Optimal. Leaf size=25 \[ -x+\log \left (4 e^{20+e^{\log (5) \log (x)}-x} \log \left (x^2\right )\right ) \]
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Rubi [A]
time = 0.14, antiderivative size = 13, normalized size of antiderivative = 0.52, number of steps
used = 6, number of rules used = 5, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.152, Rules used = {6820, 2306, 30,
2339, 29} \begin {gather*} x^{\log (5)}+\log \left (\log \left (x^2\right )\right )-2 x \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 30
Rule 2306
Rule 2339
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2+\frac {5^{\log (x)} \log (5)}{x}+\frac {2}{x \log \left (x^2\right )}\right ) \, dx\\ &=-2 x+2 \int \frac {1}{x \log \left (x^2\right )} \, dx+\log (5) \int \frac {5^{\log (x)}}{x} \, dx\\ &=-2 x+\log (5) \int x^{-1+\log (5)} \, dx+\text {Subst}\left (\int \frac {1}{x} \, dx,x,\log \left (x^2\right )\right )\\ &=-2 x+x^{\log (5)}+\log \left (\log \left (x^2\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 13, normalized size = 0.52 \begin {gather*} 5^{\log (x)}-2 x+\log \left (\log \left (x^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.17, size = 16, normalized size = 0.64
method | result | size |
default | \(-2 x +{\mathrm e}^{\ln \left (5\right ) \ln \left (x \right )}+\ln \left (\ln \left (x^{2}\right )\right )\) | \(16\) |
norman | \(-2 x +{\mathrm e}^{\ln \left (5\right ) \ln \left (x \right )}+\ln \left (\ln \left (x^{2}\right )\right )\) | \(16\) |
risch | \(-2 x +\ln \left (\ln \left (x \right )-\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (\mathrm {csgn}\left (i x \right )^{2}-2 \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x \right )+\mathrm {csgn}\left (i x^{2}\right )^{2}\right )}{4}\right )+x^{\ln \left (5\right )}\) | \(55\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 15, normalized size = 0.60 \begin {gather*} -2 \, x + e^{\left (\log \left (5\right ) \log \left (x\right )\right )} + \log \left (\log \left (x^{2}\right )\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 = 0.52 \begin {gather*} -2 \, x + e^{\left (\log \left (5\right ) \log \left (x\right )\right )} + \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.27, size = 17, normalized size = 0.68 \begin {gather*} - 2 x + e^{\log {\left (5 \right )} \log {\left (x \right )}} + \log {\left (\log {\left (x^{2} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 15, normalized size = 0.60 \begin {gather*} -2 \, x + e^{\left (\log \left (5\right ) \log \left (x\right )\right )} + \log \left (\log \left (x^{2}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.81, size = 13, normalized size = 0.52 \begin {gather*} \ln \left (\ln \left (x^2\right )\right )-2\,x+x^{\ln \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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