Optimal. Leaf size=17 \[ \frac {1}{4} e^{25} \log (-4+4 x+\log (6 x)) \]
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Rubi [F]
time = 0.09, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {e^{25} (1+4 x)}{4 \left (-4 x+4 x^2+x \log (6 x)\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} e^{25} \int \frac {1+4 x}{-4 x+4 x^2+x \log (6 x)} \, dx\\ &=\frac {1}{4} e^{25} \int \left (\frac {4}{-4+4 x+\log (6 x)}+\frac {1}{x (-4+4 x+\log (6 x))}\right ) \, dx\\ &=\frac {1}{4} e^{25} \int \frac {1}{x (-4+4 x+\log (6 x))} \, dx+e^{25} \int \frac {1}{-4+4 x+\log (6 x)} \, dx\\ &=\frac {1}{4} e^{25} \int \frac {1}{x (-4+4 x+\log (6 x))} \, dx+\frac {1}{2} e^{25} \text {Subst}\left (\int \frac {1}{-4+2 x+\log (3 x)} \, dx,x,2 x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 19, normalized size = 1.12 \begin {gather*} \frac {1}{4} e^{25} \log (12-12 x-3 \log (6 x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 2.18, size = 17, normalized size = 1.00
method | result | size |
norman | \(\frac {\ln \left (\ln \left (6 x \right )+4 x -4\right ) {\mathrm e}^{25}}{4}\) | \(15\) |
risch | \(\frac {\ln \left (\ln \left (6 x \right )+4 x -4\right ) {\mathrm e}^{25}}{4}\) | \(15\) |
default | \(\frac {{\mathrm e}^{25} \ln \left (\ln \left (2\right )+\ln \left (3\right )+\ln \left (x \right )+4 x -4\right )}{4}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.53, size = 16, normalized size = 0.94 \begin {gather*} \frac {1}{4} \, e^{25} \log \left (4 \, x + \log \left (3\right ) + \log \left (2\right ) + \log \left (x\right ) - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 18, normalized size = 1.06 \begin {gather*} e^{\left (-2 \, \log \left (2\right ) + 25\right )} \log \left (4 \, x + \log \left (6 \, x\right ) - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 15, normalized size = 0.88 \begin {gather*} \frac {e^{25} \log {\left (4 x + \log {\left (6 x \right )} - 4 \right )}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 14, normalized size = 0.82 \begin {gather*} \frac {1}{4} \, e^{25} \log \left (4 \, x + \log \left (6\right ) + \log \left (x\right ) - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.57, size = 14, normalized size = 0.82 \begin {gather*} \frac {{\mathrm {e}}^{25}\,\ln \left (4\,x+\ln \left (6\,x\right )-4\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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