Optimal. Leaf size=19 \[ -1-x+\frac {3}{4} (2 x+x \log (4)+\log (x)) \]
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Rubi [A]
time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.84, number of steps
used = 4, number of rules used = 3, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.176, Rules used = {6, 12, 45}
\begin {gather*} \frac {1}{4} x (2+\log (64))+\frac {3 \log (x)}{4} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 45
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3+x (2+3 \log (4))}{4 x} \, dx\\ &=\frac {1}{4} \int \frac {3+x (2+3 \log (4))}{x} \, dx\\ &=\frac {1}{4} \int \left (2+\frac {3}{x}+\log (64)\right ) \, dx\\ &=\frac {1}{4} x (2+\log (64))+\frac {3 \log (x)}{4}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 15, normalized size = 0.79 \begin {gather*} \frac {1}{4} (x (2+\log (64))+3 \log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 6.19, size = 14, normalized size = 0.74
method | result | size |
default | \(\frac {3 x \ln \left (2\right )}{2}+\frac {x}{2}+\frac {3 \ln \left (x \right )}{4}\) | \(14\) |
norman | \(\left (\frac {3 \ln \left (2\right )}{2}+\frac {1}{2}\right ) x +\frac {3 \ln \left (x \right )}{4}\) | \(14\) |
risch | \(\frac {3 x \ln \left (2\right )}{2}+\frac {x}{2}+\frac {3 \ln \left (x \right )}{4}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 14, normalized size = 0.74 \begin {gather*} \frac {1}{2} \, x {\left (3 \, \log \left (2\right ) + 1\right )} + \frac {3}{4} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 13, normalized size = 0.68 \begin {gather*} \frac {3}{2} \, x \log \left (2\right ) + \frac {1}{2} \, x + \frac {3}{4} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 15, normalized size = 0.79 \begin {gather*} \frac {x \left (2 + 6 \log {\left (2 \right )}\right )}{4} + \frac {3 \log {\left (x \right )}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 14, normalized size = 0.74 \begin {gather*} \frac {3}{2} \, x \log \left (2\right ) + \frac {1}{2} \, x + \frac {3}{4} \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.36, size = 13, normalized size = 0.68 \begin {gather*} \frac {3\,\ln \left (x\right )}{4}+x\,\left (\frac {\ln \left (64\right )}{4}+\frac {1}{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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