Optimal. Leaf size=21 \[ e^{\frac {x^2 (4+\log (169))}{20 \log (50-x)}} \]
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Rubi [A]
time = 1.13, antiderivative size = 35, normalized size of antiderivative = 1.67, number of steps
used = 4, number of rules used = 4, integrand size = 83, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {6, 6873, 12,
6838} \begin {gather*} 13^{\frac {x^2}{10 \log (50-x)}} e^{\frac {x^2}{5 \log (50-x)}} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 6838
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {4 x^2+x^2 \log (169)}{20 \log (50-x)}} \left (x^2 (-4-\log (169))+\left (-400 x+8 x^2+\left (-100 x+2 x^2\right ) \log (169)\right ) \log (50-x)\right )}{(-1000+20 x) \log ^2(50-x)} \, dx\\ &=\int \frac {e^{\frac {x^2 (4+\log (169))}{20 \log (50-x)}} x (4+\log (169)) (x+100 \log (50-x)-2 x \log (50-x))}{(1000-20 x) \log ^2(50-x)} \, dx\\ &=(4+\log (169)) \int \frac {e^{\frac {x^2 (4+\log (169))}{20 \log (50-x)}} x (x+100 \log (50-x)-2 x \log (50-x))}{(1000-20 x) \log ^2(50-x)} \, dx\\ &=13^{\frac {x^2}{10 \log (50-x)}} e^{\frac {x^2}{5 \log (50-x)}}\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(48\) vs. \(2(21)=42\).
time = 0.16, size = 48, normalized size = 2.29 \begin {gather*} \frac {13^{\frac {x^2}{10 \log (50-x)}} e^{\frac {x^2}{5 \log (50-x)}} (4+\log (169))}{2 (2+\log (13))} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.46, size = 19, normalized size = 0.90
method | result | size |
risch | \({\mathrm e}^{\frac {x^{2} \left (\ln \left (13\right )+2\right )}{10 \ln \left (-x +50\right )}}\) | \(19\) |
norman | \({\mathrm e}^{\frac {2 x^{2} \ln \left (13\right )+4 x^{2}}{20 \ln \left (-x +50\right )}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 23, normalized size = 1.10 \begin {gather*} e^{\left (\frac {x^{2} \log \left (13\right ) + 2 \, x^{2}}{10 \, \log \left (-x + 50\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 30, normalized size = 1.43 \begin {gather*} e^{\left (\frac {x^{2} \log \left (13\right )}{10 \, \log \left (-x + 50\right )} + \frac {x^{2}}{5 \, \log \left (-x + 50\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.52, size = 23, normalized size = 1.10 \begin {gather*} {\mathrm {e}}^{\frac {x^2\,\ln \left (13\right )+2\,x^2}{10\,\ln \left (50-x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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