Optimal. Leaf size=15 \[ x \left (7+x+\frac {4}{\left (10+e^3+x\right )^2}\right ) \]
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Rubi [B] time = 0.11, antiderivative size = 32, normalized size of antiderivative = 2.13, number of steps used = 2, number of rules used = 1, integrand size = 104, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.010, Rules used = {2074} \begin {gather*} x^2+7 x+\frac {4}{x+e^3+10}-\frac {4 \left (10+e^3\right )}{\left (x+e^3+10\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (7+2 x+\frac {8 \left (10+e^3\right )}{\left (10+e^3+x\right )^3}-\frac {4}{\left (10+e^3+x\right )^2}\right ) \, dx\\ &=7 x+x^2-\frac {4 \left (10+e^3\right )}{\left (10+e^3+x\right )^2}+\frac {4}{10+e^3+x}\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.04, size = 48, normalized size = 3.20 \begin {gather*} -\frac {4 \left (10+e^3\right )}{\left (10+e^3+x\right )^2}+\frac {4}{10+e^3+x}+\left (-13-2 e^3\right ) \left (10+e^3+x\right )+\left (10+e^3+x\right )^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.68, size = 63, normalized size = 4.20 \begin {gather*} \frac {x^{4} + 27 \, x^{3} + 240 \, x^{2} + {\left (x^{2} + 7 \, x\right )} e^{6} + 2 \, {\left (x^{3} + 17 \, x^{2} + 70 \, x\right )} e^{3} + 704 \, x}{x^{2} + 2 \, {\left (x + 10\right )} e^{3} + 20 \, x + e^{6} + 100} \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*} \int \frac {2 \, x^{4} + 67 \, x^{3} + 810 \, x^{2} + {\left (2 \, x + 7\right )} e^{9} + 3 \, {\left (2 \, x^{2} + 27 \, x + 70\right )} e^{6} + {\left (6 \, x^{3} + 141 \, x^{2} + 1020 \, x + 2104\right )} e^{3} + 4096 \, x + 7040}{x^{3} + 30 \, x^{2} + 3 \, {\left (x + 10\right )} e^{6} + 3 \, {\left (x^{2} + 20 \, x + 100\right )} e^{3} + 300 \, x + e^{9} + 1000}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.11, size = 32, normalized size = 2.13
method | result | size |
risch | \(x^{2}+7 x +\frac {4 x}{{\mathrm e}^{6}+2 x \,{\mathrm e}^{3}+x^{2}+20 \,{\mathrm e}^{3}+20 x +100}\) | \(32\) |
norman | \(\frac {x^{4}+\left (27+2 \,{\mathrm e}^{3}\right ) x^{3}-24000+\left (-2 \,{\mathrm e}^{9}-81 \,{\mathrm e}^{6}-1020 \,{\mathrm e}^{3}-4096\right ) x -{\mathrm e}^{12}-54 \,{\mathrm e}^{9}-1020 \,{\mathrm e}^{6}-8200 \,{\mathrm e}^{3}}{\left (10+{\mathrm e}^{3}+x \right )^{2}}\) | \(66\) |
default | \(7 x +x^{2}+\frac {4 \left (\munderset {\textit {\_R} =\RootOf \left (\textit {\_Z}^{3}+\left (3 \,{\mathrm e}^{3}+30\right ) \textit {\_Z}^{2}+\left (60 \,{\mathrm e}^{3}+3 \,{\mathrm e}^{6}+300\right ) \textit {\_Z} +300 \,{\mathrm e}^{3}+{\mathrm e}^{9}+30 \,{\mathrm e}^{6}+1000\right )}{\sum }\frac {\left (10-\textit {\_R} +{\mathrm e}^{3}\right ) \ln \left (x -\textit {\_R} \right )}{100+{\mathrm e}^{6}+2 \textit {\_R} \,{\mathrm e}^{3}+\textit {\_R}^{2}+20 \,{\mathrm e}^{3}+20 \textit {\_R}}\right )}{3}\) | \(86\) |
gosper | \(-\frac {{\mathrm e}^{12}+2 x \,{\mathrm e}^{9}-2 x^{3} {\mathrm e}^{3}-x^{4}+54 \,{\mathrm e}^{9}+81 x \,{\mathrm e}^{6}-27 x^{3}+1020 \,{\mathrm e}^{6}+1020 x \,{\mathrm e}^{3}+8200 \,{\mathrm e}^{3}+4096 x +24000}{{\mathrm e}^{6}+2 x \,{\mathrm e}^{3}+x^{2}+20 \,{\mathrm e}^{3}+20 x +100}\) | \(87\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.38, size = 30, normalized size = 2.00 \begin {gather*} x^{2} + 7 \, x + \frac {4 \, x}{x^{2} + 2 \, x {\left (e^{3} + 10\right )} + e^{6} + 20 \, e^{3} + 100} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.09, size = 31, normalized size = 2.07 \begin {gather*} 7\,x+\frac {4\,x}{x^2+\left (2\,{\mathrm {e}}^3+20\right )\,x+20\,{\mathrm {e}}^3+{\mathrm {e}}^6+100}+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.30, size = 31, normalized size = 2.07 \begin {gather*} x^{2} + 7 x + \frac {4 x}{x^{2} + x \left (20 + 2 e^{3}\right ) + 100 + 20 e^{3} + e^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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