(-30+x) \left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x^2 \log ^2(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+\int \frac {x^2 \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx\\ &=e^{x^2}-2 \int \frac {x^2 \log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+2 \int \frac {x^2 \log ^2(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-2 \int \frac {x^2 \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+2 \int \frac {x \log ^2(-30+x)}{-x+\log ^2(-30+x) (x+\log (x))} \, dx-60 \int \frac {x \log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-1800 \int \frac {\log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-54000 \int \frac {\log (-30+x)}{(-30+x) \left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x^2 \log ^2(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+\int \frac {x^2 \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.13, size = 33, normalized size = 1.14 \begin {gather*} e^{x^2}+\frac {x^2 \log ^2(-30+x)}{-x+\log ^2(-30+x) (x+\log (x))} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(58\) vs.
\(2(28)=56\).
time = 0.48, size = 59, normalized size = 2.03
method | result | size |
risch | \(\frac {x^{2}+{\mathrm e}^{x^{2}} x +{\mathrm e}^{x^{2}} \ln \left (x \right )}{x +\ln \left (x \right )}+\frac {x^{3}}{\left (x +\ln \left (x \right )\right ) \left (\ln \left (x -30\right )^{2} \ln \left (x \right )+x \ln \left (x -30\right )^{2}-x \right )}\) | \(59\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 49 vs.
\(2 (24) = 48\).
time = 0.37, size = 49, normalized size = 1.69 \begin {gather*} \frac {x^{2} \log \left (x - 30\right )^{2} + {\left ({\left (x + \log \left (x\right )\right )} \log \left (x - 30\right )^{2} - x\right )} e^{\left (x^{2}\right )}}{{\left (x + \log \left (x\right )\right )} \log \left (x - 30\right )^{2} - x} \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. 62 vs.
\(2 (24) = 48\).
time = 0.36, size = 62, normalized size = 2.14 \begin {gather*} \frac {e^{\left (x^{2}\right )} \log \left (x - 30\right )^{2} \log \left (x\right ) + {\left (x^{2} + x e^{\left (x^{2}\right )}\right )} \log \left (x - 30\right )^{2} - x e^{\left (x^{2}\right )}}{x \log \left (x - 30\right )^{2} + \log \left (x - 30\right )^{2} \log \left (x\right ) - x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 46 vs.
\(2 (20) = 40\).
time = 0.45, size = 46, normalized size = 1.59 \begin {gather*} \frac {x^{3}}{- x^{2} - x \log {\left (x \right )} + \left (x^{2} + 2 x \log {\left (x \right )} + \log {\left (x \right )}^{2}\right ) \log {\left (x - 30 \right )}^{2}} + \frac {x^{2}}{x + \log {\left (x \right )}} + e^{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 67 vs.
\(2 (24) = 48\).
time = 0.66, size = 67, normalized size = 2.31 \begin {gather*} \frac {x^{2} \log \left (x - 30\right )^{2} + x e^{\left (x^{2}\right )} \log \left (x - 30\right )^{2} + e^{\left (x^{2}\right )} \log \left (x - 30\right )^{2} \log \left (x\right ) - x e^{\left (x^{2}\right )}}{x \log \left (x - 30\right )^{2} + \log \left (x - 30\right )^{2} \log \left (x\right ) - x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.17, size = 317, normalized size = 10.93 \begin {gather*} 2\,x+{\mathrm {e}}^{x^2}+\frac {2}{x+1}-\frac {\frac {x^2\,\left (x-1\right )}{x+1}+\frac {2\,x^2\,\ln \left (x\right )}{x+1}}{x+\ln \left (x\right )}+\frac {x^2\,{\left (30\,x-x^2\right )}^2\,\left (4\,x^4+12\,x^3\,\ln \left (x\right )+11\,x^2\,{\ln \left (x\right )}^2+2\,x^2\,\ln \left (x\right )-x^2+4\,x\,{\ln \left (x\right )}^3+60\,x\,{\ln \left (x\right )}^2-120\,x\,\ln \left (x\right )+60\,x-900\,{\ln \left (x\right )}^2+1800\,\ln \left (x\right )-900\right )}{\left (x-{\ln \left (x-30\right )}^2\,\left (x+\ln \left (x\right )\right )\right )\,\left (x-30\right )\,\left (-4\,x^7-16\,x^6\,\ln \left (x\right )+120\,x^6-23\,x^5\,{\ln \left (x\right )}^2+478\,x^5\,\ln \left (x\right )+x^5-15\,x^4\,{\ln \left (x\right )}^3+628\,x^4\,{\ln \left (x\right )}^2+181\,x^4\,\ln \left (x\right )-90\,x^4-4\,x^3\,{\ln \left (x\right )}^4+390\,x^3\,{\ln \left (x\right )}^3+2880\,x^3\,{\ln \left (x\right )}^2-5490\,x^3\,\ln \left (x\right )+2700\,x^3+120\,x^2\,{\ln \left (x\right )}^4+2700\,x^2\,{\ln \left (x\right )}^3-32400\,x^2\,{\ln \left (x\right )}^2+56700\,x^2\,\ln \left (x\right )-27000\,x^2-27000\,x\,{\ln \left (x\right )}^3+54000\,x\,{\ln \left (x\right )}^2-27000\,x\,\ln \left (x\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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