Optimal. Leaf size=19 \[ \left (e^{5+\frac {x}{3}}+x+\log (625-x)\right )^2 \]
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Rubi [A] time = 0.25, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 79, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {6688, 12, 6686} \begin {gather*} \left (x+e^{\frac {x}{3}+5}+\log (625-x)\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (e^{5+\frac {x}{3}} (-625+x)+3 (-624+x)\right ) \left (-e^{5+\frac {x}{3}}-x-\log (625-x)\right )}{3 (625-x)} \, dx\\ &=\frac {2}{3} \int \frac {\left (e^{5+\frac {x}{3}} (-625+x)+3 (-624+x)\right ) \left (-e^{5+\frac {x}{3}}-x-\log (625-x)\right )}{625-x} \, dx\\ &=\left (e^{5+\frac {x}{3}}+x+\log (625-x)\right )^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 19, normalized size = 1.00 \begin {gather*} \left (e^{5+\frac {x}{3}}+x+\log (625-x)\right )^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.50, size = 43, normalized size = 2.26 \begin {gather*} x^{2} + 2 \, x e^{\left (\frac {1}{3} \, x + 5\right )} + 2 \, {\left (x + e^{\left (\frac {1}{3} \, x + 5\right )}\right )} \log \left (-x + 625\right ) + \log \left (-x + 625\right )^{2} + e^{\left (\frac {2}{3} \, x + 10\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.13, size = 50, normalized size = 2.63 \begin {gather*} x^{2} + 2 \, x e^{\left (\frac {1}{3} \, x + 5\right )} + 2 \, x \log \left (-x + 625\right ) + 2 \, e^{\left (\frac {1}{3} \, x + 5\right )} \log \left (-x + 625\right ) + \log \left (-x + 625\right )^{2} + e^{\left (\frac {2}{3} \, x + 10\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.29, size = 47, normalized size = 2.47
method | result | size |
risch | \(\ln \left (-x +625\right )^{2}+\left (2 x +2 \,{\mathrm e}^{\frac {x}{3}+5}\right ) \ln \left (-x +625\right )+x^{2}+2 \,{\mathrm e}^{\frac {x}{3}+5} x +{\mathrm e}^{\frac {2 x}{3}+10}\) | \(47\) |
norman | \(x^{2}+{\mathrm e}^{\frac {2 x}{3}+10}+\ln \left (-x +625\right )^{2}+2 \,{\mathrm e}^{\frac {x}{3}+5} x +2 \,{\mathrm e}^{\frac {x}{3}+5} \ln \left (-x +625\right )+2 \ln \left (-x +625\right ) x\) | \(53\) |
default | \(2 \,{\mathrm e}^{\frac {x}{3}+5} x +2 \,{\mathrm e}^{\frac {x}{3}+5} \ln \left (-x +625\right )+{\mathrm e}^{\frac {2 x}{3}+10}+x^{2}+1250 \ln \left (x -625\right )-2 \left (-x +625\right ) \ln \left (-x +625\right )+1250+\ln \left (-x +625\right )^{2}\) | \(64\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} x^{2} + 1248 \, e^{\frac {640}{3}} E_{1}\left (-\frac {1}{3} \, x + \frac {625}{3}\right ) - 625 \, \log \left (x - 625\right )^{2} + 2 \, {\left (x + 625 \, \log \left (x - 625\right )\right )} \log \left (-x + 625\right ) + 2 \, e^{\left (\frac {1}{3} \, x + 5\right )} \log \left (-x + 625\right ) - 624 \, \log \left (-x + 625\right )^{2} + e^{\left (\frac {2}{3} \, x + 10\right )} + \frac {2}{3} \, \int \frac {{\left (x^{2} e^{5} - 622 \, x e^{5} - 3 \, e^{5}\right )} e^{\left (\frac {1}{3} \, x\right )}}{x - 625}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.23, size = 46, normalized size = 2.42 \begin {gather*} {\mathrm {e}}^{\frac {2\,x}{3}+10}+{\ln \left (625-x\right )}^2+\ln \left (625-x\right )\,\left (2\,x+2\,{\mathrm {e}}^{\frac {x}{3}+5}\right )+2\,x\,{\mathrm {e}}^{\frac {x}{3}+5}+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.45, size = 42, normalized size = 2.21 \begin {gather*} x^{2} + 2 x \log {\left (625 - x \right )} + \left (2 x + 2 \log {\left (625 - x \right )}\right ) e^{\frac {x}{3} + 5} + e^{\frac {2 x}{3} + 10} + \log {\left (625 - x \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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