Optimal. Leaf size=19 \[ \frac{a x^2}{2}+\frac{2}{5} b x^{5/2} \]
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Rubi [A] time = 0.0156251, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{a x^2}{2}+\frac{2}{5} b x^{5/2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])*x,x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a \int x\, dx + \frac{2 b x^{\frac{5}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(a+b*x**(1/2)),x)
[Out]
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Mathematica [A] time = 0.00517189, size = 19, normalized size = 1. \[ \frac{a x^2}{2}+\frac{2}{5} b x^{5/2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])*x,x]
[Out]
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Maple [A] time = 0.002, size = 14, normalized size = 0.7 \[{\frac{a{x}^{2}}{2}}+{\frac{2\,b}{5}{x}^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(a+b*x^(1/2)),x)
[Out]
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Maxima [A] time = 1.43598, size = 86, normalized size = 4.53 \[ \frac{2 \,{\left (b \sqrt{x} + a\right )}^{5}}{5 \, b^{4}} - \frac{3 \,{\left (b \sqrt{x} + a\right )}^{4} a}{2 \, b^{4}} + \frac{2 \,{\left (b \sqrt{x} + a\right )}^{3} a^{2}}{b^{4}} - \frac{{\left (b \sqrt{x} + a\right )}^{2} a^{3}}{b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)*x,x, algorithm="maxima")
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Fricas [A] time = 0.23097, size = 18, normalized size = 0.95 \[ \frac{2}{5} \, b x^{\frac{5}{2}} + \frac{1}{2} \, a x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.18036, size = 15, normalized size = 0.79 \[ \frac{a x^{2}}{2} + \frac{2 b x^{\frac{5}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(a+b*x**(1/2)),x)
[Out]
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GIAC/XCAS [A] time = 0.213773, size = 18, normalized size = 0.95 \[ \frac{2}{5} \, b x^{\frac{5}{2}} + \frac{1}{2} \, a x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)*x,x, algorithm="giac")
[Out]