3.265 \(\int x^3 \log (x) \, dx\)

Optimal. Leaf size=17 \[ \frac{1}{4} x^4 \log (x)-\frac{x^4}{16} \]

[Out]

-x^4/16 + (x^4*Log[x])/4

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Rubi [A]  time = 0.0120768, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ \frac{1}{4} x^4 \log (x)-\frac{x^4}{16} \]

Antiderivative was successfully verified.

[In]  Int[x^3*Log[x],x]

[Out]

-x^4/16 + (x^4*Log[x])/4

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Rubi in Sympy [A]  time = 1.10186, size = 12, normalized size = 0.71 \[ \frac{x^{4} \log{\left (x \right )}}{4} - \frac{x^{4}}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**3*ln(x),x)

[Out]

x**4*log(x)/4 - x**4/16

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Mathematica [A]  time = 0.00172183, size = 17, normalized size = 1. \[ \frac{1}{4} x^4 \log (x)-\frac{x^4}{16} \]

Antiderivative was successfully verified.

[In]  Integrate[x^3*Log[x],x]

[Out]

-x^4/16 + (x^4*Log[x])/4

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Maple [A]  time = 0.001, size = 14, normalized size = 0.8 \[ -{\frac{{x}^{4}}{16}}+{\frac{{x}^{4}\ln \left ( x \right ) }{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^3*ln(x),x)

[Out]

-1/16*x^4+1/4*x^4*ln(x)

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Maxima [A]  time = 1.34176, size = 18, normalized size = 1.06 \[ \frac{1}{4} \, x^{4} \log \left (x\right ) - \frac{1}{16} \, x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3*log(x),x, algorithm="maxima")

[Out]

1/4*x^4*log(x) - 1/16*x^4

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Fricas [A]  time = 0.207398, size = 18, normalized size = 1.06 \[ \frac{1}{4} \, x^{4} \log \left (x\right ) - \frac{1}{16} \, x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3*log(x),x, algorithm="fricas")

[Out]

1/4*x^4*log(x) - 1/16*x^4

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Sympy [A]  time = 0.080395, size = 12, normalized size = 0.71 \[ \frac{x^{4} \log{\left (x \right )}}{4} - \frac{x^{4}}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**3*ln(x),x)

[Out]

x**4*log(x)/4 - x**4/16

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GIAC/XCAS [A]  time = 0.199077, size = 18, normalized size = 1.06 \[ \frac{1}{4} \, x^{4}{\rm ln}\left (x\right ) - \frac{1}{16} \, x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3*log(x),x, algorithm="giac")

[Out]

1/4*x^4*ln(x) - 1/16*x^4