Optimal. Leaf size=24 \[ 5 e^{-\left (\frac {5}{x}-9 (-5+x-\log (9))\right )^2} x \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(60\) vs. \(2(24)=48\).
time = 2.53, antiderivative size = 60, normalized size of antiderivative = 2.50, number of steps
used = 1, number of rules used = 1, integrand size = 94, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.011, Rules used = {6838}
\begin {gather*} 5\ 9^{-\frac {-162 x^3+810 x^2+90 x}{x^2}} x \exp \left (-\frac {81 x^4-810 x^3+1935 x^2+81 x^2 \log ^2(9)+450 x+25}{x^2}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=5\ 9^{-\frac {90 x+810 x^2-162 x^3}{x^2}} \exp \left (-\frac {25+450 x+1935 x^2-810 x^3+81 x^4+81 x^2 \log ^2(9)}{x^2}\right ) x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 2.52, size = 43, normalized size = 1.79 \begin {gather*} 5\ 9^{-810-\frac {90}{x}+162 x} e^{-1935-\frac {25}{x^2}-\frac {450}{x}+810 x-81 x^2-81 \log ^2(9)} 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. \(60\) vs.
\(2(24)=48\).
time = 0.32, size = 61, normalized size = 2.54
method | result | size |
norman | \({\mathrm e}^{\frac {x^{2} \ln \left (5 x \right )-324 x^{2} \ln \left (3\right )^{2}+2 \left (162 x^{3}-810 x^{2}-90 x \right ) \ln \left (3\right )-81 x^{4}+810 x^{3}-1935 x^{2}-450 x -25}{x^{2}}}\) | \(61\) |
gosper | \({\mathrm e}^{-\frac {324 x^{2} \ln \left (3\right )^{2}-324 x^{3} \ln \left (3\right )+81 x^{4}+1620 x^{2} \ln \left (3\right )-x^{2} \ln \left (5 x \right )-810 x^{3}+180 x \ln \left (3\right )+1935 x^{2}+450 x +25}{x^{2}}}\) | \(64\) |
risch | \({\mathrm e}^{-\frac {324 x^{2} \ln \left (3\right )^{2}-324 x^{3} \ln \left (3\right )+81 x^{4}+1620 x^{2} \ln \left (3\right )-x^{2} \ln \left (5 x \right )-810 x^{3}+180 x \ln \left (3\right )+1935 x^{2}+450 x +25}{x^{2}}}\) | \(64\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.63, size = 42, normalized size = 1.75 \begin {gather*} \frac {5}{86383867871673826572978861593354619709321595508485014582990287188689462436872226650900170661043350993254637605029418092439720229755340868074170726301296321390097307188788479519139587964183142500321482377189328775881269326610028276279072547253461228924104664935801001522070992979234927439187840707470959385793060329379283707416545532751864980334662263108134935239462783872941285026598053272563292621639606298708727433962291991485280632308262684517754816475945148403472812657381733225002421264581883968002061218385871956150848906843214599207272427063929382671957896693499203116961768099411781704649236073764630307296619390810063699878410370621965032638363273868287001907848035975577147151105611174978197441983851555485552229411876067486755845380695890336993315151043395936401} \, x e^{\left (-81 \, x^{2} + 324 \, x \log \left (3\right ) - 324 \, \log \left (3\right )^{2} + 810 \, x - \frac {180 \, \log \left (3\right )}{x} - \frac {450}{x} - \frac {25}{x^{2}} - 1935\right )} \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 = 0.46, size = 62, normalized size = 2.58 \begin {gather*} e^{\left (-\frac {81 \, x^{4} + 324 \, x^{2} \log \left (3\right )^{2} - 810 \, x^{3} - x^{2} \log \left (5 \, x\right ) + 1935 \, x^{2} - 36 \, {\left (9 \, x^{3} - 45 \, x^{2} - 5 \, x\right )} \log \left (3\right ) + 450 \, x + 25}{x^{2}}\right )} \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. 60 vs.
\(2 (19) = 38\).
time = 0.25, size = 60, normalized size = 2.50 \begin {gather*} e^{\frac {- 81 x^{4} + 810 x^{3} + x^{2} \log {\left (5 x \right )} - 1935 x^{2} - 324 x^{2} \log {\left (3 \right )}^{2} - 450 x + \left (324 x^{3} - 1620 x^{2} - 180 x\right ) \log {\left (3 \right )} - 25}{x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 47, normalized size = 1.96 \begin {gather*} e^{\left (-81 \, x^{2} + 324 \, x \log \left (3\right ) - 324 \, \log \left (3\right )^{2} + 810 \, x - \frac {180 \, \log \left (3\right )}{x} - \frac {450}{x} - \frac {25}{x^{2}} - 1620 \, \log \left (3\right ) + \log \left (5 \, x\right ) - 1935\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.07, size = 48, normalized size = 2.00 \begin {gather*} \frac {5\,3^{324\,x}\,x\,{\mathrm {e}}^{810\,x}\,{\mathrm {e}}^{-1935}\,{\mathrm {e}}^{-324\,{\ln \left (3\right )}^2}\,{\mathrm {e}}^{-\frac {25}{x^2}}\,{\mathrm {e}}^{-81\,x^2}\,{\mathrm {e}}^{-\frac {450}{x}}}{86383867871673826572978861593354619709321595508485014582990287188689462436872226650900170661043350993254637605029418092439720229755340868074170726301296321390097307188788479519139587964183142500321482377189328775881269326610028276279072547253461228924104664935801001522070992979234927439187840707470959385793060329379283707416545532751864980334662263108134935239462783872941285026598053272563292621639606298708727433962291991485280632308262684517754816475945148403472812657381733225002421264581883968002061218385871956150848906843214599207272427063929382671957896693499203116961768099411781704649236073764630307296619390810063699878410370621965032638363273868287001907848035975577147151105611174978197441983851555485552229411876067486755845380695890336993315151043395936401\,3^{180/x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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