Optimal. Leaf size=16 \[ -5+e^x+\frac {7 x}{3}+\log \left (\frac {12}{x}\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.81, number of steps
used = 6, number of rules used = 4, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 14, 2225,
45} \begin {gather*} \frac {7 x}{3}+e^x-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 45
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \frac {-3+7 x+3 e^x x}{x} \, dx\\ &=\frac {1}{3} \int \left (3 e^x+\frac {-3+7 x}{x}\right ) \, dx\\ &=\frac {1}{3} \int \frac {-3+7 x}{x} \, dx+\int e^x \, dx\\ &=e^x+\frac {1}{3} \int \left (7-\frac {3}{x}\right ) \, dx\\ &=e^x+\frac {7 x}{3}-\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 13, normalized size = 0.81 \begin {gather*} e^x+\frac {7 x}{3}-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 11, normalized size = 0.69
method | result | size |
default | \(\frac {7 x}{3}-\ln \left (x \right )+{\mathrm e}^{x}\) | \(11\) |
norman | \(\frac {7 x}{3}-\ln \left (x \right )+{\mathrm e}^{x}\) | \(11\) |
risch | \(\frac {7 x}{3}-\ln \left (x \right )+{\mathrm e}^{x}\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 10, normalized size = 0.62 \begin {gather*} \frac {7}{3} \, x + e^{x} - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 10, normalized size = 0.62 \begin {gather*} \frac {7}{3} \, x + e^{x} - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 10, normalized size = 0.62 \begin {gather*} \frac {7 x}{3} + e^{x} - \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 10, normalized size = 0.62 \begin {gather*} \frac {7}{3} \, x + e^{x} - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 10, normalized size = 0.62 \begin {gather*} \frac {7\,x}{3}+{\mathrm {e}}^x-\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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