Optimal. Leaf size=28 \[ e^{3-x+x^{-1+\frac {x}{5 (2-x)}}+9 x \log (x)} \]
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Rubi [F]
time = 9.36, 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^{\frac {3 x-x^2+x^{-\frac {x}{-10+5 x}}+9 x^2 \log (x)}{x}} \left (160 x^2-160 x^3+40 x^4+\left (180 x^2-180 x^3+45 x^4\right ) \log (x)+x^{-\frac {x}{-10+5 x}} \left (-20+22 x-6 x^2+2 x \log (x)\right )\right )}{20 x^2-20 x^3+5 x^4} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {3 x-x^2+x^{-\frac {x}{-10+5 x}}+9 x^2 \log (x)}{x}} \left (160 x^2-160 x^3+40 x^4+\left (180 x^2-180 x^3+45 x^4\right ) \log (x)+x^{-\frac {x}{-10+5 x}} \left (-20+22 x-6 x^2+2 x \log (x)\right )\right )}{x^2 \left (20-20 x+5 x^2\right )} \, dx\\ &=\int \frac {e^{\frac {3 x-x^2+x^{-\frac {x}{-10+5 x}}+9 x^2 \log (x)}{x}} \left (160 x^2-160 x^3+40 x^4+\left (180 x^2-180 x^3+45 x^4\right ) \log (x)+x^{-\frac {x}{-10+5 x}} \left (-20+22 x-6 x^2+2 x \log (x)\right )\right )}{5 (-2+x)^2 x^2} \, dx\\ &=\frac {1}{5} \int \frac {e^{\frac {3 x-x^2+x^{-\frac {x}{-10+5 x}}+9 x^2 \log (x)}{x}} \left (160 x^2-160 x^3+40 x^4+\left (180 x^2-180 x^3+45 x^4\right ) \log (x)+x^{-\frac {x}{-10+5 x}} \left (-20+22 x-6 x^2+2 x \log (x)\right )\right )}{(-2+x)^2 x^2} \, dx\\ &=\frac {1}{5} \int \frac {e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} \left (160 x^2-160 x^3+40 x^4+\left (180 x^2-180 x^3+45 x^4\right ) \log (x)+x^{-\frac {x}{-10+5 x}} \left (-20+22 x-6 x^2+2 x \log (x)\right )\right )}{(2-x)^2 x^2} \, dx\\ &=\frac {1}{5} \int \left (5 e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} (8+9 \log (x))-\frac {2 e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} x^{-2+\frac {x}{10-5 x}} \left (10-11 x+3 x^2-x \log (x)\right )}{(-2+x)^2}\right ) \, dx\\ &=-\left (\frac {2}{5} \int \frac {e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} x^{-2+\frac {x}{10-5 x}} \left (10-11 x+3 x^2-x \log (x)\right )}{(-2+x)^2} \, dx\right )+\int e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} (8+9 \log (x)) \, dx\\ &=-\left (\frac {2}{5} \int \left (\frac {e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} x^{-2+\frac {x}{10-5 x}} (-5+3 x)}{-2+x}-\frac {e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} x^{-1+\frac {x}{10-5 x}} \log (x)}{(-2+x)^2}\right ) \, dx\right )+\int \left (8 e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)}+9 e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} \log (x)\right ) \, dx\\ &=-\left (\frac {2}{5} \int \frac {e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} x^{-2+\frac {x}{10-5 x}} (-5+3 x)}{-2+x} \, dx\right )+\frac {2}{5} \int \frac {e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} x^{-1+\frac {x}{10-5 x}} \log (x)}{(-2+x)^2} \, dx+8 \int e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} \, dx+9 \int e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} \log (x) \, dx\\ &=-\left (\frac {2}{5} \int \left (3 e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} x^{-2+\frac {x}{10-5 x}}+\frac {e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} x^{-2+\frac {x}{10-5 x}}}{-2+x}\right ) \, dx\right )+\frac {2}{5} \int \frac {e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} x^{-1+\frac {x}{10-5 x}} \log (x)}{(-2+x)^2} \, dx+8 \int e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} \, dx+9 \int e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} \log (x) \, dx\\ &=-\left (\frac {2}{5} \int \frac {e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} x^{-2+\frac {x}{10-5 x}}}{-2+x} \, dx\right )+\frac {2}{5} \int \frac {e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} x^{-1+\frac {x}{10-5 x}} \log (x)}{(-2+x)^2} \, dx-\frac {6}{5} \int e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} x^{-2+\frac {x}{10-5 x}} \, dx+8 \int e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} \, dx+9 \int e^{3-x+x^{-1-\frac {x}{-10+5 x}}+9 x \log (x)} \log (x) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.20, size = 27, normalized size = 0.96 \begin {gather*} e^{3-x+x^{-1-\frac {x}{5 (-2+x)}}} x^{9 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 32, normalized size = 1.14
method | result | size |
risch | \(x^{9 x} {\mathrm e}^{-\frac {x^{2}-x^{-\frac {x}{5 \left (x -2\right )}}-3 x}{x}}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.47, size = 46, normalized size = 1.64 \begin {gather*} e^{\left (\frac {{\left (9 \, x^{2} \log \left (x\right ) - x^{2} + 3 \, x\right )} x^{\frac {x}{5 \, {\left (x - 2\right )}}} + 1}{x x^{\frac {x}{5 \, {\left (x - 2\right )}}}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.89, size = 31, normalized size = 1.11 \begin {gather*} e^{\frac {9 x^{2} \log {\left (x \right )} - x^{2} + 3 x + e^{- \frac {x \log {\left (x \right )}}{5 x - 10}}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [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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Mupad [B]
time = 0.69, size = 28, normalized size = 1.00 \begin {gather*} x^{9\,x}\,{\mathrm {e}}^{\frac {1}{x^{\frac {x}{5\,x-10}+1}}}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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