Optimal. Leaf size=22 \[ x+\log \left (\frac {1}{5} \left (3+\frac {3}{e^3}-x+\log (5+\log (x))\right )\right ) \]
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Rubi [A]
time = 0.89, antiderivative size = 26, normalized size of antiderivative = 1.18, number of steps
used = 4, number of rules used = 3, integrand size = 118, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.025, Rules used = {6873, 6874,
6816} \begin {gather*} x+\log \left (-e^3 x+e^3 \log (\log (x)+5)+3 \left (1+e^3\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rule 6873
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {15 x+e^3 \left (1+10 x-5 x^2\right )+\left (3 x+e^3 \left (2 x-x^2\right )\right ) \log (x)+\left (5 e^3 x+e^3 x \log (x)\right ) \log (5+\log (x))}{x (5+\log (x)) \left (3 \left (1+e^3\right )-e^3 x+e^3 \log (5+\log (x))\right )} \, dx\\ &=\int \left (1+\frac {e^3 (1-5 x-x \log (x))}{x (5+\log (x)) \left (3 \left (1+e^3\right )-e^3 x+e^3 \log (5+\log (x))\right )}\right ) \, dx\\ &=x+e^3 \int \frac {1-5 x-x \log (x)}{x (5+\log (x)) \left (3 \left (1+e^3\right )-e^3 x+e^3 \log (5+\log (x))\right )} \, dx\\ &=x+\log \left (3 \left (1+e^3\right )-e^3 x+e^3 \log (5+\log (x))\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 25, normalized size = 1.14 \begin {gather*} x+\log \left (3+3 e^3-e^3 x+e^3 \log (5+\log (x))\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 3.77, size = 23, normalized size = 1.05
method | result | size |
default | \(x +\ln \left (x \,{\mathrm e}^{3}-{\mathrm e}^{3} \ln \left (5+\ln \left (x \right )\right )-3 \,{\mathrm e}^{3}-3\right )\) | \(23\) |
norman | \(x +\ln \left (x \,{\mathrm e}^{3}-{\mathrm e}^{3} \ln \left (5+\ln \left (x \right )\right )-3 \,{\mathrm e}^{3}-3\right )\) | \(23\) |
risch | \(x +\ln \left (\ln \left (5+\ln \left (x \right )\right )-\left (x \,{\mathrm e}^{3}-3 \,{\mathrm e}^{3}-3\right ) {\mathrm e}^{-3}\right )\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 26, normalized size = 1.18 \begin {gather*} x + \log \left (-{\left (x e^{3} - e^{3} \log \left (\log \left (x\right ) + 5\right ) - 3 \, e^{3} - 3\right )} e^{\left (-3\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 20, normalized size = 0.91 \begin {gather*} x + \log \left (-{\left (x - 3\right )} e^{3} + e^{3} \log \left (\log \left (x\right ) + 5\right ) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.16, size = 24, normalized size = 1.09 \begin {gather*} x + \log {\left (\frac {- x e^{3} + 3 + 3 e^{3}}{e^{3}} + \log {\left (\log {\left (x \right )} + 5 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 22, normalized size = 1.00 \begin {gather*} x + \log \left (-x e^{3} + e^{3} \log \left (\log \left (x\right ) + 5\right ) + 3 \, e^{3} + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.83, size = 17, normalized size = 0.77 \begin {gather*} x+\ln \left (3\,{\mathrm {e}}^{-3}-x+\ln \left (\ln \left (x\right )+5\right )+3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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