Optimal. Leaf size=20 \[ x+e^{2 x} x^2+\log \left (33+x+x^2+\log (x)\right ) \]
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Rubi [F] time = 0.66, 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 {1+34 x+3 x^2+x^3+e^{2 x} \left (66 x^2+68 x^3+4 x^4+2 x^5\right )+\left (x+e^{2 x} \left (2 x^2+2 x^3\right )\right ) \log (x)}{33 x+x^2+x^3+x \log (x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (2 e^{2 x} x (1+x)+\frac {34}{33+x+x^2+\log (x)}+\frac {1}{x \left (33+x+x^2+\log (x)\right )}+\frac {3 x}{33+x+x^2+\log (x)}+\frac {x^2}{33+x+x^2+\log (x)}+\frac {\log (x)}{33+x+x^2+\log (x)}\right ) \, dx\\ &=2 \int e^{2 x} x (1+x) \, dx+3 \int \frac {x}{33+x+x^2+\log (x)} \, dx+34 \int \frac {1}{33+x+x^2+\log (x)} \, dx+\int \frac {1}{x \left (33+x+x^2+\log (x)\right )} \, dx+\int \frac {x^2}{33+x+x^2+\log (x)} \, dx+\int \frac {\log (x)}{33+x+x^2+\log (x)} \, dx\\ &=2 \int \left (e^{2 x} x+e^{2 x} x^2\right ) \, dx+3 \int \frac {x}{33+x+x^2+\log (x)} \, dx+34 \int \frac {1}{33+x+x^2+\log (x)} \, dx+\int \frac {1}{x \left (33+x+x^2+\log (x)\right )} \, dx+\int \frac {x^2}{33+x+x^2+\log (x)} \, dx+\int \left (1+\frac {-33-x-x^2}{33+x+x^2+\log (x)}\right ) \, dx\\ &=x+2 \int e^{2 x} x \, dx+2 \int e^{2 x} x^2 \, dx+3 \int \frac {x}{33+x+x^2+\log (x)} \, dx+34 \int \frac {1}{33+x+x^2+\log (x)} \, dx+\int \frac {1}{x \left (33+x+x^2+\log (x)\right )} \, dx+\int \frac {x^2}{33+x+x^2+\log (x)} \, dx+\int \frac {-33-x-x^2}{33+x+x^2+\log (x)} \, dx\\ &=x+e^{2 x} x+e^{2 x} x^2-2 \int e^{2 x} x \, dx+3 \int \frac {x}{33+x+x^2+\log (x)} \, dx+34 \int \frac {1}{33+x+x^2+\log (x)} \, dx-\int e^{2 x} \, dx+\int \frac {1}{x \left (33+x+x^2+\log (x)\right )} \, dx+\int \frac {x^2}{33+x+x^2+\log (x)} \, dx+\int \left (-\frac {33}{33+x+x^2+\log (x)}-\frac {x}{33+x+x^2+\log (x)}-\frac {x^2}{33+x+x^2+\log (x)}\right ) \, dx\\ &=-\frac {e^{2 x}}{2}+x+e^{2 x} x^2+3 \int \frac {x}{33+x+x^2+\log (x)} \, dx-33 \int \frac {1}{33+x+x^2+\log (x)} \, dx+34 \int \frac {1}{33+x+x^2+\log (x)} \, dx+\int e^{2 x} \, dx+\int \frac {1}{x \left (33+x+x^2+\log (x)\right )} \, dx-\int \frac {x}{33+x+x^2+\log (x)} \, dx\\ &=x+e^{2 x} x^2+3 \int \frac {x}{33+x+x^2+\log (x)} \, dx-33 \int \frac {1}{33+x+x^2+\log (x)} \, dx+34 \int \frac {1}{33+x+x^2+\log (x)} \, dx+\int \frac {1}{x \left (33+x+x^2+\log (x)\right )} \, dx-\int \frac {x}{33+x+x^2+\log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.36, size = 20, normalized size = 1.00 \begin {gather*} x+e^{2 x} x^2+\log \left (33+x+x^2+\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 19, normalized size = 0.95 \begin {gather*} x^{2} e^{\left (2 \, x\right )} + x + \log \left (x^{2} + x + \log \relax (x) + 33\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 19, normalized size = 0.95 \begin {gather*} x^{2} e^{\left (2 \, x\right )} + x + \log \left (x^{2} + x + \log \relax (x) + 33\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 20, normalized size = 1.00
method | result | size |
risch | \(\ln \left (x +x^{2}+33+\ln \relax (x )\right )+{\mathrm e}^{2 x} x^{2}+x\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 19, normalized size = 0.95 \begin {gather*} x^{2} e^{\left (2 \, x\right )} + x + \log \left (x^{2} + x + \log \relax (x) + 33\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.17, size = 19, normalized size = 0.95 \begin {gather*} x+\ln \left (x+\ln \relax (x)+x^2+33\right )+x^2\,{\mathrm {e}}^{2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.39, size = 20, normalized size = 1.00 \begin {gather*} x^{2} e^{2 x} + x + \log {\left (x^{2} + x + \log {\relax (x )} + 33 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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