Optimal. Leaf size=14 \[ \frac {3}{-4+(x-\log (x))^4} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(40\) vs. \(2(14)=28\).
time = 0.54, antiderivative size = 40, normalized size of antiderivative = 2.86, number of steps
used = 3, number of rules used = 3, integrand size = 157, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6820, 12,
6818} \begin {gather*} -\frac {3}{-x^4+4 x^3 \log (x)-6 x^2 \log ^2(x)-\log ^4(x)+4 x \log ^3(x)+4} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {12 (1-x) (x-\log (x))^3}{x \left (4-x^4+4 x^3 \log (x)-6 x^2 \log ^2(x)+4 x \log ^3(x)-\log ^4(x)\right )^2} \, dx\\ &=12 \int \frac {(1-x) (x-\log (x))^3}{x \left (4-x^4+4 x^3 \log (x)-6 x^2 \log ^2(x)+4 x \log ^3(x)-\log ^4(x)\right )^2} \, dx\\ &=-\frac {3}{4-x^4+4 x^3 \log (x)-6 x^2 \log ^2(x)+4 x \log ^3(x)-\log ^4(x)}\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(36\) vs. \(2(14)=28\).
time = 0.02, size = 36, normalized size = 2.57 \begin {gather*} \frac {3}{-4+x^4-4 x^3 \log (x)+6 x^2 \log ^2(x)-4 x \log ^3(x)+\log ^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. \(36\) vs.
\(2(14)=28\).
time = 6.96, size = 37, normalized size = 2.64
method | result | size |
default | \(\frac {3}{\ln \left (x \right )^{4}-4 x \ln \left (x \right )^{3}+6 x^{2} \ln \left (x \right )^{2}-4 x^{3} \ln \left (x \right )+x^{4}-4}\) | \(37\) |
risch | \(\frac {3}{\ln \left (x \right )^{4}-4 x \ln \left (x \right )^{3}+6 x^{2} \ln \left (x \right )^{2}-4 x^{3} \ln \left (x \right )+x^{4}-4}\) | \(37\) |
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. 36 vs.
\(2 (14) = 28\).
time = 0.31, size = 36, normalized size = 2.57 \begin {gather*} \frac {3}{x^{4} - 4 \, x^{3} \log \left (x\right ) + 6 \, x^{2} \log \left (x\right )^{2} - 4 \, x \log \left (x\right )^{3} + \log \left (x\right )^{4} - 4} \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. 36 vs.
\(2 (14) = 28\).
time = 0.36, size = 36, normalized size = 2.57 \begin {gather*} \frac {3}{x^{4} - 4 \, x^{3} \log \left (x\right ) + 6 \, x^{2} \log \left (x\right )^{2} - 4 \, x \log \left (x\right )^{3} + \log \left (x\right )^{4} - 4} \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. 37 vs.
\(2 (8) = 16\).
time = 0.16, size = 37, normalized size = 2.64 \begin {gather*} \frac {3}{x^{4} - 4 x^{3} \log {\left (x \right )} + 6 x^{2} \log {\left (x \right )}^{2} - 4 x \log {\left (x \right )}^{3} + \log {\left (x \right )}^{4} - 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. 36 vs.
\(2 (14) = 28\).
time = 0.43, size = 36, normalized size = 2.57 \begin {gather*} \frac {3}{x^{4} - 4 \, x^{3} \log \left (x\right ) + 6 \, x^{2} \log \left (x\right )^{2} - 4 \, x \log \left (x\right )^{3} + \log \left (x\right )^{4} - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.07 \begin {gather*} \int \frac {{\ln \left (x\right )}^2\,\left (36\,x-36\,x^2\right )-\ln \left (x\right )\,\left (36\,x^2-36\,x^3\right )+12\,x^3-12\,x^4+{\ln \left (x\right )}^3\,\left (12\,x-12\right )}{16\,x+\ln \left (x\right )\,\left (32\,x^4-8\,x^8\right )-{\ln \left (x\right )}^4\,\left (8\,x-70\,x^5\right )+x\,{\ln \left (x\right )}^8-{\ln \left (x\right )}^2\,\left (48\,x^3-28\,x^7\right )+{\ln \left (x\right )}^3\,\left (32\,x^2-56\,x^6\right )-8\,x^2\,{\ln \left (x\right )}^7+28\,x^3\,{\ln \left (x\right )}^6-56\,x^4\,{\ln \left (x\right )}^5-8\,x^5+x^9} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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