Optimal. Leaf size=63 \[ \frac{2}{3} a^2 A x^{3/2}+\frac{2}{15} b x^{15/2} (2 a B+A b)+\frac{2}{9} a x^{9/2} (a B+2 A b)+\frac{2}{21} b^2 B x^{21/2} \]
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Rubi [A] time = 0.0962474, 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 \[ \frac{2}{3} a^2 A x^{3/2}+\frac{2}{15} b x^{15/2} (2 a B+A b)+\frac{2}{9} a x^{9/2} (a B+2 A b)+\frac{2}{21} b^2 B x^{21/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x]*(a + b*x^3)^2*(A + B*x^3),x]
[Out]
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Rubi in Sympy [A] time = 11.0932, size = 63, normalized size = 1. \[ \frac{2 A a^{2} x^{\frac{3}{2}}}{3} + \frac{2 B b^{2} x^{\frac{21}{2}}}{21} + \frac{2 a x^{\frac{9}{2}} \left (2 A b + B a\right )}{9} + \frac{2 b x^{\frac{15}{2}} \left (A b + 2 B a\right )}{15} \]
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 = 0.0360365, size = 53, normalized size = 0.84 \[ \frac{2}{315} x^{3/2} \left (105 a^2 A+21 b x^6 (2 a B+A b)+35 a x^3 (a B+2 A b)+15 b^2 B x^9\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x]*(a + b*x^3)^2*(A + B*x^3),x]
[Out]
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Maple [A] time = 0.01, size = 56, normalized size = 0.9 \[{\frac{30\,B{x}^{9}{b}^{2}+42\,A{b}^{2}{x}^{6}+84\,B{x}^{6}ab+140\,aAb{x}^{3}+70\,B{x}^{3}{a}^{2}+210\,A{a}^{2}}{315}{x}^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^2*(B*x^3+A)*x^(1/2),x)
[Out]
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Maxima [A] time = 1.50146, size = 69, normalized size = 1.1 \[ \frac{2}{21} \, B b^{2} x^{\frac{21}{2}} + \frac{2}{15} \,{\left (2 \, B a b + A b^{2}\right )} x^{\frac{15}{2}} + \frac{2}{9} \,{\left (B a^{2} + 2 \, A a b\right )} x^{\frac{9}{2}} + \frac{2}{3} \, A a^{2} x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2*sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.229277, size = 73, normalized size = 1.16 \[ \frac{2}{315} \,{\left (15 \, B b^{2} x^{10} + 21 \,{\left (2 \, B a b + A b^{2}\right )} x^{7} + 35 \,{\left (B a^{2} + 2 \, A a b\right )} x^{4} + 105 \, A a^{2} x\right )} \sqrt{x} \]
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 = 14.1647, size = 66, normalized size = 1.05 \[ \frac{2 A a^{2} x^{\frac{3}{2}}}{3} + \frac{2 B b^{2} x^{\frac{21}{2}}}{21} + \frac{2 x^{\frac{15}{2}} \left (A b^{2} + 2 B a b\right )}{15} + \frac{2 x^{\frac{9}{2}} \left (2 A a b + B a^{2}\right )}{9} \]
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 = 0.211709, size = 72, normalized size = 1.14 \[ \frac{2}{21} \, B b^{2} x^{\frac{21}{2}} + \frac{4}{15} \, B a b x^{\frac{15}{2}} + \frac{2}{15} \, A b^{2} x^{\frac{15}{2}} + \frac{2}{9} \, B a^{2} x^{\frac{9}{2}} + \frac{4}{9} \, A a b x^{\frac{9}{2}} + \frac{2}{3} \, A a^{2} x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2*sqrt(x),x, algorithm="giac")
[Out]