Optimal. Leaf size=30 \[ 4+\frac {\left (1-x-\frac {(-5+x) (1+x+4 (x+\log (4)))}{x}\right )^2}{x} \]
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Rubi [A]
time = 0.03, antiderivative size = 48, normalized size of antiderivative = 1.60, number of steps
used = 2, number of rules used = 1, integrand size = 47, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.021, Rules used = {14}
\begin {gather*} \frac {25 (1+\log (256))^2}{x^3}+\frac {10 \left (25-16 \log ^2(4)+96 \log (4)\right )}{x^2}+36 x+\frac {565+16 \log ^2(4)-440 \log (4)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (36+\frac {-565+440 \log (4)-16 \log ^2(4)}{x^2}+\frac {20 \left (-25-96 \log (4)+16 \log ^2(4)\right )}{x^3}-\frac {75 (1+\log (256))^2}{x^4}\right ) \, dx\\ &=36 x+\frac {10 \left (25+96 \log (4)-16 \log ^2(4)\right )}{x^2}+\frac {565-440 \log (4)+16 \log ^2(4)}{x}+\frac {25 (1+\log (256))^2}{x^3}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 53, normalized size = 1.77 \begin {gather*} \frac {565}{x}+36 x-\frac {440 \log (4)}{x}+\frac {16 \log ^2(4)}{x}-\frac {10 \left (-25-96 \log (4)+16 \log ^2(4)\right )}{x^2}+\frac {25 (1+\log (256))^2}{x^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.24, size = 56, normalized size = 1.87
method | result | size |
risch | \(36 x +\frac {\left (64 \ln \left (2\right )^{2}-880 \ln \left (2\right )+565\right ) x^{2}+\left (-640 \ln \left (2\right )^{2}+1920 \ln \left (2\right )+250\right ) x +1600 \ln \left (2\right )^{2}+400 \ln \left (2\right )+25}{x^{3}}\) | \(51\) |
norman | \(\frac {\left (-640 \ln \left (2\right )^{2}+1920 \ln \left (2\right )+250\right ) x +\left (64 \ln \left (2\right )^{2}-880 \ln \left (2\right )+565\right ) x^{2}+36 x^{4}+1600 \ln \left (2\right )^{2}+400 \ln \left (2\right )+25}{x^{3}}\) | \(52\) |
default | \(36 x -\frac {-4800 \ln \left (2\right )^{2}-1200 \ln \left (2\right )-75}{3 x^{3}}-\frac {1280 \ln \left (2\right )^{2}-3840 \ln \left (2\right )-500}{2 x^{2}}-\frac {-64 \ln \left (2\right )^{2}+880 \ln \left (2\right )-565}{x}\) | \(56\) |
gosper | \(\frac {64 x^{2} \ln \left (2\right )^{2}+36 x^{4}-640 x \ln \left (2\right )^{2}-880 x^{2} \ln \left (2\right )+1600 \ln \left (2\right )^{2}+1920 x \ln \left (2\right )+565 x^{2}+400 \ln \left (2\right )+250 x +25}{x^{3}}\) | \(58\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 51, normalized size = 1.70 \begin {gather*} 36 \, x + \frac {{\left (64 \, \log \left (2\right )^{2} - 880 \, \log \left (2\right ) + 565\right )} x^{2} - 10 \, {\left (64 \, \log \left (2\right )^{2} - 192 \, \log \left (2\right ) - 25\right )} x + 1600 \, \log \left (2\right )^{2} + 400 \, \log \left (2\right ) + 25}{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 47, normalized size = 1.57 \begin {gather*} \frac {36 \, x^{4} + 64 \, {\left (x^{2} - 10 \, x + 25\right )} \log \left (2\right )^{2} + 565 \, x^{2} - 80 \, {\left (11 \, x^{2} - 24 \, x - 5\right )} \log \left (2\right ) + 250 \, x + 25}{x^{3}} \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. 51 vs.
\(2 (22) = 44\).
time = 0.33, size = 51, normalized size = 1.70 \begin {gather*} 36 x + \frac {x^{2} \left (- 880 \log {\left (2 \right )} + 64 \log {\left (2 \right )}^{2} + 565\right ) + x \left (- 640 \log {\left (2 \right )}^{2} + 250 + 1920 \log {\left (2 \right )}\right ) + 25 + 400 \log {\left (2 \right )} + 1600 \log {\left (2 \right )}^{2}}{x^{3}} \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. 56 vs.
\(2 (27) = 54\).
time = 0.42, size = 56, normalized size = 1.87 \begin {gather*} 36 \, x + \frac {64 \, x^{2} \log \left (2\right )^{2} - 880 \, x^{2} \log \left (2\right ) - 640 \, x \log \left (2\right )^{2} + 565 \, x^{2} + 1920 \, x \log \left (2\right ) + 1600 \, \log \left (2\right )^{2} + 250 \, x + 400 \, \log \left (2\right ) + 25}{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.19, size = 47, normalized size = 1.57 \begin {gather*} 36\,x+\frac {25\,{\left (\ln \left (256\right )+1\right )}^2}{x^3}+\frac {64\,{\ln \left (2\right )}^2-880\,\ln \left (2\right )+565}{x}+\frac {1920\,\ln \left (2\right )-640\,{\ln \left (2\right )}^2+250}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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