Optimal. Leaf size=73 \[ \frac{a^5 x^4}{4}+\frac{10}{9} a^4 b x^{9/2}+2 a^3 b^2 x^5+\frac{20}{11} a^2 b^3 x^{11/2}+\frac{5}{6} a b^4 x^6+\frac{2}{13} b^5 x^{13/2} \]
[Out]
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Rubi [A] time = 0.103858, antiderivative size = 73, 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 \[ \frac{a^5 x^4}{4}+\frac{10}{9} a^4 b x^{9/2}+2 a^3 b^2 x^5+\frac{20}{11} a^2 b^3 x^{11/2}+\frac{5}{6} a b^4 x^6+\frac{2}{13} b^5 x^{13/2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^5*x^3,x]
[Out]
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Rubi in Sympy [A] time = 16.011, size = 71, normalized size = 0.97 \[ \frac{a^{5} x^{4}}{4} + \frac{10 a^{4} b x^{\frac{9}{2}}}{9} + 2 a^{3} b^{2} x^{5} + \frac{20 a^{2} b^{3} x^{\frac{11}{2}}}{11} + \frac{5 a b^{4} x^{6}}{6} + \frac{2 b^{5} x^{\frac{13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(a+b*x**(1/2))**5,x)
[Out]
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Mathematica [A] time = 0.013598, size = 73, normalized size = 1. \[ \frac{a^5 x^4}{4}+\frac{10}{9} a^4 b x^{9/2}+2 a^3 b^2 x^5+\frac{20}{11} a^2 b^3 x^{11/2}+\frac{5}{6} a b^4 x^6+\frac{2}{13} b^5 x^{13/2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^5*x^3,x]
[Out]
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Maple [A] time = 0.003, size = 58, normalized size = 0.8 \[{\frac{{a}^{5}{x}^{4}}{4}}+{\frac{10\,{a}^{4}b}{9}{x}^{{\frac{9}{2}}}}+2\,{a}^{3}{b}^{2}{x}^{5}+{\frac{20\,{a}^{2}{b}^{3}}{11}{x}^{{\frac{11}{2}}}}+{\frac{5\,a{b}^{4}{x}^{6}}{6}}+{\frac{2\,{b}^{5}}{13}{x}^{{\frac{13}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(a+b*x^(1/2))^5,x)
[Out]
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Maxima [A] time = 1.44719, size = 178, normalized size = 2.44 \[ \frac{2 \,{\left (b \sqrt{x} + a\right )}^{13}}{13 \, b^{8}} - \frac{7 \,{\left (b \sqrt{x} + a\right )}^{12} a}{6 \, b^{8}} + \frac{42 \,{\left (b \sqrt{x} + a\right )}^{11} a^{2}}{11 \, b^{8}} - \frac{7 \,{\left (b \sqrt{x} + a\right )}^{10} a^{3}}{b^{8}} + \frac{70 \,{\left (b \sqrt{x} + a\right )}^{9} a^{4}}{9 \, b^{8}} - \frac{21 \,{\left (b \sqrt{x} + a\right )}^{8} a^{5}}{4 \, b^{8}} + \frac{2 \,{\left (b \sqrt{x} + a\right )}^{7} a^{6}}{b^{8}} - \frac{{\left (b \sqrt{x} + a\right )}^{6} a^{7}}{3 \, b^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^5*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.232221, size = 85, normalized size = 1.16 \[ \frac{5}{6} \, a b^{4} x^{6} + 2 \, a^{3} b^{2} x^{5} + \frac{1}{4} \, a^{5} x^{4} + \frac{2}{1287} \,{\left (99 \, b^{5} x^{6} + 1170 \, a^{2} b^{3} x^{5} + 715 \, a^{4} b x^{4}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^5*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.41764, size = 71, normalized size = 0.97 \[ \frac{a^{5} x^{4}}{4} + \frac{10 a^{4} b x^{\frac{9}{2}}}{9} + 2 a^{3} b^{2} x^{5} + \frac{20 a^{2} b^{3} x^{\frac{11}{2}}}{11} + \frac{5 a b^{4} x^{6}}{6} + \frac{2 b^{5} x^{\frac{13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(a+b*x**(1/2))**5,x)
[Out]
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GIAC/XCAS [A] time = 0.215554, size = 77, normalized size = 1.05 \[ \frac{2}{13} \, b^{5} x^{\frac{13}{2}} + \frac{5}{6} \, a b^{4} x^{6} + \frac{20}{11} \, a^{2} b^{3} x^{\frac{11}{2}} + 2 \, a^{3} b^{2} x^{5} + \frac{10}{9} \, a^{4} b x^{\frac{9}{2}} + \frac{1}{4} \, a^{5} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^5*x^3,x, algorithm="giac")
[Out]