Optimal. Leaf size=22 \[ 4 \left (36 x^2 (-x+x \log (4))^2+\log (5)\right )^2 \]
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Rubi [A]
time = 0.01, antiderivative size = 29, normalized size of antiderivative = 1.32, number of steps
used = 9, number of rules used = 3, integrand size = 65, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.046, Rules used = {6, 12, 30}
\begin {gather*} 5184 x^8 (1-\log (4))^4+288 x^4 (1-\log (4))^2 \log (5) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (x^7 (41472-165888 \log (4))+248832 x^7 \log ^2(4)-165888 x^7 \log ^3(4)+41472 x^7 \log ^4(4)+\left (1152 x^3-2304 x^3 \log (4)+1152 x^3 \log ^2(4)\right ) \log (5)\right ) \, dx\\ &=\int \left (-165888 x^7 \log ^3(4)+41472 x^7 \log ^4(4)+x^7 \left (41472-165888 \log (4)+248832 \log ^2(4)\right )+\left (1152 x^3-2304 x^3 \log (4)+1152 x^3 \log ^2(4)\right ) \log (5)\right ) \, dx\\ &=\int \left (x^7 \left (41472-165888 \log (4)+248832 \log ^2(4)\right )+x^7 \left (-165888 \log ^3(4)+41472 \log ^4(4)\right )+\left (1152 x^3-2304 x^3 \log (4)+1152 x^3 \log ^2(4)\right ) \log (5)\right ) \, dx\\ &=\int \left (x^7 \left (41472-165888 \log (4)+248832 \log ^2(4)-165888 \log ^3(4)+41472 \log ^4(4)\right )+\left (1152 x^3-2304 x^3 \log (4)+1152 x^3 \log ^2(4)\right ) \log (5)\right ) \, dx\\ &=5184 x^8 (1-\log (4))^4+\log (5) \int \left (1152 x^3-2304 x^3 \log (4)+1152 x^3 \log ^2(4)\right ) \, dx\\ &=5184 x^8 (1-\log (4))^4+\log (5) \int \left (x^3 (1152-2304 \log (4))+1152 x^3 \log ^2(4)\right ) \, dx\\ &=5184 x^8 (1-\log (4))^4+\log (5) \int x^3 \left (1152-2304 \log (4)+1152 \log ^2(4)\right ) \, dx\\ &=5184 x^8 (1-\log (4))^4+\left (1152 (1-\log (4))^2 \log (5)\right ) \int x^3 \, dx\\ &=5184 x^8 (1-\log (4))^4+288 x^4 (1-\log (4))^2 \log (5)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 31, normalized size = 1.41 \begin {gather*} 1152 (-1+\log (4))^2 \left (\frac {9}{2} x^8 (-1+\log (4))^2+\frac {1}{4} x^4 \log (5)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 51, normalized size = 2.32
method | result | size |
gosper | \(288 \left (4 \ln \left (2\right )^{2}-4 \ln \left (2\right )+1\right ) \left (72 x^{4} \ln \left (2\right )^{2}-72 x^{4} \ln \left (2\right )+18 x^{4}+\ln \left (5\right )\right ) x^{4}\) | \(42\) |
default | \(\frac {4 \left (2 \ln \left (2\right )-1\right )^{2} \left (144 x^{4} \ln \left (2\right )^{2}-144 x^{4} \ln \left (2\right )+36 x^{4}+\ln \left (5\right )\right )^{2}}{4 \ln \left (2\right )^{2}-4 \ln \left (2\right )+1}\) | \(51\) |
norman | \(\left (1152 \ln \left (2\right )^{2} \ln \left (5\right )-1152 \ln \left (2\right ) \ln \left (5\right )+288 \ln \left (5\right )\right ) x^{4}+\left (82944 \ln \left (2\right )^{4}-165888 \ln \left (2\right )^{3}+124416 \ln \left (2\right )^{2}-41472 \ln \left (2\right )+5184\right ) x^{8}\) | \(53\) |
risch | \(82944 x^{8} \ln \left (2\right )^{4}-165888 x^{8} \ln \left (2\right )^{3}+124416 \ln \left (2\right )^{2} x^{8}-41472 x^{8} \ln \left (2\right )+5184 x^{8}+1152 x^{4} \ln \left (5\right ) \ln \left (2\right )^{2}-1152 x^{4} \ln \left (5\right ) \ln \left (2\right )+288 x^{4} \ln \left (5\right )\) | \(68\) |
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. 64 vs.
\(2 (23) = 46\).
time = 0.25, size = 64, normalized size = 2.91 \begin {gather*} 82944 \, x^{8} \log \left (2\right )^{4} - 165888 \, x^{8} \log \left (2\right )^{3} + 124416 \, x^{8} \log \left (2\right )^{2} - 41472 \, x^{8} \log \left (2\right ) + 5184 \, x^{8} + 288 \, {\left (4 \, x^{4} \log \left (2\right )^{2} - 4 \, x^{4} \log \left (2\right ) + x^{4}\right )} \log \left (5\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. 64 vs.
\(2 (23) = 46\).
time = 0.37, size = 64, normalized size = 2.91 \begin {gather*} 82944 \, x^{8} \log \left (2\right )^{4} - 165888 \, x^{8} \log \left (2\right )^{3} + 124416 \, x^{8} \log \left (2\right )^{2} - 41472 \, x^{8} \log \left (2\right ) + 5184 \, x^{8} + 288 \, {\left (4 \, x^{4} \log \left (2\right )^{2} - 4 \, x^{4} \log \left (2\right ) + x^{4}\right )} \log \left (5\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. 56 vs.
\(2 (24) = 48\).
time = 0.01, size = 56, normalized size = 2.55 \begin {gather*} x^{8} \left (- 165888 \log {\left (2 \right )}^{3} - 41472 \log {\left (2 \right )} + 5184 + 82944 \log {\left (2 \right )}^{4} + 124416 \log {\left (2 \right )}^{2}\right ) + x^{4} \left (- 1152 \log {\left (2 \right )} \log {\left (5 \right )} + 288 \log {\left (5 \right )} + 1152 \log {\left (2 \right )}^{2} \log {\left (5 \right )}\right ) \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. 64 vs.
\(2 (23) = 46\).
time = 0.39, size = 64, normalized size = 2.91 \begin {gather*} 82944 \, x^{8} \log \left (2\right )^{4} - 165888 \, x^{8} \log \left (2\right )^{3} + 124416 \, x^{8} \log \left (2\right )^{2} - 41472 \, x^{8} \log \left (2\right ) + 5184 \, x^{8} + 288 \, {\left (4 \, x^{4} \log \left (2\right )^{2} - 4 \, x^{4} \log \left (2\right ) + x^{4}\right )} \log \left (5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.08, size = 37, normalized size = 1.68 \begin {gather*} 288\,x^4\,{\left (2\,\ln \left (2\right )-1\right )}^2\,\left (\ln \left (5\right )+72\,x^4\,{\ln \left (2\right )}^2-72\,x^4\,\ln \left (2\right )+18\,x^4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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