Optimal. Leaf size=32 \[ \frac{a^2 x^2}{2}+\frac{4}{5} a b x^{5/2}+\frac{b^2 x^3}{3} \]
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Rubi [A] time = 0.055199, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{a^2 x^2}{2}+\frac{4}{5} a b x^{5/2}+\frac{b^2 x^3}{3} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^2*x,x]
[Out]
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Rubi in Sympy [A] time = 7.14808, size = 27, normalized size = 0.84 \[ \frac{a^{2} x^{2}}{2} + \frac{4 a b x^{\frac{5}{2}}}{5} + \frac{b^{2} x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(a+b*x**(1/2))**2,x)
[Out]
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Mathematica [A] time = 0.0119123, size = 28, normalized size = 0.88 \[ \frac{1}{30} x^2 \left (15 a^2+24 a b \sqrt{x}+10 b^2 x\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^2*x,x]
[Out]
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Maple [A] time = 0.002, size = 25, normalized size = 0.8 \[{\frac{{a}^{2}{x}^{2}}{2}}+{\frac{4\,ab}{5}{x}^{{\frac{5}{2}}}}+{\frac{{b}^{2}{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(a+b*x^(1/2))^2,x)
[Out]
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Maxima [A] time = 1.44159, size = 86, normalized size = 2.69 \[ \frac{{\left (b \sqrt{x} + a\right )}^{6}}{3 \, b^{4}} - \frac{6 \,{\left (b \sqrt{x} + a\right )}^{5} a}{5 \, b^{4}} + \frac{3 \,{\left (b \sqrt{x} + a\right )}^{4} a^{2}}{2 \, b^{4}} - \frac{2 \,{\left (b \sqrt{x} + a\right )}^{3} a^{3}}{3 \, b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.230921, size = 32, normalized size = 1. \[ \frac{1}{3} \, b^{2} x^{3} + \frac{4}{5} \, a b x^{\frac{5}{2}} + \frac{1}{2} \, a^{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.27143, size = 27, normalized size = 0.84 \[ \frac{a^{2} x^{2}}{2} + \frac{4 a b x^{\frac{5}{2}}}{5} + \frac{b^{2} x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(a+b*x**(1/2))**2,x)
[Out]
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GIAC/XCAS [A] time = 0.215989, size = 32, normalized size = 1. \[ \frac{1}{3} \, b^{2} x^{3} + \frac{4}{5} \, a b x^{\frac{5}{2}} + \frac{1}{2} \, a^{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2*x,x, algorithm="giac")
[Out]