Optimal. Leaf size=35 \[ 5 (5+x) \left (-x+\left (\frac {4}{x}-\log (x)\right )^{\frac {x}{2 \left (-x+\log \left (x^2\right )\right )}}\right ) \]
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Rubi [F] time = 34.78, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {200 x^2+80 x^3+\left (-50 x^3-20 x^4\right ) \log (x)+\left (-400 x-160 x^2+\left (100 x^2+40 x^3\right ) \log (x)\right ) \log \left (x^2\right )+\left (200+80 x+\left (-50 x-20 x^2\right ) \log (x)\right ) \log ^2\left (x^2\right )+\left (\frac {4-x \log (x)}{x}\right )^{\frac {x}{-2 x+2 \log \left (x^2\right )}} \left (-100 x-85 x^2-5 x^3+10 x^3 \log (x)+\left (100+125 x+5 x^2-20 x^2 \log (x)\right ) \log \left (x^2\right )+(-40+10 x \log (x)) \log ^2\left (x^2\right )+\left (200+40 x+\left (-50 x-10 x^2\right ) \log (x)+\left (-100-20 x+\left (25 x+5 x^2\right ) \log (x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {4-x \log (x)}{x}\right )\right )}{-8 x^2+2 x^3 \log (x)+\left (16 x-4 x^2 \log (x)\right ) \log \left (x^2\right )+(-8+2 x \log (x)) \log ^2\left (x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5 \left (-40 x^2-16 x^3+2 x^3 (5+2 x) \log (x)-4 x (5+2 x) (-4+x \log (x)) \log \left (x^2\right )+2 (5+2 x) (-4+x \log (x)) \log ^2\left (x^2\right )-\left (\frac {4}{x}-\log (x)\right )^{\frac {x}{-2 x+2 \log \left (x^2\right )}} \left (-20 x-17 x^2-x^3+2 x^3 \log (x)+\left (20+25 x+x^2-4 x^2 \log (x)\right ) \log \left (x^2\right )+2 (-4+x \log (x)) \log ^2\left (x^2\right )+(5+x) (-4+x \log (x)) \left (-2+\log \left (x^2\right )\right ) \log \left (\frac {4}{x}-\log (x)\right )\right )\right )}{2 (4-x \log (x)) \left (x-\log \left (x^2\right )\right )^2} \, dx\\ &=\frac {5}{2} \int \frac {-40 x^2-16 x^3+2 x^3 (5+2 x) \log (x)-4 x (5+2 x) (-4+x \log (x)) \log \left (x^2\right )+2 (5+2 x) (-4+x \log (x)) \log ^2\left (x^2\right )-\left (\frac {4}{x}-\log (x)\right )^{\frac {x}{-2 x+2 \log \left (x^2\right )}} \left (-20 x-17 x^2-x^3+2 x^3 \log (x)+\left (20+25 x+x^2-4 x^2 \log (x)\right ) \log \left (x^2\right )+2 (-4+x \log (x)) \log ^2\left (x^2\right )+(5+x) (-4+x \log (x)) \left (-2+\log \left (x^2\right )\right ) \log \left (\frac {4}{x}-\log (x)\right )\right )}{(4-x \log (x)) \left (x-\log \left (x^2\right )\right )^2} \, dx\\ &=\frac {5}{2} \int \left (\frac {40 x^2}{(-4+x \log (x)) \left (x-\log \left (x^2\right )\right )^2}+\frac {16 x^3}{(-4+x \log (x)) \left (x-\log \left (x^2\right )\right )^2}-\frac {2 x^3 (5+2 x) \log (x)}{(-4+x \log (x)) \left (x-\log \left (x^2\right )\right )^2}+\frac {4 x (5+2 x) \log \left (x^2\right )}{\left (x-\log \left (x^2\right )\right )^2}-\frac {2 (5+2 x) \log ^2\left (x^2\right )}{\left (x-\log \left (x^2\right )\right )^2}+\frac {\left (\frac {4}{x}-\log (x)\right )^{-\frac {x}{2 \left (x-\log \left (x^2\right )\right )}} \left (20 x+17 x^2+x^3-2 x^3 \log (x)-20 \log \left (x^2\right )-25 x \log \left (x^2\right )-x^2 \log \left (x^2\right )+4 x^2 \log (x) \log \left (x^2\right )+8 \log ^2\left (x^2\right )-2 x \log (x) \log ^2\left (x^2\right )-40 \log \left (\frac {4}{x}-\log (x)\right )-8 x \log \left (\frac {4}{x}-\log (x)\right )+10 x \log (x) \log \left (\frac {4}{x}-\log (x)\right )+2 x^2 \log (x) \log \left (\frac {4}{x}-\log (x)\right )+20 \log \left (x^2\right ) \log \left (\frac {4}{x}-\log (x)\right )+4 x \log \left (x^2\right ) \log \left (\frac {4}{x}-\log (x)\right )-5 x \log (x) \log \left (x^2\right ) \log \left (\frac {4}{x}-\log (x)\right )-x^2 \log (x) \log \left (x^2\right ) \log \left (\frac {4}{x}-\log (x)\right )\right )}{(4-x \log (x)) \left (x-\log \left (x^2\right )\right )^2}\right ) \, dx\\ &=\frac {5}{2} \int \frac {\left (\frac {4}{x}-\log (x)\right )^{-\frac {x}{2 \left (x-\log \left (x^2\right )\right )}} \left (20 x+17 x^2+x^3-2 x^3 \log (x)-20 \log \left (x^2\right )-25 x \log \left (x^2\right )-x^2 \log \left (x^2\right )+4 x^2 \log (x) \log \left (x^2\right )+8 \log ^2\left (x^2\right )-2 x \log (x) \log ^2\left (x^2\right )-40 \log \left (\frac {4}{x}-\log (x)\right )-8 x \log \left (\frac {4}{x}-\log (x)\right )+10 x \log (x) \log \left (\frac {4}{x}-\log (x)\right )+2 x^2 \log (x) \log \left (\frac {4}{x}-\log (x)\right )+20 \log \left (x^2\right ) \log \left (\frac {4}{x}-\log (x)\right )+4 x \log \left (x^2\right ) \log \left (\frac {4}{x}-\log (x)\right )-5 x \log (x) \log \left (x^2\right ) \log \left (\frac {4}{x}-\log (x)\right )-x^2 \log (x) \log \left (x^2\right ) \log \left (\frac {4}{x}-\log (x)\right )\right )}{(4-x \log (x)) \left (x-\log \left (x^2\right )\right )^2} \, dx-5 \int \frac {x^3 (5+2 x) \log (x)}{(-4+x \log (x)) \left (x-\log \left (x^2\right )\right )^2} \, dx-5 \int \frac {(5+2 x) \log ^2\left (x^2\right )}{\left (x-\log \left (x^2\right )\right )^2} \, dx+10 \int \frac {x (5+2 x) \log \left (x^2\right )}{\left (x-\log \left (x^2\right )\right )^2} \, dx+40 \int \frac {x^3}{(-4+x \log (x)) \left (x-\log \left (x^2\right )\right )^2} \, dx+100 \int \frac {x^2}{(-4+x \log (x)) \left (x-\log \left (x^2\right )\right )^2} \, dx\\ &=\frac {5}{2} \int \frac {\left (\frac {4}{x}-\log (x)\right )^{-\frac {x}{2 \left (x-\log \left (x^2\right )\right )}} \left (20 x+17 x^2+x^3+8 \log ^2\left (x^2\right )-40 \log \left (\frac {4}{x}-\log (x)\right )-8 x \log \left (\frac {4}{x}-\log (x)\right )-\log \left (x^2\right ) \left (20+25 x+x^2-4 (5+x) \log \left (\frac {4}{x}-\log (x)\right )\right )-x \log (x) \left (2 \log ^2\left (x^2\right )+2 \left (x^2-(5+x) \log \left (\frac {4}{x}-\log (x)\right )\right )+\log \left (x^2\right ) \left (-4 x+(5+x) \log \left (\frac {4}{x}-\log (x)\right )\right )\right )\right )}{(4-x \log (x)) \left (x-\log \left (x^2\right )\right )^2} \, dx-5 \int \left (\frac {5 x^3 \log (x)}{(-4+x \log (x)) \left (x-\log \left (x^2\right )\right )^2}+\frac {2 x^4 \log (x)}{(-4+x \log (x)) \left (x-\log \left (x^2\right )\right )^2}\right ) \, dx-5 \int \left (5+2 x+\frac {x^2 (5+2 x)}{\left (x-\log \left (x^2\right )\right )^2}-\frac {2 x (5+2 x)}{x-\log \left (x^2\right )}\right ) \, dx+10 \int \left (\frac {x^2 (5+2 x)}{\left (x-\log \left (x^2\right )\right )^2}-\frac {x (5+2 x)}{x-\log \left (x^2\right )}\right ) \, dx+40 \int \frac {x^3}{(-4+x \log (x)) \left (x-\log \left (x^2\right )\right )^2} \, dx+100 \int \frac {x^2}{(-4+x \log (x)) \left (x-\log \left (x^2\right )\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.35, size = 65, normalized size = 1.86 \begin {gather*} \frac {5}{2} \left (-10 x-2 x^2+\frac {2 \left (\frac {4}{x}-\log (x)\right )^{-\frac {x}{2 \left (x-\log \left (x^2\right )\right )}} \left (-20-4 x+5 x \log (x)+x^2 \log (x)\right )}{-4+x \log (x)}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 63, normalized size = 1.80 \begin {gather*} -\frac {5 \, {\left ({\left (x^{2} + 5 \, x\right )} \left (-\frac {x \log \relax (x) - 4}{x}\right )^{\frac {x}{2 \, {\left (x - 2 \, \log \relax (x)\right )}}} - x - 5\right )}}{\left (-\frac {x \log \relax (x) - 4}{x}\right )^{\frac {x}{2 \, {\left (x - 2 \, \log \relax (x)\right )}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {5 \, {\left (16 \, x^{3} - 2 \, {\left ({\left (2 \, x^{2} + 5 \, x\right )} \log \relax (x) - 8 \, x - 20\right )} \log \left (x^{2}\right )^{2} + 40 \, x^{2} - 4 \, {\left (8 \, x^{2} - {\left (2 \, x^{3} + 5 \, x^{2}\right )} \log \relax (x) + 20 \, x\right )} \log \left (x^{2}\right ) - 2 \, {\left (2 \, x^{4} + 5 \, x^{3}\right )} \log \relax (x) + \frac {2 \, x^{3} \log \relax (x) - x^{3} + 2 \, {\left (x \log \relax (x) - 4\right )} \log \left (x^{2}\right )^{2} - 17 \, x^{2} - {\left (4 \, x^{2} \log \relax (x) - x^{2} - 25 \, x - 20\right )} \log \left (x^{2}\right ) + {\left ({\left ({\left (x^{2} + 5 \, x\right )} \log \relax (x) - 4 \, x - 20\right )} \log \left (x^{2}\right ) - 2 \, {\left (x^{2} + 5 \, x\right )} \log \relax (x) + 8 \, x + 40\right )} \log \left (-\frac {x \log \relax (x) - 4}{x}\right ) - 20 \, x}{\left (-\frac {x \log \relax (x) - 4}{x}\right )^{\frac {x}{2 \, {\left (x - \log \left (x^{2}\right )\right )}}}}\right )}}{2 \, {\left (x^{3} \log \relax (x) + {\left (x \log \relax (x) - 4\right )} \log \left (x^{2}\right )^{2} - 4 \, x^{2} - 2 \, {\left (x^{2} \log \relax (x) - 4 \, x\right )} \log \left (x^{2}\right )\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 1.07, size = 224, normalized size = 6.40
method | result | size |
risch | \(-5 x^{2}-25 x +\left (25+5 x \right ) {\mathrm e}^{-\frac {x \left (-i \pi \mathrm {csgn}\left (\frac {i \left (x \ln \relax (x )-4\right )}{x}\right )^{3}-i \pi \mathrm {csgn}\left (\frac {i \left (x \ln \relax (x )-4\right )}{x}\right )^{2} \mathrm {csgn}\left (\frac {i}{x}\right )-i \pi \mathrm {csgn}\left (\frac {i \left (x \ln \relax (x )-4\right )}{x}\right )^{2} \mathrm {csgn}\left (i \left (x \ln \relax (x )-4\right )\right )+i \pi \,\mathrm {csgn}\left (\frac {i \left (x \ln \relax (x )-4\right )}{x}\right ) \mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (i \left (x \ln \relax (x )-4\right )\right )+2 i \pi \mathrm {csgn}\left (\frac {i \left (x \ln \relax (x )-4\right )}{x}\right )^{2}-2 i \pi +2 \ln \relax (x )-2 \ln \left (x \ln \relax (x )-4\right )\right )}{2 \left (-i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+2 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+4 \ln \relax (x )-2 x \right )}}\) | \(224\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -25 \, x - 10 \, \int x\,{d x} + \frac {5}{2} \, \int \frac {{\left (x^{\frac {7}{2}} {\left (2 \, \log \relax (x) - 1\right )} - {\left (2 \, \log \relax (x)^{3} + 6 \, \log \relax (x)^{2} - 2 \, \log \relax (x) + 17\right )} x^{\frac {5}{2}} - 2 \, {\left (\log \relax (x)^{3} - 9 \, \log \relax (x)^{2} - 21 \, \log \relax (x) + 10\right )} x^{\frac {3}{2}} + 8 \, \sqrt {x} \log \relax (x)^{2} + 2 \, {\left ({\left (\log \relax (x)^{2} - \log \relax (x)\right )} x^{\frac {5}{2}} + {\left (5 \, \log \relax (x)^{2} - 9 \, \log \relax (x) + 4\right )} x^{\frac {3}{2}} - 20 \, \sqrt {x} {\left (\log \relax (x) - 1\right )}\right )} \log \left (-x \log \relax (x) + 4\right )\right )} e^{\left (-\frac {\log \left (-x \log \relax (x) + 4\right ) \log \relax (x)}{x - 2 \, \log \relax (x)} + \frac {\log \relax (x)^{2}}{x - 2 \, \log \relax (x)}\right )}}{{\left (x^{3} \log \relax (x) - 4 \, {\left (\log \relax (x)^{2} + 1\right )} x^{2} + 4 \, {\left (\log \relax (x)^{3} + 4 \, \log \relax (x)\right )} x - 16 \, \log \relax (x)^{2}\right )} \sqrt {-x \log \relax (x) + 4}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.90, size = 37, normalized size = 1.06 \begin {gather*} -5\,\left (x+5\right )\,\left (x-\frac {1}{{\left (-\frac {x\,\ln \relax (x)-4}{x}\right )}^{\frac {x}{2\,x-2\,\ln \left (x^2\right )}}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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