Optimal. Leaf size=83 \[ -\frac{2 a^3 A}{\sqrt{x}}+\frac{2}{5} a^2 x^{5/2} (a B+3 A b)+\frac{2}{17} b^2 x^{17/2} (3 a B+A b)+\frac{6}{11} a b x^{11/2} (a B+A b)+\frac{2}{23} b^3 B x^{23/2} \]
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Rubi [A] time = 0.126183, antiderivative size = 83, 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 \[ -\frac{2 a^3 A}{\sqrt{x}}+\frac{2}{5} a^2 x^{5/2} (a B+3 A b)+\frac{2}{17} b^2 x^{17/2} (3 a B+A b)+\frac{6}{11} a b x^{11/2} (a B+A b)+\frac{2}{23} b^3 B x^{23/2} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^3)^3*(A + B*x^3))/x^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 14.1562, size = 83, normalized size = 1. \[ - \frac{2 A a^{3}}{\sqrt{x}} + \frac{2 B b^{3} x^{\frac{23}{2}}}{23} + \frac{2 a^{2} x^{\frac{5}{2}} \left (3 A b + B a\right )}{5} + \frac{6 a b x^{\frac{11}{2}} \left (A b + B a\right )}{11} + \frac{2 b^{2} x^{\frac{17}{2}} \left (A b + 3 B a\right )}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**3*(B*x**3+A)/x**(3/2),x)
[Out]
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Mathematica [A] time = 0.0675491, size = 83, normalized size = 1. \[ -\frac{2 a^3 A}{\sqrt{x}}+\frac{2}{5} a^2 x^{5/2} (a B+3 A b)+\frac{2}{17} b^2 x^{17/2} (3 a B+A b)+\frac{6}{11} a b x^{11/2} (a B+A b)+\frac{2}{23} b^3 B x^{23/2} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^3)^3*(A + B*x^3))/x^(3/2),x]
[Out]
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Maple [A] time = 0.009, size = 80, normalized size = 1. \[ -{\frac{-1870\,{b}^{3}B{x}^{12}-2530\,{x}^{9}{b}^{3}A-7590\,{x}^{9}a{b}^{2}B-11730\,{x}^{6}a{b}^{2}A-11730\,{x}^{6}{a}^{2}bB-25806\,{x}^{3}A{a}^{2}b-8602\,{x}^{3}B{a}^{3}+43010\,A{a}^{3}}{21505}{\frac{1}{\sqrt{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^3*(B*x^3+A)/x^(3/2),x)
[Out]
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Maxima [A] time = 1.36665, size = 99, normalized size = 1.19 \[ \frac{2}{23} \, B b^{3} x^{\frac{23}{2}} + \frac{2}{17} \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{\frac{17}{2}} + \frac{6}{11} \,{\left (B a^{2} b + A a b^{2}\right )} x^{\frac{11}{2}} - \frac{2 \, A a^{3}}{\sqrt{x}} + \frac{2}{5} \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^3/x^(3/2),x, algorithm="maxima")
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Fricas [A] time = 0.23055, size = 101, normalized size = 1.22 \[ \frac{2 \,{\left (935 \, B b^{3} x^{12} + 1265 \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{9} + 5865 \,{\left (B a^{2} b + A a b^{2}\right )} x^{6} - 21505 \, A a^{3} + 4301 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x^{3}\right )}}{21505 \, \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^3/x^(3/2),x, algorithm="fricas")
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Sympy [A] time = 71.2225, size = 112, normalized size = 1.35 \[ - \frac{2 A a^{3}}{\sqrt{x}} + \frac{6 A a^{2} b x^{\frac{5}{2}}}{5} + \frac{6 A a b^{2} x^{\frac{11}{2}}}{11} + \frac{2 A b^{3} x^{\frac{17}{2}}}{17} + \frac{2 B a^{3} x^{\frac{5}{2}}}{5} + \frac{6 B a^{2} b x^{\frac{11}{2}}}{11} + \frac{6 B a b^{2} x^{\frac{17}{2}}}{17} + \frac{2 B b^{3} x^{\frac{23}{2}}}{23} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**3*(B*x**3+A)/x**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.210629, size = 104, normalized size = 1.25 \[ \frac{2}{23} \, B b^{3} x^{\frac{23}{2}} + \frac{6}{17} \, B a b^{2} x^{\frac{17}{2}} + \frac{2}{17} \, A b^{3} x^{\frac{17}{2}} + \frac{6}{11} \, B a^{2} b x^{\frac{11}{2}} + \frac{6}{11} \, A a b^{2} x^{\frac{11}{2}} + \frac{2}{5} \, B a^{3} x^{\frac{5}{2}} + \frac{6}{5} \, A a^{2} b x^{\frac{5}{2}} - \frac{2 \, A a^{3}}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^3/x^(3/2),x, algorithm="giac")
[Out]