Optimal. Leaf size=63 \[ \frac{2}{9} a^2 A x^{9/2}+\frac{2}{21} b x^{21/2} (2 a B+A b)+\frac{2}{15} a x^{15/2} (a B+2 A b)+\frac{2}{27} b^2 B x^{27/2} \]
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Rubi [A] time = 0.104011, 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 \[ \frac{2}{9} a^2 A x^{9/2}+\frac{2}{21} b x^{21/2} (2 a B+A b)+\frac{2}{15} a x^{15/2} (a B+2 A b)+\frac{2}{27} b^2 B x^{27/2} \]
Antiderivative was successfully verified.
[In] Int[x^(7/2)*(a + b*x^3)^2*(A + B*x^3),x]
[Out]
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Rubi in Sympy [A] time = 10.7559, size = 63, normalized size = 1. \[ \frac{2 A a^{2} x^{\frac{9}{2}}}{9} + \frac{2 B b^{2} x^{\frac{27}{2}}}{27} + \frac{2 a x^{\frac{15}{2}} \left (2 A b + B a\right )}{15} + \frac{2 b x^{\frac{21}{2}} \left (A b + 2 B a\right )}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(7/2)*(b*x**3+a)**2*(B*x**3+A),x)
[Out]
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Mathematica [A] time = 0.0367779, size = 53, normalized size = 0.84 \[ \frac{2}{945} x^{9/2} \left (105 a^2 A+45 b x^6 (2 a B+A b)+63 a x^3 (a B+2 A b)+35 b^2 B x^9\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^(7/2)*(a + b*x^3)^2*(A + B*x^3),x]
[Out]
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Maple [A] time = 0.007, size = 56, normalized size = 0.9 \[{\frac{70\,B{x}^{9}{b}^{2}+90\,A{b}^{2}{x}^{6}+180\,B{x}^{6}ab+252\,aAb{x}^{3}+126\,B{x}^{3}{a}^{2}+210\,A{a}^{2}}{945}{x}^{{\frac{9}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(7/2)*(b*x^3+a)^2*(B*x^3+A),x)
[Out]
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Maxima [A] time = 1.61315, size = 69, normalized size = 1.1 \[ \frac{2}{27} \, B b^{2} x^{\frac{27}{2}} + \frac{2}{21} \,{\left (2 \, B a b + A b^{2}\right )} x^{\frac{21}{2}} + \frac{2}{15} \,{\left (B a^{2} + 2 \, A a b\right )} x^{\frac{15}{2}} + \frac{2}{9} \, A a^{2} x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2*x^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.234867, size = 76, normalized size = 1.21 \[ \frac{2}{945} \,{\left (35 \, B b^{2} x^{13} + 45 \,{\left (2 \, B a b + A b^{2}\right )} x^{10} + 63 \,{\left (B a^{2} + 2 \, A a b\right )} x^{7} + 105 \, A a^{2} x^{4}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2*x^(7/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 167.797, size = 80, normalized size = 1.27 \[ \frac{2 A a^{2} x^{\frac{9}{2}}}{9} + \frac{4 A a b x^{\frac{15}{2}}}{15} + \frac{2 A b^{2} x^{\frac{21}{2}}}{21} + \frac{2 B a^{2} x^{\frac{15}{2}}}{15} + \frac{4 B a b x^{\frac{21}{2}}}{21} + \frac{2 B b^{2} x^{\frac{27}{2}}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(7/2)*(b*x**3+a)**2*(B*x**3+A),x)
[Out]
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GIAC/XCAS [A] time = 0.215062, size = 72, normalized size = 1.14 \[ \frac{2}{27} \, B b^{2} x^{\frac{27}{2}} + \frac{4}{21} \, B a b x^{\frac{21}{2}} + \frac{2}{21} \, A b^{2} x^{\frac{21}{2}} + \frac{2}{15} \, B a^{2} x^{\frac{15}{2}} + \frac{4}{15} \, A a b x^{\frac{15}{2}} + \frac{2}{9} \, A a^{2} x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2*x^(7/2),x, algorithm="giac")
[Out]