Optimal. Leaf size=44 \[ \frac{a^3 x^2}{2}+\frac{6}{5} a^2 b x^{5/2}+a b^2 x^3+\frac{2}{7} b^3 x^{7/2} \]
[Out]
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Rubi [A] time = 0.0640526, antiderivative size = 44, 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 \[ \frac{a^3 x^2}{2}+\frac{6}{5} a^2 b x^{5/2}+a b^2 x^3+\frac{2}{7} b^3 x^{7/2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^3*x,x]
[Out]
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Rubi in Sympy [A] time = 9.17054, size = 41, normalized size = 0.93 \[ \frac{a^{3} x^{2}}{2} + \frac{6 a^{2} b x^{\frac{5}{2}}}{5} + a b^{2} x^{3} + \frac{2 b^{3} x^{\frac{7}{2}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(a+b*x**(1/2))**3,x)
[Out]
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Mathematica [A] time = 0.0109396, size = 44, normalized size = 1. \[ \frac{a^3 x^2}{2}+\frac{6}{5} a^2 b x^{5/2}+a b^2 x^3+\frac{2}{7} b^3 x^{7/2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^3*x,x]
[Out]
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Maple [A] time = 0.002, size = 35, normalized size = 0.8 \[{\frac{{x}^{2}{a}^{3}}{2}}+{\frac{6\,{a}^{2}b}{5}{x}^{{\frac{5}{2}}}}+a{b}^{2}{x}^{3}+{\frac{2\,{b}^{3}}{7}{x}^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(a+b*x^(1/2))^3,x)
[Out]
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Maxima [A] time = 1.42754, size = 86, normalized size = 1.95 \[ \frac{2 \,{\left (b \sqrt{x} + a\right )}^{7}}{7 \, b^{4}} - \frac{{\left (b \sqrt{x} + a\right )}^{6} a}{b^{4}} + \frac{6 \,{\left (b \sqrt{x} + a\right )}^{5} a^{2}}{5 \, b^{4}} - \frac{{\left (b \sqrt{x} + a\right )}^{4} a^{3}}{2 \, b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.232691, size = 54, normalized size = 1.23 \[ a b^{2} x^{3} + \frac{1}{2} \, a^{3} x^{2} + \frac{2}{35} \,{\left (5 \, b^{3} x^{3} + 21 \, a^{2} b x^{2}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.43852, size = 41, normalized size = 0.93 \[ \frac{a^{3} x^{2}}{2} + \frac{6 a^{2} b x^{\frac{5}{2}}}{5} + a b^{2} x^{3} + \frac{2 b^{3} x^{\frac{7}{2}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(a+b*x**(1/2))**3,x)
[Out]
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GIAC/XCAS [A] time = 0.217415, size = 46, normalized size = 1.05 \[ \frac{2}{7} \, b^{3} x^{\frac{7}{2}} + a b^{2} x^{3} + \frac{6}{5} \, a^{2} b x^{\frac{5}{2}} + \frac{1}{2} \, a^{3} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3*x,x, algorithm="giac")
[Out]