Optimal. Leaf size=21 \[ \left (4-\frac {x^2 \log (25) \log (x)}{16 \log ^2(4 x)}\right )^2 \]
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Rubi [A]
time = 0.29, antiderivative size = 39, normalized size of antiderivative = 1.86, number of steps
used = 5, number of rules used = 3, integrand size = 86, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.035, Rules used = {12, 6820, 6844}
\begin {gather*} \frac {x^4 \log ^2(25) \log ^2(x)}{256 \log ^4(4 x)}-\frac {x^2 \log (25) \log (x)}{2 \log ^2(4 x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6820
Rule 6844
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{128} \int \frac {-2 x^3 \log ^2(25) \log ^2(x)+\left (x^3 \log ^2(25) \log (x)+2 x^3 \log ^2(25) \log ^2(x)\right ) \log (4 x)+128 x \log (25) \log (x) \log ^2(4 x)+(-64 x \log (25)-128 x \log (25) \log (x)) \log ^3(4 x)}{\log ^5(4 x)} \, dx\\ &=\frac {1}{128} \int \frac {x \log (25) (2 \log (x) (-1+\log (4 x))+\log (4 x)) \left (x^2 \log (25) \log (x)-64 \log ^2(4 x)\right )}{\log ^5(4 x)} \, dx\\ &=\frac {1}{128} \log (25) \int \frac {x (2 \log (x) (-1+\log (4 x))+\log (4 x)) \left (x^2 \log (25) \log (x)-64 \log ^2(4 x)\right )}{\log ^5(4 x)} \, dx\\ &=\frac {1}{128} \text {Subst}\left (\int (-64+x) \, dx,x,\frac {x^2 \log (25) \log (x)}{\log ^2(4 x)}\right )\\ &=\frac {x^4 \log ^2(25) \log ^2(x)}{256 \log ^4(4 x)}-\frac {x^2 \log (25) \log (x)}{2 \log ^2(4 x)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 34, normalized size = 1.62 \begin {gather*} \frac {x^2 \log (25) \log (x) \left (x^2 \log (25) \log (x)-128 \log ^2(4 x)\right )}{256 \log ^4(4 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(41\) vs.
\(2(19)=38\).
time = 1.58, size = 42, normalized size = 2.00
method | result | size |
default | \(-\frac {\ln \left (5\right ) \ln \left (x \right ) x^{2}}{\left (\ln \left (x \right )+2 \ln \left (2\right )\right )^{2}}+\frac {\ln \left (5\right )^{2} \ln \left (x \right )^{2} x^{4}}{64 \left (\ln \left (x \right )+2 \ln \left (2\right )\right )^{4}}\) | \(42\) |
risch | \(-\frac {\ln \left (5\right ) x^{2} \ln \left (x \right ) \left (-x^{2} \ln \left (5\right ) \ln \left (x \right )+256 \ln \left (2\right )^{2}+256 \ln \left (2\right ) \ln \left (x \right )+64 \ln \left (x \right )^{2}\right )}{4 \left (4 \ln \left (2\right )+2 \ln \left (x \right )\right )^{4}}\) | \(49\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 90 vs.
\(2 (20) = 40\).
time = 0.57, size = 90, normalized size = 4.29 \begin {gather*} -\frac {256 \, x^{2} \log \left (5\right ) \log \left (2\right )^{2} \log \left (x\right ) + 64 \, x^{2} \log \left (5\right ) \log \left (x\right )^{3} - {\left (x^{4} \log \left (5\right )^{2} - 256 \, x^{2} \log \left (5\right ) \log \left (2\right )\right )} \log \left (x\right )^{2}}{64 \, {\left (16 \, \log \left (2\right )^{4} + 32 \, \log \left (2\right )^{3} \log \left (x\right ) + 24 \, \log \left (2\right )^{2} \log \left (x\right )^{2} + 8 \, \log \left (2\right ) \log \left (x\right )^{3} + \log \left (x\right )^{4}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 90 vs.
\(2 (20) = 40\).
time = 0.41, size = 90, normalized size = 4.29 \begin {gather*} -\frac {256 \, x^{2} \log \left (5\right ) \log \left (2\right )^{2} \log \left (x\right ) + 64 \, x^{2} \log \left (5\right ) \log \left (x\right )^{3} - {\left (x^{4} \log \left (5\right )^{2} - 256 \, x^{2} \log \left (5\right ) \log \left (2\right )\right )} \log \left (x\right )^{2}}{64 \, {\left (16 \, \log \left (2\right )^{4} + 32 \, \log \left (2\right )^{3} \log \left (x\right ) + 24 \, \log \left (2\right )^{2} \log \left (x\right )^{2} + 8 \, \log \left (2\right ) \log \left (x\right )^{3} + \log \left (x\right )^{4}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 100 vs.
\(2 (20) = 40\).
time = 0.12, size = 100, normalized size = 4.76 \begin {gather*} \frac {- 64 x^{2} \log {\left (5 \right )} \log {\left (x \right )}^{3} - 256 x^{2} \log {\left (2 \right )}^{2} \log {\left (5 \right )} \log {\left (x \right )} + \left (x^{4} \log {\left (5 \right )}^{2} - 256 x^{2} \log {\left (2 \right )} \log {\left (5 \right )}\right ) \log {\left (x \right )}^{2}}{64 \log {\left (x \right )}^{4} + 512 \log {\left (2 \right )} \log {\left (x \right )}^{3} + 1536 \log {\left (2 \right )}^{2} \log {\left (x \right )}^{2} + 2048 \log {\left (2 \right )}^{3} \log {\left (x \right )} + 1024 \log {\left (2 \right )}^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 207 vs.
\(2 (20) = 40\).
time = 0.42, size = 207, normalized size = 9.86 \begin {gather*} \frac {x^{4} \log \left (5\right )^{2} \log \left (x\right )^{2}}{64 \, {\left (16 \, \log \left (2\right )^{4} + 32 \, \log \left (2\right )^{3} \log \left (x\right ) + 24 \, \log \left (2\right )^{2} \log \left (x\right )^{2} + 8 \, \log \left (2\right ) \log \left (x\right )^{3} + \log \left (x\right )^{4}\right )}} - \frac {4 \, x^{2} \log \left (5\right ) \log \left (2\right )^{2} \log \left (x\right )}{16 \, \log \left (2\right )^{4} + 32 \, \log \left (2\right )^{3} \log \left (x\right ) + 24 \, \log \left (2\right )^{2} \log \left (x\right )^{2} + 8 \, \log \left (2\right ) \log \left (x\right )^{3} + \log \left (x\right )^{4}} - \frac {4 \, x^{2} \log \left (5\right ) \log \left (2\right ) \log \left (x\right )^{2}}{16 \, \log \left (2\right )^{4} + 32 \, \log \left (2\right )^{3} \log \left (x\right ) + 24 \, \log \left (2\right )^{2} \log \left (x\right )^{2} + 8 \, \log \left (2\right ) \log \left (x\right )^{3} + \log \left (x\right )^{4}} - \frac {x^{2} \log \left (5\right ) \log \left (x\right )^{3}}{16 \, \log \left (2\right )^{4} + 32 \, \log \left (2\right )^{3} \log \left (x\right ) + 24 \, \log \left (2\right )^{2} \log \left (x\right )^{2} + 8 \, \log \left (2\right ) \log \left (x\right )^{3} + \log \left (x\right )^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.76, size = 1277, normalized size = 60.81 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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