Optimal. Leaf size=39 \[ -\frac{3 x^4}{128}+\frac{1}{4} x^4 \log ^3(x)-\frac{3}{16} x^4 \log ^2(x)+\frac{3}{32} x^4 \log (x) \]
[Out]
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Rubi [A] time = 0.0485654, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ -\frac{3 x^4}{128}+\frac{1}{4} x^4 \log ^3(x)-\frac{3}{16} x^4 \log ^2(x)+\frac{3}{32} x^4 \log (x) \]
Antiderivative was successfully verified.
[In] Int[x^3*Log[x]^3,x]
[Out]
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Rubi in Sympy [A] time = 2.80623, size = 37, normalized size = 0.95 \[ \frac{x^{4} \log{\left (x \right )}^{3}}{4} - \frac{3 x^{4} \log{\left (x \right )}^{2}}{16} + \frac{3 x^{4} \log{\left (x \right )}}{32} - \frac{3 x^{4}}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*ln(x)**3,x)
[Out]
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Mathematica [A] time = 0.00378348, size = 39, normalized size = 1. \[ -\frac{3 x^4}{128}+\frac{1}{4} x^4 \log ^3(x)-\frac{3}{16} x^4 \log ^2(x)+\frac{3}{32} x^4 \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[x^3*Log[x]^3,x]
[Out]
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Maple [A] time = 0.003, size = 32, normalized size = 0.8 \[ -{\frac{3\,{x}^{4}}{128}}+{\frac{3\,{x}^{4}\ln \left ( x \right ) }{32}}-{\frac{3\,{x}^{4} \left ( \ln \left ( x \right ) \right ) ^{2}}{16}}+{\frac{{x}^{4} \left ( \ln \left ( x \right ) \right ) ^{3}}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*ln(x)^3,x)
[Out]
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Maxima [A] time = 1.56424, size = 31, normalized size = 0.79 \[ \frac{1}{128} \,{\left (32 \, \log \left (x\right )^{3} - 24 \, \log \left (x\right )^{2} + 12 \, \log \left (x\right ) - 3\right )} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*log(x)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204995, size = 42, normalized size = 1.08 \[ \frac{1}{4} \, x^{4} \log \left (x\right )^{3} - \frac{3}{16} \, x^{4} \log \left (x\right )^{2} + \frac{3}{32} \, x^{4} \log \left (x\right ) - \frac{3}{128} \, x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*log(x)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.113336, size = 37, normalized size = 0.95 \[ \frac{x^{4} \log{\left (x \right )}^{3}}{4} - \frac{3 x^{4} \log{\left (x \right )}^{2}}{16} + \frac{3 x^{4} \log{\left (x \right )}}{32} - \frac{3 x^{4}}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*ln(x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.215188, size = 42, normalized size = 1.08 \[ \frac{1}{4} \, x^{4}{\rm ln}\left (x\right )^{3} - \frac{3}{16} \, x^{4}{\rm ln}\left (x\right )^{2} + \frac{3}{32} \, x^{4}{\rm ln}\left (x\right ) - \frac{3}{128} \, x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*log(x)^3,x, algorithm="giac")
[Out]