Optimal. Leaf size=20 \[ -\frac {1}{80} 3^{7+x^2} x^{-9-x^2} \]
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Rubi [F]
time = 0.48, 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}{80} 3^{5+x^2} x^{-10-x^2} \left (81+9 x^2+18 x^2 \log \left (\frac {x}{3}\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{80} \int 3^{5+x^2} x^{-10-x^2} \left (81+9 x^2+18 x^2 \log \left (\frac {x}{3}\right )\right ) \, dx\\ &=\frac {1}{80} \int 3^{7+x^2} x^{-10-x^2} \left (9+x^2+2 x^2 \log \left (\frac {x}{3}\right )\right ) \, dx\\ &=\frac {1}{80} \int \left (3^{9+x^2} x^{-10-x^2}+3^{7+x^2} x^{-8-x^2}+2\ 3^{7+x^2} x^{-8-x^2} \log \left (\frac {x}{3}\right )\right ) \, dx\\ &=\frac {1}{80} \int 3^{9+x^2} x^{-10-x^2} \, dx+\frac {1}{80} \int 3^{7+x^2} x^{-8-x^2} \, dx+\frac {1}{40} \int 3^{7+x^2} x^{-8-x^2} \log \left (\frac {x}{3}\right ) \, dx\\ &=\frac {1}{80} \int 3^{9+x^2} x^{-10-x^2} \, dx+\frac {1}{80} \int 3^{7+x^2} x^{-8-x^2} \, dx-\frac {1}{40} \int \frac {\int 3^{7+x^2} x^{-8-x^2} \, dx}{x} \, dx+\frac {1}{40} \log \left (\frac {x}{3}\right ) \int 3^{7+x^2} x^{-8-x^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.08, size = 20, normalized size = 1.00 \begin {gather*} -\frac {1}{80} 3^{7+x^2} x^{-9-x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.18, size = 17, normalized size = 0.85
method | result | size |
risch | \(-\frac {9 \left (\frac {x}{3}\right )^{-x^{2}-5}}{80 x^{4}}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.52, size = 20, normalized size = 1.00 \begin {gather*} -\frac {2187 \, e^{\left (x^{2} \log \left (3\right ) - x^{2} \log \left (x\right )\right )}}{80 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 16, normalized size = 0.80 \begin {gather*} -\frac {9}{80 \, \left (\frac {1}{3} \, x\right )^{x^{2} + 5} x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 19, normalized size = 0.95 \begin {gather*} - \frac {9 e^{- \left (x^{2} + 5\right ) \log {\left (\frac {x}{3} \right )}}}{80 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 14, normalized size = 0.70 \begin {gather*} -\frac {2187}{80 \, \left (\frac {1}{3} \, x\right )^{\left (x^{2}\right )} x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.29, size = 16, normalized size = 0.80 \begin {gather*} -\frac {2187\,3^{x^2}}{80\,x^{x^2+9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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