Optimal. Leaf size=19 \[ -3+x+3 \left (x+800 x^2 \left (e^x+x\right )\right ) \log (5) \]
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Rubi [A]
time = 0.04, antiderivative size = 24, normalized size of antiderivative = 1.26, number of steps
used = 10, number of rules used = 4, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.148, Rules used = {1607, 2227,
2207, 2225} \begin {gather*} 2400 x^3 \log (5)+2400 e^x x^2 \log (5)+x+3 x \log (5) \end {gather*}
Antiderivative was successfully verified.
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Rule 1607
Rule 2207
Rule 2225
Rule 2227
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+\log (5) \int e^x \left (4800 x+2400 x^2\right ) \, dx+\log (5) \int \left (3+7200 x^2\right ) \, dx\\ &=x+3 x \log (5)+2400 x^3 \log (5)+\log (5) \int e^x x (4800+2400 x) \, dx\\ &=x+3 x \log (5)+2400 x^3 \log (5)+\log (5) \int \left (4800 e^x x+2400 e^x x^2\right ) \, dx\\ &=x+3 x \log (5)+2400 x^3 \log (5)+(2400 \log (5)) \int e^x x^2 \, dx+(4800 \log (5)) \int e^x x \, dx\\ &=x+3 x \log (5)+4800 e^x x \log (5)+2400 e^x x^2 \log (5)+2400 x^3 \log (5)-(4800 \log (5)) \int e^x \, dx-(4800 \log (5)) \int e^x x \, dx\\ &=x-4800 e^x \log (5)+3 x \log (5)+2400 e^x x^2 \log (5)+2400 x^3 \log (5)+(4800 \log (5)) \int e^x \, dx\\ &=x+3 x \log (5)+2400 e^x x^2 \log (5)+2400 x^3 \log (5)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 24, normalized size = 1.26 \begin {gather*} x+3 x \log (5)+2400 e^x x^2 \log (5)+2400 x^3 \log (5) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 24, normalized size = 1.26
method | result | size |
default | \(x +2400 x^{3} \ln \left (5\right )+3 x \ln \left (5\right )+2400 x^{2} \ln \left (5\right ) {\mathrm e}^{x}\) | \(24\) |
risch | \(x +2400 x^{3} \ln \left (5\right )+3 x \ln \left (5\right )+2400 x^{2} \ln \left (5\right ) {\mathrm e}^{x}\) | \(24\) |
norman | \(\left (3 \ln \left (5\right )+1\right ) x +2400 x^{3} \ln \left (5\right )+2400 x^{2} \ln \left (5\right ) {\mathrm e}^{x}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 22, normalized size = 1.16 \begin {gather*} 2400 \, x^{2} e^{x} \log \left (5\right ) + 3 \, {\left (800 \, x^{3} + x\right )} \log \left (5\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.30, size = 22, normalized size = 1.16 \begin {gather*} 2400 \, x^{2} e^{x} \log \left (5\right ) + 3 \, {\left (800 \, x^{3} + x\right )} \log \left (5\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 27, normalized size = 1.42 \begin {gather*} 2400 x^{3} \log {\left (5 \right )} + 2400 x^{2} e^{x} \log {\left (5 \right )} + x \left (1 + 3 \log {\left (5 \right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 22, normalized size = 1.16 \begin {gather*} 2400 \, x^{2} e^{x} \log \left (5\right ) + 3 \, {\left (800 \, x^{3} + x\right )} \log \left (5\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.14, size = 23, normalized size = 1.21 \begin {gather*} x\,\left (\ln \left (125\right )+1\right )+2400\,x^3\,\ln \left (5\right )+2400\,x^2\,{\mathrm {e}}^x\,\ln \left (5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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