3.30 \(\int t^2 \log (t) \, dt\)

Optimal. Leaf size=17 \[ \frac{1}{3} t^3 \log (t)-\frac{t^3}{9} \]

[Out]

-t^3/9 + (t^3*Log[t])/3

_______________________________________________________________________________________

Rubi [A]  time = 0.0132054, 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 \[ \frac{1}{3} t^3 \log (t)-\frac{t^3}{9} \]

Antiderivative was successfully verified.

[In]  Int[t^2*Log[t],t]

[Out]

-t^3/9 + (t^3*Log[t])/3

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 1.12878, size = 12, normalized size = 0.71 \[ \frac{t^{3} \log{\left (t \right )}}{3} - \frac{t^{3}}{9} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(t**2*ln(t),t)

[Out]

t**3*log(t)/3 - t**3/9

_______________________________________________________________________________________

Mathematica [A]  time = 0.00172183, size = 17, normalized size = 1. \[ \frac{1}{3} t^3 \log (t)-\frac{t^3}{9} \]

Antiderivative was successfully verified.

[In]  Integrate[t^2*Log[t],t]

[Out]

-t^3/9 + (t^3*Log[t])/3

_______________________________________________________________________________________

Maple [A]  time = 0.003, size = 14, normalized size = 0.8 \[ -{\frac{{t}^{3}}{9}}+{\frac{{t}^{3}\ln \left ( t \right ) }{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(t^2*ln(t),t)

[Out]

-1/9*t^3+1/3*t^3*ln(t)

_______________________________________________________________________________________

Maxima [A]  time = 1.41644, size = 18, normalized size = 1.06 \[ \frac{1}{3} \, t^{3} \log \left (t\right ) - \frac{1}{9} \, t^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(t^2*log(t),t, algorithm="maxima")

[Out]

1/3*t^3*log(t) - 1/9*t^3

_______________________________________________________________________________________

Fricas [A]  time = 0.220029, size = 18, normalized size = 1.06 \[ \frac{1}{3} \, t^{3} \log \left (t\right ) - \frac{1}{9} \, t^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(t^2*log(t),t, algorithm="fricas")

[Out]

1/3*t^3*log(t) - 1/9*t^3

_______________________________________________________________________________________

Sympy [A]  time = 0.082239, size = 12, normalized size = 0.71 \[ \frac{t^{3} \log{\left (t \right )}}{3} - \frac{t^{3}}{9} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(t**2*ln(t),t)

[Out]

t**3*log(t)/3 - t**3/9

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.200718, size = 18, normalized size = 1.06 \[ \frac{1}{3} \, t^{3}{\rm ln}\left (t\right ) - \frac{1}{9} \, t^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(t^2*log(t),t, algorithm="giac")

[Out]

1/3*t^3*ln(t) - 1/9*t^3