Optimal. Leaf size=24 \[ \frac {1}{x}-x+\frac {3-4 (-2+\log (5))+\log (x)}{4 x} \]
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Rubi [A]
time = 0.02, antiderivative size = 33, normalized size of antiderivative = 1.38, number of steps
used = 6, number of rules used = 3, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.136, Rules used = {12, 14, 2341}
\begin {gather*} -x+\frac {1}{4 x}+\frac {\log (x)}{4 x}+\frac {7-\log (25)}{2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2341
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {-14-4 x^2+4 \log (5)-\log (x)}{x^2} \, dx\\ &=\frac {1}{4} \int \left (-\frac {2 \left (7+2 x^2-2 \log (5)\right )}{x^2}-\frac {\log (x)}{x^2}\right ) \, dx\\ &=-\left (\frac {1}{4} \int \frac {\log (x)}{x^2} \, dx\right )-\frac {1}{2} \int \frac {7+2 x^2-2 \log (5)}{x^2} \, dx\\ &=\frac {1}{4 x}+\frac {\log (x)}{4 x}-\frac {1}{2} \int \left (2+\frac {7-2 \log (5)}{x^2}\right ) \, dx\\ &=\frac {1}{4 x}-x+\frac {7-\log (25)}{2 x}+\frac {\log (x)}{4 x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 24, normalized size = 1.00 \begin {gather*} \frac {15}{4 x}-x+\frac {\log \left (\frac {x}{625}\right )}{4 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 24, normalized size = 1.00
method | result | size |
default | \(-x +\frac {\ln \left (x \right )}{4 x}+\frac {15}{4 x}-\frac {\ln \left (5\right )}{x}\) | \(24\) |
risch | \(\frac {\ln \left (x \right )}{4 x}-\frac {4 x^{2}+4 \ln \left (5\right )-15}{4 x}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 23, normalized size = 0.96 \begin {gather*} -x - \frac {\log \left (5\right )}{x} + \frac {\log \left (x\right )}{4 \, x} + \frac {15}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.32, size = 20, normalized size = 0.83 \begin {gather*} -\frac {4 \, x^{2} + 4 \, \log \left (5\right ) - \log \left (x\right ) - 15}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 17, normalized size = 0.71 \begin {gather*} - x + \frac {\log {\left (x \right )}}{4 x} - \frac {-15 + 4 \log {\left (5 \right )}}{4 x} \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 = 0.92 \begin {gather*} -x - \frac {4 \, \log \left (5\right ) - 15}{4 \, x} + \frac {\log \left (x\right )}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.38, size = 18, normalized size = 0.75 \begin {gather*} \frac {\frac {\ln \left (x\right )}{4}-\ln \left (5\right )+\frac {15}{4}}{x}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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