Optimal. Leaf size=61 \[ 2 a^2 A \sqrt{x}+\frac{2}{13} b x^{13/2} (2 a B+A b)+\frac{2}{7} a x^{7/2} (a B+2 A b)+\frac{2}{19} b^2 B x^{19/2} \]
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Rubi [A] time = 0.0976163, 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 \[ 2 a^2 A \sqrt{x}+\frac{2}{13} b x^{13/2} (2 a B+A b)+\frac{2}{7} a x^{7/2} (a B+2 A b)+\frac{2}{19} b^2 B x^{19/2} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^3)^2*(A + B*x^3))/Sqrt[x],x]
[Out]
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Rubi in Sympy [A] time = 10.7851, size = 61, normalized size = 1. \[ 2 A a^{2} \sqrt{x} + \frac{2 B b^{2} x^{\frac{19}{2}}}{19} + \frac{2 a x^{\frac{7}{2}} \left (2 A b + B a\right )}{7} + \frac{2 b x^{\frac{13}{2}} \left (A b + 2 B a\right )}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**2*(B*x**3+A)/x**(1/2),x)
[Out]
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Mathematica [A] time = 0.0362192, size = 53, normalized size = 0.87 \[ \frac{2 \sqrt{x} \left (1729 a^2 A+133 b x^6 (2 a B+A b)+247 a x^3 (a B+2 A b)+91 b^2 B x^9\right )}{1729} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^3)^2*(A + B*x^3))/Sqrt[x],x]
[Out]
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Maple [A] time = 0.007, size = 56, normalized size = 0.9 \[{\frac{182\,B{x}^{9}{b}^{2}+266\,A{b}^{2}{x}^{6}+532\,B{x}^{6}ab+988\,aAb{x}^{3}+494\,B{x}^{3}{a}^{2}+3458\,A{a}^{2}}{1729}\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^2*(B*x^3+A)/x^(1/2),x)
[Out]
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Maxima [A] time = 1.42428, size = 69, normalized size = 1.13 \[ \frac{2}{19} \, B b^{2} x^{\frac{19}{2}} + \frac{2}{13} \,{\left (2 \, B a b + A b^{2}\right )} x^{\frac{13}{2}} + \frac{2}{7} \,{\left (B a^{2} + 2 \, A a b\right )} x^{\frac{7}{2}} + 2 \, A a^{2} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.231278, size = 72, normalized size = 1.18 \[ \frac{2}{1729} \,{\left (91 \, B b^{2} x^{9} + 133 \,{\left (2 \, B a b + A b^{2}\right )} x^{6} + 247 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} + 1729 \, A a^{2}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 24.1036, size = 78, normalized size = 1.28 \[ 2 A a^{2} \sqrt{x} + \frac{4 A a b x^{\frac{7}{2}}}{7} + \frac{2 A b^{2} x^{\frac{13}{2}}}{13} + \frac{2 B a^{2} x^{\frac{7}{2}}}{7} + \frac{4 B a b x^{\frac{13}{2}}}{13} + \frac{2 B b^{2} x^{\frac{19}{2}}}{19} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**2*(B*x**3+A)/x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.21072, size = 72, normalized size = 1.18 \[ \frac{2}{19} \, B b^{2} x^{\frac{19}{2}} + \frac{4}{13} \, B a b x^{\frac{13}{2}} + \frac{2}{13} \, A b^{2} x^{\frac{13}{2}} + \frac{2}{7} \, B a^{2} x^{\frac{7}{2}} + \frac{4}{7} \, A a b x^{\frac{7}{2}} + 2 \, A a^{2} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/sqrt(x),x, algorithm="giac")
[Out]