Optimal. Leaf size=63 \[ -\frac{2 a^2 A}{3 x^{3/2}}+\frac{2}{9} b x^{9/2} (2 a B+A b)+\frac{2}{3} a x^{3/2} (a B+2 A b)+\frac{2}{15} b^2 B x^{15/2} \]
[Out]
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Rubi [A] time = 0.0994123, antiderivative size = 63, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{2 a^2 A}{3 x^{3/2}}+\frac{2}{9} b x^{9/2} (2 a B+A b)+\frac{2}{3} a x^{3/2} (a B+2 A b)+\frac{2}{15} b^2 B x^{15/2} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^3)^2*(A + B*x^3))/x^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 10.7985, size = 63, normalized size = 1. \[ - \frac{2 A a^{2}}{3 x^{\frac{3}{2}}} + \frac{2 B b^{2} x^{\frac{15}{2}}}{15} + \frac{2 a x^{\frac{3}{2}} \left (2 A b + B a\right )}{3} + \frac{2 b x^{\frac{9}{2}} \left (A b + 2 B a\right )}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**2*(B*x**3+A)/x**(5/2),x)
[Out]
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Mathematica [A] time = 0.0307331, size = 57, normalized size = 0.9 \[ \frac{-30 a^2 \left (A-B x^3\right )+20 a b x^3 \left (3 A+B x^3\right )+2 b^2 x^6 \left (5 A+3 B x^3\right )}{45 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^3)^2*(A + B*x^3))/x^(5/2),x]
[Out]
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Maple [A] time = 0.008, size = 56, normalized size = 0.9 \[ -{\frac{-6\,B{x}^{9}{b}^{2}-10\,A{b}^{2}{x}^{6}-20\,B{x}^{6}ab-60\,aAb{x}^{3}-30\,B{x}^{3}{a}^{2}+30\,A{a}^{2}}{45}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^2*(B*x^3+A)/x^(5/2),x)
[Out]
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Maxima [A] time = 1.4551, size = 69, normalized size = 1.1 \[ \frac{2}{15} \, B b^{2} x^{\frac{15}{2}} + \frac{2}{9} \,{\left (2 \, B a b + A b^{2}\right )} x^{\frac{9}{2}} + \frac{2}{3} \,{\left (B a^{2} + 2 \, A a b\right )} x^{\frac{3}{2}} - \frac{2 \, A a^{2}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.229495, size = 72, normalized size = 1.14 \[ \frac{2 \,{\left (3 \, B b^{2} x^{9} + 5 \,{\left (2 \, B a b + A b^{2}\right )} x^{6} + 15 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} - 15 \, A a^{2}\right )}}{45 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 33.5563, size = 80, normalized size = 1.27 \[ - \frac{2 A a^{2}}{3 x^{\frac{3}{2}}} + \frac{4 A a b x^{\frac{3}{2}}}{3} + \frac{2 A b^{2} x^{\frac{9}{2}}}{9} + \frac{2 B a^{2} x^{\frac{3}{2}}}{3} + \frac{4 B a b x^{\frac{9}{2}}}{9} + \frac{2 B b^{2} x^{\frac{15}{2}}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**2*(B*x**3+A)/x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.212635, size = 72, normalized size = 1.14 \[ \frac{2}{15} \, B b^{2} x^{\frac{15}{2}} + \frac{4}{9} \, B a b x^{\frac{9}{2}} + \frac{2}{9} \, A b^{2} x^{\frac{9}{2}} + \frac{2}{3} \, B a^{2} x^{\frac{3}{2}} + \frac{4}{3} \, A a b x^{\frac{3}{2}} - \frac{2 \, A a^{2}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/x^(5/2),x, algorithm="giac")
[Out]