Optimal. Leaf size=21 \[ \frac{2}{3} x^{3/2} \log (x)-\frac{4 x^{3/2}}{9} \]
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Rubi [A] time = 0.0114925, 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 \[ \frac{2}{3} x^{3/2} \log (x)-\frac{4 x^{3/2}}{9} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x]*Log[x],x]
[Out]
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Rubi in Sympy [A] time = 1.07153, size = 19, normalized size = 0.9 \[ \frac{2 x^{\frac{3}{2}} \log{\left (x \right )}}{3} - \frac{4 x^{\frac{3}{2}}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(ln(x)*x**(1/2),x)
[Out]
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Mathematica [A] time = 0.0041041, size = 15, normalized size = 0.71 \[ \frac{2}{9} x^{3/2} (3 \log (x)-2) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x]*Log[x],x]
[Out]
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Maple [A] time = 0.001, size = 14, normalized size = 0.7 \[ -{\frac{4}{9}{x}^{{\frac{3}{2}}}}+{\frac{2\,\ln \left ( x \right ) }{3}{x}^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(ln(x)*x^(1/2),x)
[Out]
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Maxima [A] time = 1.54764, size = 18, normalized size = 0.86 \[ \frac{2}{3} \, x^{\frac{3}{2}} \log \left (x\right ) - \frac{4}{9} \, x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)*log(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211946, size = 19, normalized size = 0.9 \[ \frac{2}{9} \,{\left (3 \, x \log \left (x\right ) - 2 \, x\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)*log(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.09091, size = 66, normalized size = 3.14 \[ \begin{cases} \frac{2 x^{\frac{3}{2}} \log{\left (x \right )}}{3} - \frac{4 x^{\frac{3}{2}}}{9} & \text{for}\: \left |{x}\right | < 1 \\- \frac{2 x^{\frac{3}{2}} \log{\left (\frac{1}{x} \right )}}{3} - \frac{4 x^{\frac{3}{2}}}{9} & \text{for}\: \left |{\frac{1}{x}}\right | < 1 \\-{G_{3, 3}^{2, 1}\left (\begin{matrix} 1 & \frac{5}{2}, \frac{5}{2} \\\frac{3}{2}, \frac{3}{2} & 0 \end{matrix} \middle |{x} \right )} +{G_{3, 3}^{0, 3}\left (\begin{matrix} \frac{5}{2}, \frac{5}{2}, 1 & \\ & \frac{3}{2}, \frac{3}{2}, 0 \end{matrix} \middle |{x} \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(ln(x)*x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.204378, size = 18, normalized size = 0.86 \[ \frac{2}{3} \, x^{\frac{3}{2}}{\rm ln}\left (x\right ) - \frac{4}{9} \, x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)*log(x),x, algorithm="giac")
[Out]