Optimal. Leaf size=47 \[ \frac{a^3 x^4}{4}+\frac{2}{3} a^2 b x^{9/2}+\frac{3}{5} a b^2 x^5+\frac{2}{11} b^3 x^{11/2} \]
[Out]
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Rubi [A] time = 0.0739327, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{a^3 x^4}{4}+\frac{2}{3} a^2 b x^{9/2}+\frac{3}{5} a b^2 x^5+\frac{2}{11} b^3 x^{11/2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^3*x^3,x]
[Out]
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Rubi in Sympy [A] time = 10.7863, size = 44, normalized size = 0.94 \[ \frac{a^{3} x^{4}}{4} + \frac{2 a^{2} b x^{\frac{9}{2}}}{3} + \frac{3 a b^{2} x^{5}}{5} + \frac{2 b^{3} x^{\frac{11}{2}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(a+b*x**(1/2))**3,x)
[Out]
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Mathematica [A] time = 0.0110557, size = 47, normalized size = 1. \[ \frac{a^3 x^4}{4}+\frac{2}{3} a^2 b x^{9/2}+\frac{3}{5} a b^2 x^5+\frac{2}{11} b^3 x^{11/2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^3*x^3,x]
[Out]
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Maple [A] time = 0.002, size = 36, normalized size = 0.8 \[{\frac{{a}^{3}{x}^{4}}{4}}+{\frac{2\,{a}^{2}b}{3}{x}^{{\frac{9}{2}}}}+{\frac{3\,a{b}^{2}{x}^{5}}{5}}+{\frac{2\,{b}^{3}}{11}{x}^{{\frac{11}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(a+b*x^(1/2))^3,x)
[Out]
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Maxima [A] time = 1.44976, size = 178, normalized size = 3.79 \[ \frac{2 \,{\left (b \sqrt{x} + a\right )}^{11}}{11 \, b^{8}} - \frac{7 \,{\left (b \sqrt{x} + a\right )}^{10} a}{5 \, b^{8}} + \frac{14 \,{\left (b \sqrt{x} + a\right )}^{9} a^{2}}{3 \, b^{8}} - \frac{35 \,{\left (b \sqrt{x} + a\right )}^{8} a^{3}}{4 \, b^{8}} + \frac{10 \,{\left (b \sqrt{x} + a\right )}^{7} a^{4}}{b^{8}} - \frac{7 \,{\left (b \sqrt{x} + a\right )}^{6} a^{5}}{b^{8}} + \frac{14 \,{\left (b \sqrt{x} + a\right )}^{5} a^{6}}{5 \, b^{8}} - \frac{{\left (b \sqrt{x} + a\right )}^{4} a^{7}}{2 \, b^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.244725, size = 55, normalized size = 1.17 \[ \frac{3}{5} \, a b^{2} x^{5} + \frac{1}{4} \, a^{3} x^{4} + \frac{2}{33} \,{\left (3 \, b^{3} x^{5} + 11 \, a^{2} b x^{4}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.42545, size = 44, normalized size = 0.94 \[ \frac{a^{3} x^{4}}{4} + \frac{2 a^{2} b x^{\frac{9}{2}}}{3} + \frac{3 a b^{2} x^{5}}{5} + \frac{2 b^{3} x^{\frac{11}{2}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(a+b*x**(1/2))**3,x)
[Out]
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GIAC/XCAS [A] time = 0.212665, size = 47, normalized size = 1. \[ \frac{2}{11} \, b^{3} x^{\frac{11}{2}} + \frac{3}{5} \, a b^{2} x^{5} + \frac{2}{3} \, a^{2} b x^{\frac{9}{2}} + \frac{1}{4} \, a^{3} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^3*x^3,x, algorithm="giac")
[Out]