Optimal. Leaf size=21 \[ \log \left (10+e^{\frac {9}{\log (3 x+x \log (16))}}+3 x\right ) \]
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Rubi [A]
time = 0.24, antiderivative size = 19, normalized size of antiderivative = 0.90, number of steps
used = 3, number of rules used = 3, integrand size = 85, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.035, Rules used = {6820, 12, 6816}
\begin {gather*} \log \left (3 x+e^{\frac {9}{\log (x (3+\log (16)))}}+10\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6816
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 \left (-3 e^{\frac {9}{\log (x (3+\log (16)))}}+x \log ^2(x (3+\log (16)))\right )}{x \left (10+e^{\frac {9}{\log (x (3+\log (16)))}}+3 x\right ) \log ^2(x (3+\log (16)))} \, dx\\ &=3 \int \frac {-3 e^{\frac {9}{\log (x (3+\log (16)))}}+x \log ^2(x (3+\log (16)))}{x \left (10+e^{\frac {9}{\log (x (3+\log (16)))}}+3 x\right ) \log ^2(x (3+\log (16)))} \, dx\\ &=\log \left (10+e^{\frac {9}{\log (x (3+\log (16)))}}+3 x\right )\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(45\) vs. \(2(21)=42\).
time = 0.26, size = 45, normalized size = 2.14 \begin {gather*} \log \left (30+3 e^{\frac {9}{\log (x (3+\log (16)))}}+10 \log (16)+e^{\frac {9}{\log (x (3+\log (16)))}} \log (16)+3 x (3+\log (16))\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.26, size = 22, normalized size = 1.05
method | result | size |
norman | \(\ln \left ({\mathrm e}^{\frac {9}{\ln \left (4 x \ln \left (2\right )+3 x \right )}}+10+3 x \right )\) | \(22\) |
risch | \(\ln \left ({\mathrm e}^{\frac {9}{\ln \left (4 x \ln \left (2\right )+3 x \right )}}+10+3 x \right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.55, size = 21, normalized size = 1.00 \begin {gather*} \log \left (3 \, x + e^{\left (\frac {9}{\log \left (x\right ) + \log \left (4 \, \log \left (2\right ) + 3\right )}\right )} + 10\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 21, normalized size = 1.00 \begin {gather*} \log \left (3 \, x + e^{\left (\frac {9}{\log \left (4 \, x \log \left (2\right ) + 3 \, x\right )}\right )} + 10\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 20, normalized size = 0.95 \begin {gather*} \log {\left (3 x + e^{\frac {9}{\log {\left (4 x \log {\left (2 \right )} + 3 x \right )}}} + 10 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 21, normalized size = 1.00 \begin {gather*} \log \left (3 \, x + e^{\left (\frac {9}{\log \left (4 \, x \log \left (2\right ) + 3 \, x\right )}\right )} + 10\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.62, size = 18, normalized size = 0.86 \begin {gather*} \ln \left (x+\frac {{\mathrm {e}}^{\frac {9}{\ln \left (x\,\left (\ln \left (16\right )+3\right )\right )}}}{3}+\frac {10}{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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