Optimal. Leaf size=18 \[ -3+\frac {\left (3+e^{-1+e^3+x}\right ) x}{\log (75)} \]
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Rubi [B] time = 0.02, antiderivative size = 38, normalized size of antiderivative = 2.11, number of steps used = 4, number of rules used = 3, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {12, 2176, 2194} \begin {gather*} \frac {3 x}{\log (75)}-\frac {e^{x+e^3-1}}{\log (75)}+\frac {e^{x+e^3-1} (x+1)}{\log (75)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2176
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (3+e^{-1+e^3+x} (1+x)\right ) \, dx}{\log (75)}\\ &=\frac {3 x}{\log (75)}+\frac {\int e^{-1+e^3+x} (1+x) \, dx}{\log (75)}\\ &=\frac {3 x}{\log (75)}+\frac {e^{-1+e^3+x} (1+x)}{\log (75)}-\frac {\int e^{-1+e^3+x} \, dx}{\log (75)}\\ &=-\frac {e^{-1+e^3+x}}{\log (75)}+\frac {3 x}{\log (75)}+\frac {e^{-1+e^3+x} (1+x)}{\log (75)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 1.06 \begin {gather*} \frac {3 x+e^{-1+e^3+x} x}{\log (75)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.35, size = 17, normalized size = 0.94 \begin {gather*} \frac {x e^{\left (x + e^{3} - 1\right )} + 3 \, x}{\log \left (75\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 17, normalized size = 0.94 \begin {gather*} \frac {x e^{\left (x + e^{3} - 1\right )} + 3 \, x}{\log \left (75\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 21, normalized size = 1.17
method | result | size |
norman | \(\frac {x \,{\mathrm e}^{{\mathrm e}^{3}+x -1}}{\ln \left (75\right )}+\frac {3 x}{\ln \left (75\right )}\) | \(21\) |
risch | \(\frac {{\mathrm e}^{{\mathrm e}^{3}+x -1} x}{\ln \relax (3)+2 \ln \relax (5)}+\frac {3 x}{\ln \relax (3)+2 \ln \relax (5)}\) | \(31\) |
default | \(\frac {3 x +{\mathrm e}^{{\mathrm e}^{3}+x -1} \left ({\mathrm e}^{3}+x -1\right )+{\mathrm e}^{{\mathrm e}^{3}+x -1}-{\mathrm e}^{{\mathrm e}^{3}+x -1} {\mathrm e}^{3}}{\ln \left (75\right )}\) | \(38\) |
derivativedivides | \(\frac {3 \,{\mathrm e}^{3}+3 x -3+{\mathrm e}^{{\mathrm e}^{3}+x -1} \left ({\mathrm e}^{3}+x -1\right )+{\mathrm e}^{{\mathrm e}^{3}+x -1}-{\mathrm e}^{{\mathrm e}^{3}+x -1} {\mathrm e}^{3}}{\ln \left (75\right )}\) | \(43\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 31, normalized size = 1.72 \begin {gather*} \frac {{\left (x e^{\left (e^{3}\right )} - e^{\left (e^{3}\right )}\right )} e^{\left (x - 1\right )} + 3 \, x + e^{\left (x + e^{3} - 1\right )}}{\log \left (75\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.74, size = 19, normalized size = 1.06 \begin {gather*} \frac {x\,{\mathrm {e}}^{-1}\,\left (3\,\mathrm {e}+{\mathrm {e}}^{{\mathrm {e}}^3}\,{\mathrm {e}}^x\right )}{\ln \left (75\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 19, normalized size = 1.06 \begin {gather*} \frac {x e^{x - 1 + e^{3}}}{\log {\left (75 \right )}} + \frac {3 x}{\log {\left (75 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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