Optimal. Leaf size=37 \[ 2 \sqrt{x} (a B+A b)-\frac{2 a A}{5 x^{5/2}}+\frac{2}{7} b B x^{7/2} \]
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Rubi [A] time = 0.0584551, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ 2 \sqrt{x} (a B+A b)-\frac{2 a A}{5 x^{5/2}}+\frac{2}{7} b B x^{7/2} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^3)*(A + B*x^3))/x^(7/2),x]
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Rubi in Sympy [A] time = 6.12636, size = 37, normalized size = 1. \[ - \frac{2 A a}{5 x^{\frac{5}{2}}} + \frac{2 B b x^{\frac{7}{2}}}{7} + \sqrt{x} \left (2 A b + 2 B a\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)*(B*x**3+A)/x**(7/2),x)
[Out]
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Mathematica [A] time = 0.0202911, size = 33, normalized size = 0.89 \[ \frac{2 \left (35 x^3 (a B+A b)-7 a A+5 b B x^6\right )}{35 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^3)*(A + B*x^3))/x^(7/2),x]
[Out]
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Maple [A] time = 0.004, size = 32, normalized size = 0.9 \[ -{\frac{-10\,bB{x}^{6}-70\,A{x}^{3}b-70\,B{x}^{3}a+14\,Aa}{35}{x}^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)*(B*x^3+A)/x^(7/2),x)
[Out]
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Maxima [A] time = 1.8591, size = 36, normalized size = 0.97 \[ \frac{2}{7} \, B b x^{\frac{7}{2}} + 2 \,{\left (B a + A b\right )} \sqrt{x} - \frac{2 \, A a}{5 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)/x^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.228116, size = 39, normalized size = 1.05 \[ \frac{2 \,{\left (5 \, B b x^{6} + 35 \,{\left (B a + A b\right )} x^{3} - 7 \, A a\right )}}{35 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)/x^(7/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 14.7258, size = 42, normalized size = 1.14 \[ - \frac{2 A a}{5 x^{\frac{5}{2}}} + 2 A b \sqrt{x} + 2 B a \sqrt{x} + \frac{2 B b x^{\frac{7}{2}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)*(B*x**3+A)/x**(7/2),x)
[Out]
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GIAC/XCAS [A] time = 0.212451, size = 39, normalized size = 1.05 \[ \frac{2}{7} \, B b x^{\frac{7}{2}} + 2 \, B a \sqrt{x} + 2 \, A b \sqrt{x} - \frac{2 \, A a}{5 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)/x^(7/2),x, algorithm="giac")
[Out]