Optimal. Leaf size=61 \[ -\frac{2 a^2 A}{\sqrt{x}}+\frac{2}{11} b x^{11/2} (2 a B+A b)+\frac{2}{5} a x^{5/2} (a B+2 A b)+\frac{2}{17} b^2 B x^{17/2} \]
[Out]
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Rubi [A] time = 0.0994594, antiderivative size = 61, 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 \[ -\frac{2 a^2 A}{\sqrt{x}}+\frac{2}{11} b x^{11/2} (2 a B+A b)+\frac{2}{5} a x^{5/2} (a B+2 A b)+\frac{2}{17} b^2 B x^{17/2} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^3)^2*(A + B*x^3))/x^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 10.7906, size = 61, normalized size = 1. \[ - \frac{2 A a^{2}}{\sqrt{x}} + \frac{2 B b^{2} x^{\frac{17}{2}}}{17} + \frac{2 a x^{\frac{5}{2}} \left (2 A b + B a\right )}{5} + \frac{2 b x^{\frac{11}{2}} \left (A b + 2 B a\right )}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**2*(B*x**3+A)/x**(3/2),x)
[Out]
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Mathematica [A] time = 0.0360448, size = 53, normalized size = 0.87 \[ \frac{2 \left (-935 a^2 A+85 b x^6 (2 a B+A b)+187 a x^3 (a B+2 A b)+55 b^2 B x^9\right )}{935 \sqrt{x}} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^3)^2*(A + B*x^3))/x^(3/2),x]
[Out]
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Maple [A] time = 0.009, size = 56, normalized size = 0.9 \[ -{\frac{-110\,B{x}^{9}{b}^{2}-170\,A{b}^{2}{x}^{6}-340\,B{x}^{6}ab-748\,aAb{x}^{3}-374\,B{x}^{3}{a}^{2}+1870\,A{a}^{2}}{935}{\frac{1}{\sqrt{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^2*(B*x^3+A)/x^(3/2),x)
[Out]
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Maxima [A] time = 1.48656, size = 69, normalized size = 1.13 \[ \frac{2}{17} \, B b^{2} x^{\frac{17}{2}} + \frac{2}{11} \,{\left (2 \, B a b + A b^{2}\right )} x^{\frac{11}{2}} + \frac{2}{5} \,{\left (B a^{2} + 2 \, A a b\right )} x^{\frac{5}{2}} - \frac{2 \, A a^{2}}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/x^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225667, size = 72, normalized size = 1.18 \[ \frac{2 \,{\left (55 \, B b^{2} x^{9} + 85 \,{\left (2 \, B a b + A b^{2}\right )} x^{6} + 187 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} - 935 \, A a^{2}\right )}}{935 \, \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/x^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 28.5672, size = 78, normalized size = 1.28 \[ - \frac{2 A a^{2}}{\sqrt{x}} + \frac{4 A a b x^{\frac{5}{2}}}{5} + \frac{2 A b^{2} x^{\frac{11}{2}}}{11} + \frac{2 B a^{2} x^{\frac{5}{2}}}{5} + \frac{4 B a b x^{\frac{11}{2}}}{11} + \frac{2 B b^{2} x^{\frac{17}{2}}}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**2*(B*x**3+A)/x**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.211593, size = 72, normalized size = 1.18 \[ \frac{2}{17} \, B b^{2} x^{\frac{17}{2}} + \frac{4}{11} \, B a b x^{\frac{11}{2}} + \frac{2}{11} \, A b^{2} x^{\frac{11}{2}} + \frac{2}{5} \, B a^{2} x^{\frac{5}{2}} + \frac{4}{5} \, A a b x^{\frac{5}{2}} - \frac{2 \, A a^{2}}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/x^(3/2),x, algorithm="giac")
[Out]