Optimal. Leaf size=85 \[ -\frac{2 a^3 A}{3 x^{3/2}}+\frac{2}{3} a^2 x^{3/2} (a B+3 A b)+\frac{2}{15} b^2 x^{15/2} (3 a B+A b)+\frac{2}{3} a b x^{9/2} (a B+A b)+\frac{2}{21} b^3 B x^{21/2} \]
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Rubi [A] time = 0.129811, antiderivative size = 85, 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 \[ -\frac{2 a^3 A}{3 x^{3/2}}+\frac{2}{3} a^2 x^{3/2} (a B+3 A b)+\frac{2}{15} b^2 x^{15/2} (3 a B+A b)+\frac{2}{3} a b x^{9/2} (a B+A b)+\frac{2}{21} b^3 B x^{21/2} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^3)^3*(A + B*x^3))/x^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 14.3153, size = 83, normalized size = 0.98 \[ - \frac{2 A a^{3}}{3 x^{\frac{3}{2}}} + \frac{2 B b^{3} x^{\frac{21}{2}}}{21} + 2 a^{2} x^{\frac{3}{2}} \left (A b + \frac{B a}{3}\right ) + \frac{2 a b x^{\frac{9}{2}} \left (A b + B a\right )}{3} + \frac{2 b^{2} x^{\frac{15}{2}} \left (A b + 3 B a\right )}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**3*(B*x**3+A)/x**(5/2),x)
[Out]
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Mathematica [A] time = 0.0411578, size = 77, normalized size = 0.91 \[ \frac{2 \left (-35 a^3 \left (A-B x^3\right )+35 a^2 b x^3 \left (3 A+B x^3\right )+7 a b^2 x^6 \left (5 A+3 B x^3\right )+b^3 x^9 \left (7 A+5 B x^3\right )\right )}{105 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^3)^3*(A + B*x^3))/x^(5/2),x]
[Out]
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Maple [A] time = 0.01, size = 80, normalized size = 0.9 \[ -{\frac{-10\,{b}^{3}B{x}^{12}-14\,{x}^{9}{b}^{3}A-42\,{x}^{9}a{b}^{2}B-70\,{x}^{6}a{b}^{2}A-70\,{x}^{6}{a}^{2}bB-210\,{x}^{3}A{a}^{2}b-70\,{x}^{3}B{a}^{3}+70\,A{a}^{3}}{105}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^3*(B*x^3+A)/x^(5/2),x)
[Out]
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Maxima [A] time = 1.35764, size = 99, normalized size = 1.16 \[ \frac{2}{21} \, B b^{3} x^{\frac{21}{2}} + \frac{2}{15} \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{\frac{15}{2}} + \frac{2}{3} \,{\left (B a^{2} b + A a b^{2}\right )} x^{\frac{9}{2}} - \frac{2 \, A a^{3}}{3 \, x^{\frac{3}{2}}} + \frac{2}{3} \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^3/x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.238611, size = 101, normalized size = 1.19 \[ \frac{2 \,{\left (5 \, B b^{3} x^{12} + 7 \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{9} + 35 \,{\left (B a^{2} b + A a b^{2}\right )} x^{6} - 35 \, A a^{3} + 35 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x^{3}\right )}}{105 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^3/x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 80.9534, size = 112, normalized size = 1.32 \[ - \frac{2 A a^{3}}{3 x^{\frac{3}{2}}} + 2 A a^{2} b x^{\frac{3}{2}} + \frac{2 A a b^{2} x^{\frac{9}{2}}}{3} + \frac{2 A b^{3} x^{\frac{15}{2}}}{15} + \frac{2 B a^{3} x^{\frac{3}{2}}}{3} + \frac{2 B a^{2} b x^{\frac{9}{2}}}{3} + \frac{2 B a b^{2} x^{\frac{15}{2}}}{5} + \frac{2 B b^{3} x^{\frac{21}{2}}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**3*(B*x**3+A)/x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.212935, size = 104, normalized size = 1.22 \[ \frac{2}{21} \, B b^{3} x^{\frac{21}{2}} + \frac{2}{5} \, B a b^{2} x^{\frac{15}{2}} + \frac{2}{15} \, A b^{3} x^{\frac{15}{2}} + \frac{2}{3} \, B a^{2} b x^{\frac{9}{2}} + \frac{2}{3} \, A a b^{2} x^{\frac{9}{2}} + \frac{2}{3} \, B a^{3} x^{\frac{3}{2}} + 2 \, A a^{2} b x^{\frac{3}{2}} - \frac{2 \, A a^{3}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^3/x^(5/2),x, algorithm="giac")
[Out]