Optimal. Leaf size=22 \[ 4 x (-2+2 x) \left (2 x-16 x^2-\log (\log (x))\right ) \]
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Rubi [A]
time = 0.20, antiderivative size = 30, normalized size of antiderivative = 1.36, number of steps
used = 18, number of rules used = 8, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.210, Rules used = {6874, 14,
2367, 2335, 2346, 2209, 2600, 2602} \begin {gather*} -128 x^4+144 x^3-16 x^2-8 x^2 \log (\log (x))+8 x \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2209
Rule 2335
Rule 2346
Rule 2367
Rule 2600
Rule 2602
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {8 \left (-1+x+4 x \log (x)-54 x^2 \log (x)+64 x^3 \log (x)\right )}{\log (x)}-8 (-1+2 x) \log (\log (x))\right ) \, dx\\ &=-\left (8 \int \frac {-1+x+4 x \log (x)-54 x^2 \log (x)+64 x^3 \log (x)}{\log (x)} \, dx\right )-8 \int (-1+2 x) \log (\log (x)) \, dx\\ &=-\left (8 \int \left (2 x \left (2-27 x+32 x^2\right )+\frac {-1+x}{\log (x)}\right ) \, dx\right )-8 \int (-\log (\log (x))+2 x \log (\log (x))) \, dx\\ &=-\left (8 \int \frac {-1+x}{\log (x)} \, dx\right )+8 \int \log (\log (x)) \, dx-16 \int x \left (2-27 x+32 x^2\right ) \, dx-16 \int x \log (\log (x)) \, dx\\ &=8 x \log (\log (x))-8 x^2 \log (\log (x))-8 \int \left (-\frac {1}{\log (x)}+\frac {x}{\log (x)}\right ) \, dx-8 \int \frac {1}{\log (x)} \, dx+8 \int \frac {x}{\log (x)} \, dx-16 \int \left (2 x-27 x^2+32 x^3\right ) \, dx\\ &=-16 x^2+144 x^3-128 x^4+8 x \log (\log (x))-8 x^2 \log (\log (x))-8 \text {li}(x)+8 \int \frac {1}{\log (x)} \, dx-8 \int \frac {x}{\log (x)} \, dx+8 \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )\\ &=-16 x^2+144 x^3-128 x^4+8 \text {Ei}(2 \log (x))+8 x \log (\log (x))-8 x^2 \log (\log (x))-8 \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )\\ &=-16 x^2+144 x^3-128 x^4+8 x \log (\log (x))-8 x^2 \log (\log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 30, normalized size = 1.36 \begin {gather*} -16 x^2+144 x^3-128 x^4+8 x \log (\log (x))-8 x^2 \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 31, normalized size = 1.41
method | result | size |
risch | \(\left (-8 x^{2}+8 x \right ) \ln \left (\ln \left (x \right )\right )-128 x^{4}+144 x^{3}-16 x^{2}\) | \(30\) |
default | \(-8 x^{2} \ln \left (\ln \left (x \right )\right )+8 x \ln \left (\ln \left (x \right )\right )-16 x^{2}+144 x^{3}-128 x^{4}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 30, normalized size = 1.36 \begin {gather*} -128 \, x^{4} + 144 \, x^{3} - 8 \, x^{2} \log \left (\log \left (x\right )\right ) - 16 \, x^{2} + 8 \, x \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 28, normalized size = 1.27 \begin {gather*} -128 \, x^{4} + 144 \, x^{3} - 16 \, x^{2} - 8 \, {\left (x^{2} - x\right )} \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 27, normalized size = 1.23 \begin {gather*} - 128 x^{4} + 144 x^{3} - 16 x^{2} + \left (- 8 x^{2} + 8 x\right ) \log {\left (\log {\left (x \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 30, normalized size = 1.36 \begin {gather*} -128 \, x^{4} + 144 \, x^{3} - 8 \, x^{2} \log \left (\log \left (x\right )\right ) - 16 \, x^{2} + 8 \, x \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.62, size = 18, normalized size = 0.82 \begin {gather*} -8\,x\,\left (x-1\right )\,\left (\ln \left (\ln \left (x\right )\right )-2\,x+16\,x^2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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