Optimal. Leaf size=26 \[ 2+\frac {1}{3} \left (-1+x \left (2+e^{5+x}+x-\log \left (\frac {x}{4}\right )\right )\right ) \]
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Rubi [A]
time = 0.02, antiderivative size = 45, normalized size of antiderivative = 1.73, number of steps
used = 5, number of rules used = 4, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {12, 2207, 2225,
2332} \begin {gather*} \frac {x^2}{3}+\frac {2 x}{3}-\frac {e^{x+5}}{3}+\frac {1}{3} e^{x+5} (x+1)-\frac {1}{3} x \log \left (\frac {x}{4}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2207
Rule 2225
Rule 2332
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \left (1+2 x+e^{5+x} (1+x)-\log \left (\frac {x}{4}\right )\right ) \, dx\\ &=\frac {x}{3}+\frac {x^2}{3}+\frac {1}{3} \int e^{5+x} (1+x) \, dx-\frac {1}{3} \int \log \left (\frac {x}{4}\right ) \, dx\\ &=\frac {2 x}{3}+\frac {x^2}{3}+\frac {1}{3} e^{5+x} (1+x)-\frac {1}{3} x \log \left (\frac {x}{4}\right )-\frac {1}{3} \int e^{5+x} \, dx\\ &=-\frac {e^{5+x}}{3}+\frac {2 x}{3}+\frac {x^2}{3}+\frac {1}{3} e^{5+x} (1+x)-\frac {1}{3} x \log \left (\frac {x}{4}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 27, normalized size = 1.04 \begin {gather*} \frac {1}{3} \left (2 x+e^{5+x} x+x^2+x \log (4)-x \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.33, size = 32, normalized size = 1.23
method | result | size |
norman | \(\frac {2 x}{3}+\frac {x^{2}}{3}+\frac {x \,{\mathrm e}^{5+x}}{3}-\frac {x \ln \left (\frac {x}{4}\right )}{3}\) | \(24\) |
risch | \(\frac {2 x}{3}+\frac {x^{2}}{3}+\frac {x \,{\mathrm e}^{5+x}}{3}-\frac {x \ln \left (\frac {x}{4}\right )}{3}\) | \(24\) |
default | \(\frac {x^{2}}{3}+\frac {2 x}{3}+\frac {{\mathrm e}^{5+x} \left (5+x \right )}{3}-\frac {5 \,{\mathrm e}^{5+x}}{3}-\frac {x \ln \left (\frac {x}{4}\right )}{3}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 23, normalized size = 0.88 \begin {gather*} \frac {1}{3} \, x^{2} + \frac {1}{3} \, x e^{\left (x + 5\right )} - \frac {1}{3} \, x \log \left (\frac {1}{4} \, x\right ) + \frac {2}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 23, normalized size = 0.88 \begin {gather*} \frac {1}{3} \, x^{2} + \frac {1}{3} \, x e^{\left (x + 5\right )} - \frac {1}{3} \, x \log \left (\frac {1}{4} \, x\right ) + \frac {2}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 26, normalized size = 1.00 \begin {gather*} \frac {x^{2}}{3} + \frac {x e^{x + 5}}{3} - \frac {x \log {\left (\frac {x}{4} \right )}}{3} + \frac {2 x}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 23, normalized size = 0.88 \begin {gather*} \frac {1}{3} \, x^{2} + \frac {1}{3} \, x e^{\left (x + 5\right )} - \frac {1}{3} \, x \log \left (\frac {1}{4} \, x\right ) + \frac {2}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.79, size = 16, normalized size = 0.62 \begin {gather*} \frac {x\,\left (x+{\mathrm {e}}^{x+5}-\ln \left (\frac {x}{4}\right )+2\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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