Optimal. Leaf size=21 \[ \frac {9}{(4+x)^2 \left (-5-e^9+x\right )^2 \log ^2(5)} \]
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Rubi [B] time = 0.15, antiderivative size = 83, normalized size of antiderivative = 3.95, number of steps used = 3, number of rules used = 2, integrand size = 117, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {12, 2074} \begin {gather*} \frac {18}{\left (9+e^9\right )^3 (x+4) \log ^2(5)}+\frac {9}{\left (9+e^9\right )^2 (x+4)^2 \log ^2(5)}+\frac {18}{\left (9+e^9\right )^3 \left (-x+e^9+5\right ) \log ^2(5)}+\frac {9}{\left (9+e^9\right )^2 \left (-x+e^9+5\right )^2 \log ^2(5)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-18-18 e^9+36 x}{8000+1200 x-1140 x^2-119 x^3+57 x^4+3 x^5-x^6+e^{27} \left (64+48 x+12 x^2+x^3\right )+e^{18} \left (960+528 x+36 x^2-21 x^3-3 x^4\right )+e^9 \left (4800+1680 x-348 x^2-141 x^3+6 x^4+3 x^5\right )} \, dx}{\log ^2(5)}\\ &=\frac {\int \left (\frac {18}{\left (9+e^9\right )^2 \left (5+e^9-x\right )^3}+\frac {18}{\left (9+e^9\right )^3 \left (5+e^9-x\right )^2}-\frac {18}{\left (9+e^9\right )^2 (4+x)^3}-\frac {18}{\left (9+e^9\right )^3 (4+x)^2}\right ) \, dx}{\log ^2(5)}\\ &=\frac {9}{\left (9+e^9\right )^2 \left (5+e^9-x\right )^2 \log ^2(5)}+\frac {18}{\left (9+e^9\right )^3 \left (5+e^9-x\right ) \log ^2(5)}+\frac {9}{\left (9+e^9\right )^2 (4+x)^2 \log ^2(5)}+\frac {18}{\left (9+e^9\right )^3 (4+x) \log ^2(5)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 23, normalized size = 1.10 \begin {gather*} \frac {9}{\left (20+x-x^2+e^9 (4+x)\right )^2 \log ^2(5)} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.73, size = 54, normalized size = 2.57 \begin {gather*} \frac {9}{{\left (x^{4} - 2 \, x^{3} - 39 \, x^{2} + {\left (x^{2} + 8 \, x + 16\right )} e^{18} - 2 \, {\left (x^{3} + 3 \, x^{2} - 24 \, x - 80\right )} e^{9} + 40 \, x + 400\right )} \log \relax (5)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.20, size = 21, normalized size = 1.00
method | result | size |
norman | \(\frac {9}{\ln \relax (5)^{2} \left (4+x \right )^{2} \left (-x +{\mathrm e}^{9}+5\right )^{2}}\) | \(21\) |
risch | \(\frac {9}{\ln \relax (5)^{2} \left (x^{2} {\mathrm e}^{18}-2 \,{\mathrm e}^{9} x^{3}+x^{4}+8 \,{\mathrm e}^{18} x -6 x^{2} {\mathrm e}^{9}-2 x^{3}+16 \,{\mathrm e}^{18}+48 x \,{\mathrm e}^{9}-39 x^{2}+160 \,{\mathrm e}^{9}+40 x +400\right )}\) | \(65\) |
gosper | \(\frac {9}{\ln \relax (5)^{2} \left (x^{2} {\mathrm e}^{18}-2 \,{\mathrm e}^{9} x^{3}+x^{4}+8 \,{\mathrm e}^{18} x -6 x^{2} {\mathrm e}^{9}-2 x^{3}+16 \,{\mathrm e}^{18}+48 x \,{\mathrm e}^{9}-39 x^{2}+160 \,{\mathrm e}^{9}+40 x +400\right )}\) | \(71\) |
default | \(\frac {-\frac {6 \left (\munderset {\textit {\_R} =\RootOf \left (\textit {\_Z}^{3}+\left (-3 \,{\mathrm e}^{9}-15\right ) \textit {\_Z}^{2}+\left (30 \,{\mathrm e}^{9}+3 \,{\mathrm e}^{18}+75\right ) \textit {\_Z} -75 \,{\mathrm e}^{9}-{\mathrm e}^{27}-15 \,{\mathrm e}^{18}-125\right )}{\sum }\frac {\left (7440174-531441 \textit {\_R} +6022998 \,{\mathrm e}^{9}-354294 \textit {\_R} \,{\mathrm e}^{9}+46170 \,{\mathrm e}^{36}-54 \textit {\_R} \,{\mathrm e}^{45}-{\mathrm e}^{54} \textit {\_R} -1215 \,{\mathrm e}^{36} \textit {\_R} +2086398 \,{\mathrm e}^{18}-98415 \,{\mathrm e}^{18} \textit {\_R} +400950 \,{\mathrm e}^{27}-14580 \textit {\_R} \,{\mathrm e}^{27}+3186 \,{\mathrm e}^{45}+2 \,{\mathrm e}^{63}+122 \,{\mathrm e}^{54}\right ) \ln \left (x -\textit {\_R} \right )}{25-2 \textit {\_R} \,{\mathrm e}^{9}+\textit {\_R}^{2}+10 \,{\mathrm e}^{9}+{\mathrm e}^{18}-10 \textit {\_R}}\right )}{\left (729+243 \,{\mathrm e}^{9}+27 \,{\mathrm e}^{18}+{\mathrm e}^{27}\right )^{3}}-\frac {18 \left (-354294 \,{\mathrm e}^{9}-1215 \,{\mathrm e}^{36}-54 \,{\mathrm e}^{45}-{\mathrm e}^{54}-14580 \,{\mathrm e}^{27}-98415 \,{\mathrm e}^{18}-531441\right )}{\left (729+243 \,{\mathrm e}^{9}+27 \,{\mathrm e}^{18}+{\mathrm e}^{27}\right )^{3} \left (4+x \right )}-\frac {9 \left (-3720087 \,{\mathrm e}^{9}-25515 \,{\mathrm e}^{36}-1701 \,{\mathrm e}^{45}-63 \,{\mathrm e}^{54}-229635 \,{\mathrm e}^{27}-1240029 \,{\mathrm e}^{18}-{\mathrm e}^{63}-4782969\right )}{\left (729+243 \,{\mathrm e}^{9}+27 \,{\mathrm e}^{18}+{\mathrm e}^{27}\right )^{3} \left (4+x \right )^{2}}}{\ln \relax (5)^{2}}\) | \(256\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.35, size = 53, normalized size = 2.52 \begin {gather*} \frac {9}{{\left (x^{4} - 2 \, x^{3} {\left (e^{9} + 1\right )} + x^{2} {\left (e^{18} - 6 \, e^{9} - 39\right )} + 8 \, x {\left (e^{18} + 6 \, e^{9} + 5\right )} + 16 \, e^{18} + 160 \, e^{9} + 400\right )} \log \relax (5)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.44, size = 78, normalized size = 3.71 \begin {gather*} \frac {9}{{\ln \relax (5)}^2\,{\left ({\mathrm {e}}^9+9\right )}^2\,{\left (x+4\right )}^2}+\frac {18}{{\ln \relax (5)}^2\,{\left ({\mathrm {e}}^9+9\right )}^3\,\left (x+4\right )}+\frac {9\,\left (3\,{\mathrm {e}}^9-2\,x+19\right )}{{\ln \relax (5)}^2\,{\left ({\mathrm {e}}^9+9\right )}^3\,\left (x^2+\left (-2\,{\mathrm {e}}^9-10\right )\,x+10\,{\mathrm {e}}^9+{\mathrm {e}}^{18}+25\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.28, size = 116, normalized size = 5.52 \begin {gather*} \frac {9}{x^{4} \log {\relax (5 )}^{2} + x^{3} \left (- 2 e^{9} \log {\relax (5 )}^{2} - 2 \log {\relax (5 )}^{2}\right ) + x^{2} \left (- 6 e^{9} \log {\relax (5 )}^{2} - 39 \log {\relax (5 )}^{2} + e^{18} \log {\relax (5 )}^{2}\right ) + x \left (40 \log {\relax (5 )}^{2} + 48 e^{9} \log {\relax (5 )}^{2} + 8 e^{18} \log {\relax (5 )}^{2}\right ) + 400 \log {\relax (5 )}^{2} + 160 e^{9} \log {\relax (5 )}^{2} + 16 e^{18} \log {\relax (5 )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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