Optimal. Leaf size=61 \[ -\frac{2 a^2 A}{5 x^{5/2}}+\frac{2}{7} b x^{7/2} (2 a B+A b)+2 a \sqrt{x} (a B+2 A b)+\frac{2}{13} b^2 B x^{13/2} \]
[Out]
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Rubi [A] time = 0.0983477, 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 \[ -\frac{2 a^2 A}{5 x^{5/2}}+\frac{2}{7} b x^{7/2} (2 a B+A b)+2 a \sqrt{x} (a B+2 A b)+\frac{2}{13} b^2 B x^{13/2} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^3)^2*(A + B*x^3))/x^(7/2),x]
[Out]
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Rubi in Sympy [A] time = 10.894, size = 61, normalized size = 1. \[ - \frac{2 A a^{2}}{5 x^{\frac{5}{2}}} + \frac{2 B b^{2} x^{\frac{13}{2}}}{13} + 2 a \sqrt{x} \left (2 A b + B a\right ) + \frac{2 b x^{\frac{7}{2}} \left (A b + 2 B a\right )}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**2*(B*x**3+A)/x**(7/2),x)
[Out]
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Mathematica [A] time = 0.0374611, size = 53, normalized size = 0.87 \[ \frac{2 \left (-91 a^2 A+65 b x^6 (2 a B+A b)+455 a x^3 (a B+2 A b)+35 b^2 B x^9\right )}{455 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^3)^2*(A + B*x^3))/x^(7/2),x]
[Out]
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Maple [A] time = 0.009, size = 56, normalized size = 0.9 \[ -{\frac{-70\,B{x}^{9}{b}^{2}-130\,A{b}^{2}{x}^{6}-260\,B{x}^{6}ab-1820\,aAb{x}^{3}-910\,B{x}^{3}{a}^{2}+182\,A{a}^{2}}{455}{x}^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^2*(B*x^3+A)/x^(7/2),x)
[Out]
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Maxima [A] time = 1.42658, size = 69, normalized size = 1.13 \[ \frac{2}{13} \, B b^{2} x^{\frac{13}{2}} + \frac{2}{7} \,{\left (2 \, B a b + A b^{2}\right )} x^{\frac{7}{2}} + 2 \,{\left (B a^{2} + 2 \, A a b\right )} \sqrt{x} - \frac{2 \, A a^{2}}{5 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/x^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.234177, size = 72, normalized size = 1.18 \[ \frac{2 \,{\left (35 \, B b^{2} x^{9} + 65 \,{\left (2 \, B a b + A b^{2}\right )} x^{6} + 455 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} - 91 \, A a^{2}\right )}}{455 \, x^{\frac{5}{2}}} \]
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="fricas")
[Out]
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Sympy [A] time = 42.0911, size = 76, normalized size = 1.25 \[ - \frac{2 A a^{2}}{5 x^{\frac{5}{2}}} + 4 A a b \sqrt{x} + \frac{2 A b^{2} x^{\frac{7}{2}}}{7} + 2 B a^{2} \sqrt{x} + \frac{4 B a b x^{\frac{7}{2}}}{7} + \frac{2 B b^{2} x^{\frac{13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**2*(B*x**3+A)/x**(7/2),x)
[Out]
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GIAC/XCAS [A] time = 0.210256, size = 72, normalized size = 1.18 \[ \frac{2}{13} \, B b^{2} x^{\frac{13}{2}} + \frac{4}{7} \, B a b x^{\frac{7}{2}} + \frac{2}{7} \, A b^{2} x^{\frac{7}{2}} + 2 \, B a^{2} \sqrt{x} + 4 \, A a b \sqrt{x} - \frac{2 \, A a^{2}}{5 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^2/x^(7/2),x, algorithm="giac")
[Out]