Optimal. Leaf size=51 \[ \frac{2}{7} a^3 x^{7/2}+\frac{2}{3} a^2 b x^{9/2}+\frac{6}{11} a b^2 x^{11/2}+\frac{2}{13} b^3 x^{13/2} \]
[Out]
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Rubi [A] time = 0.0310032, antiderivative size = 51, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{2}{7} a^3 x^{7/2}+\frac{2}{3} a^2 b x^{9/2}+\frac{6}{11} a b^2 x^{11/2}+\frac{2}{13} b^3 x^{13/2} \]
Antiderivative was successfully verified.
[In] Int[x^(5/2)*(a + b*x)^3,x]
[Out]
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Rubi in Sympy [A] time = 5.16145, size = 49, normalized size = 0.96 \[ \frac{2 a^{3} x^{\frac{7}{2}}}{7} + \frac{2 a^{2} b x^{\frac{9}{2}}}{3} + \frac{6 a b^{2} x^{\frac{11}{2}}}{11} + \frac{2 b^{3} x^{\frac{13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(5/2)*(b*x+a)**3,x)
[Out]
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Mathematica [A] time = 0.0113069, size = 39, normalized size = 0.76 \[ \frac{2 x^{7/2} \left (429 a^3+1001 a^2 b x+819 a b^2 x^2+231 b^3 x^3\right )}{3003} \]
Antiderivative was successfully verified.
[In] Integrate[x^(5/2)*(a + b*x)^3,x]
[Out]
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Maple [A] time = 0.006, size = 36, normalized size = 0.7 \[{\frac{462\,{b}^{3}{x}^{3}+1638\,a{b}^{2}{x}^{2}+2002\,{a}^{2}bx+858\,{a}^{3}}{3003}{x}^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(5/2)*(b*x+a)^3,x)
[Out]
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Maxima [A] time = 1.33094, size = 47, normalized size = 0.92 \[ \frac{2}{13} \, b^{3} x^{\frac{13}{2}} + \frac{6}{11} \, a b^{2} x^{\frac{11}{2}} + \frac{2}{3} \, a^{2} b x^{\frac{9}{2}} + \frac{2}{7} \, a^{3} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^3*x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204472, size = 54, normalized size = 1.06 \[ \frac{2}{3003} \,{\left (231 \, b^{3} x^{6} + 819 \, a b^{2} x^{5} + 1001 \, a^{2} b x^{4} + 429 \, a^{3} x^{3}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^3*x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 6.71063, size = 49, normalized size = 0.96 \[ \frac{2 a^{3} x^{\frac{7}{2}}}{7} + \frac{2 a^{2} b x^{\frac{9}{2}}}{3} + \frac{6 a b^{2} x^{\frac{11}{2}}}{11} + \frac{2 b^{3} x^{\frac{13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(5/2)*(b*x+a)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.206502, size = 47, normalized size = 0.92 \[ \frac{2}{13} \, b^{3} x^{\frac{13}{2}} + \frac{6}{11} \, a b^{2} x^{\frac{11}{2}} + \frac{2}{3} \, a^{2} b x^{\frac{9}{2}} + \frac{2}{7} \, a^{3} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^3*x^(5/2),x, algorithm="giac")
[Out]