Optimal. Leaf size=85 \[ \frac{2}{13} A b^3 x^{13/2}+\frac{2}{15} b^2 x^{15/2} (3 A c+b B)+\frac{2}{19} c^2 x^{19/2} (A c+3 b B)+\frac{6}{17} b c x^{17/2} (A c+b B)+\frac{2}{21} B c^3 x^{21/2} \]
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Rubi [A] time = 0.122815, antiderivative size = 85, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{2}{13} A b^3 x^{13/2}+\frac{2}{15} b^2 x^{15/2} (3 A c+b B)+\frac{2}{19} c^2 x^{19/2} (A c+3 b B)+\frac{6}{17} b c x^{17/2} (A c+b B)+\frac{2}{21} B c^3 x^{21/2} \]
Antiderivative was successfully verified.
[In] Int[x^(5/2)*(A + B*x)*(b*x + c*x^2)^3,x]
[Out]
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Rubi in Sympy [A] time = 13.7307, size = 85, normalized size = 1. \[ \frac{2 A b^{3} x^{\frac{13}{2}}}{13} + \frac{2 B c^{3} x^{\frac{21}{2}}}{21} + \frac{2 b^{2} x^{\frac{15}{2}} \left (3 A c + B b\right )}{15} + \frac{6 b c x^{\frac{17}{2}} \left (A c + B b\right )}{17} + \frac{2 c^{2} x^{\frac{19}{2}} \left (A c + 3 B b\right )}{19} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(5/2)*(B*x+A)*(c*x**2+b*x)**3,x)
[Out]
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Mathematica [A] time = 0.0385861, size = 85, normalized size = 1. \[ \frac{2}{13} A b^3 x^{13/2}+\frac{2}{15} b^2 x^{15/2} (3 A c+b B)+\frac{2}{19} c^2 x^{19/2} (A c+3 b B)+\frac{6}{17} b c x^{17/2} (A c+b B)+\frac{2}{21} B c^3 x^{21/2} \]
Antiderivative was successfully verified.
[In] Integrate[x^(5/2)*(A + B*x)*(b*x + c*x^2)^3,x]
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Maple [A] time = 0.008, size = 76, normalized size = 0.9 \[{\frac{41990\,B{c}^{3}{x}^{4}+46410\,A{c}^{3}{x}^{3}+139230\,B{x}^{3}b{c}^{2}+155610\,Ab{c}^{2}{x}^{2}+155610\,B{x}^{2}{b}^{2}c+176358\,A{b}^{2}cx+58786\,Bx{b}^{3}+67830\,A{b}^{3}}{440895}{x}^{{\frac{13}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(5/2)*(B*x+A)*(c*x^2+b*x)^3,x)
[Out]
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Maxima [A] time = 0.682513, size = 99, normalized size = 1.16 \[ \frac{2}{21} \, B c^{3} x^{\frac{21}{2}} + \frac{2}{13} \, A b^{3} x^{\frac{13}{2}} + \frac{2}{19} \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{\frac{19}{2}} + \frac{6}{17} \,{\left (B b^{2} c + A b c^{2}\right )} x^{\frac{17}{2}} + \frac{2}{15} \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x^{\frac{15}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)*x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.292536, size = 105, normalized size = 1.24 \[ \frac{2}{440895} \,{\left (20995 \, B c^{3} x^{10} + 33915 \, A b^{3} x^{6} + 23205 \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{9} + 77805 \,{\left (B b^{2} c + A b c^{2}\right )} x^{8} + 29393 \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x^{7}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)*x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 46.0733, size = 114, normalized size = 1.34 \[ \frac{2 A b^{3} x^{\frac{13}{2}}}{13} + \frac{2 A b^{2} c x^{\frac{15}{2}}}{5} + \frac{6 A b c^{2} x^{\frac{17}{2}}}{17} + \frac{2 A c^{3} x^{\frac{19}{2}}}{19} + \frac{2 B b^{3} x^{\frac{15}{2}}}{15} + \frac{6 B b^{2} c x^{\frac{17}{2}}}{17} + \frac{6 B b c^{2} x^{\frac{19}{2}}}{19} + \frac{2 B c^{3} x^{\frac{21}{2}}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(5/2)*(B*x+A)*(c*x**2+b*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.269243, size = 104, normalized size = 1.22 \[ \frac{2}{21} \, B c^{3} x^{\frac{21}{2}} + \frac{6}{19} \, B b c^{2} x^{\frac{19}{2}} + \frac{2}{19} \, A c^{3} x^{\frac{19}{2}} + \frac{6}{17} \, B b^{2} c x^{\frac{17}{2}} + \frac{6}{17} \, A b c^{2} x^{\frac{17}{2}} + \frac{2}{15} \, B b^{3} x^{\frac{15}{2}} + \frac{2}{5} \, A b^{2} c x^{\frac{15}{2}} + \frac{2}{13} \, A b^{3} x^{\frac{13}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)*x^(5/2),x, algorithm="giac")
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