Optimal. Leaf size=29 \[ e^9+\frac {5}{x}-\frac {1}{2} x (-x-(3-2 x) \log (2)+\log (5)) \]
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Rubi [A]
time = 0.02, antiderivative size = 28, normalized size of antiderivative = 0.97, number of steps
used = 3, number of rules used = 2, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.057, Rules used = {12, 14}
\begin {gather*} \frac {1}{2} x^2 (1-\log (4))+\frac {5}{x}+\frac {1}{2} x \log \left (\frac {8}{5}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \frac {-10+2 x^3+\left (3 x^2-4 x^3\right ) \log (2)-x^2 \log (5)}{x^2} \, dx\\ &=\frac {1}{2} \int \left (-\frac {10}{x^2}+2 x (1-\log (4))-\log (5) \left (1-\frac {\log (8)}{\log (5)}\right )\right ) \, dx\\ &=\frac {5}{x}+\frac {1}{2} x \log \left (\frac {8}{5}\right )+\frac {1}{2} x^2 (1-\log (4))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 31, normalized size = 1.07 \begin {gather*} \frac {5}{x}+\frac {x^2}{2}+\frac {1}{2} x \log \left (\frac {8}{5}\right )-\frac {1}{2} x^2 \log (4) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.22, size = 29, normalized size = 1.00
method | result | size |
default | \(-x^{2} \ln \left (2\right )-\frac {x \ln \left (5\right )}{2}+\frac {3 x \ln \left (2\right )}{2}+\frac {x^{2}}{2}+\frac {5}{x}\) | \(29\) |
risch | \(-x^{2} \ln \left (2\right )-\frac {x \ln \left (5\right )}{2}+\frac {3 x \ln \left (2\right )}{2}+\frac {x^{2}}{2}+\frac {5}{x}\) | \(29\) |
norman | \(\frac {5+\left (-\ln \left (2\right )+\frac {1}{2}\right ) x^{3}+\left (\frac {3 \ln \left (2\right )}{2}-\frac {\ln \left (5\right )}{2}\right ) x^{2}}{x}\) | \(30\) |
gosper | \(-\frac {2 x^{3} \ln \left (2\right )+x^{2} \ln \left (5\right )-3 x^{2} \ln \left (2\right )-x^{3}-10}{2 x}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 27, normalized size = 0.93 \begin {gather*} -\frac {1}{2} \, x^{2} {\left (2 \, \log \left (2\right ) - 1\right )} - \frac {1}{2} \, x {\left (\log \left (5\right ) - 3 \, \log \left (2\right )\right )} + \frac {5}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 32, normalized size = 1.10 \begin {gather*} \frac {x^{3} - x^{2} \log \left (5\right ) - {\left (2 \, x^{3} - 3 \, x^{2}\right )} \log \left (2\right ) + 10}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 26, normalized size = 0.90 \begin {gather*} \frac {x^{2} \cdot \left (1 - 2 \log {\left (2 \right )}\right )}{2} + \frac {x \left (- \log {\left (5 \right )} + 3 \log {\left (2 \right )}\right )}{2} + \frac {5}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 28, normalized size = 0.97 \begin {gather*} -x^{2} \log \left (2\right ) + \frac {1}{2} \, x^{2} - \frac {1}{2} \, x \log \left (5\right ) + \frac {3}{2} \, x \log \left (2\right ) + \frac {5}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.13, size = 22, normalized size = 0.76 \begin {gather*} \frac {5}{x}-x^2\,\left (\frac {\ln \left (16\right )}{4}-\frac {1}{2}\right )-\frac {x\,\ln \left (\frac {5}{8}\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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