Optimal. Leaf size=21 \[ \frac{2}{3} t^{3/2} \log (t)-\frac{4 t^{3/2}}{9} \]
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Rubi [A] time = 0.0140761, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{2}{3} t^{3/2} \log (t)-\frac{4 t^{3/2}}{9} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[t]*Log[t],t]
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Rubi in Sympy [A] time = 1.10487, size = 19, normalized size = 0.9 \[ \frac{2 t^{\frac{3}{2}} \log{\left (t \right )}}{3} - \frac{4 t^{\frac{3}{2}}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(ln(t)*t**(1/2),t)
[Out]
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Mathematica [A] time = 0.00441865, size = 15, normalized size = 0.71 \[ \frac{2}{9} t^{3/2} (3 \log (t)-2) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[t]*Log[t],t]
[Out]
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Maple [A] time = 0.004, size = 14, normalized size = 0.7 \[ -{\frac{4}{9}{t}^{{\frac{3}{2}}}}+{\frac{2\,\ln \left ( t \right ) }{3}{t}^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(ln(t)*t^(1/2),t)
[Out]
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Maxima [A] time = 1.34677, size = 18, normalized size = 0.86 \[ \frac{2}{3} \, t^{\frac{3}{2}} \log \left (t\right ) - \frac{4}{9} \, t^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(t)*log(t),t, algorithm="maxima")
[Out]
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Fricas [A] time = 0.248596, size = 19, normalized size = 0.9 \[ \frac{2}{9} \,{\left (3 \, t \log \left (t\right ) - 2 \, t\right )} \sqrt{t} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(t)*log(t),t, algorithm="fricas")
[Out]
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Sympy [A] time = 3.08115, size = 66, normalized size = 3.14 \[ \begin{cases} \frac{2 t^{\frac{3}{2}} \log{\left (t \right )}}{3} - \frac{4 t^{\frac{3}{2}}}{9} & \text{for}\: \left |{t}\right | < 1 \\- \frac{2 t^{\frac{3}{2}} \log{\left (\frac{1}{t} \right )}}{3} - \frac{4 t^{\frac{3}{2}}}{9} & \text{for}\: \left |{\frac{1}{t}}\right | < 1 \\-{G_{3, 3}^{2, 1}\left (\begin{matrix} 1 & \frac{5}{2}, \frac{5}{2} \\\frac{3}{2}, \frac{3}{2} & 0 \end{matrix} \middle |{t} \right )} +{G_{3, 3}^{0, 3}\left (\begin{matrix} \frac{5}{2}, \frac{5}{2}, 1 & \\ & \frac{3}{2}, \frac{3}{2}, 0 \end{matrix} \middle |{t} \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(ln(t)*t**(1/2),t)
[Out]
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GIAC/XCAS [A] time = 0.218856, size = 18, normalized size = 0.86 \[ \frac{2}{3} \, t^{\frac{3}{2}}{\rm ln}\left (t\right ) - \frac{4}{9} \, t^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(t)*log(t),t, algorithm="giac")
[Out]