Optimal. Leaf size=85 \[ \frac{2}{11} A b^3 x^{11/2}+\frac{2}{13} b^2 x^{13/2} (3 A c+b B)+\frac{2}{17} c^2 x^{17/2} (A c+3 b B)+\frac{2}{5} b c x^{15/2} (A c+b B)+\frac{2}{19} B c^3 x^{19/2} \]
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Rubi [A] time = 0.122693, 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 \[ \frac{2}{11} A b^3 x^{11/2}+\frac{2}{13} b^2 x^{13/2} (3 A c+b B)+\frac{2}{17} c^2 x^{17/2} (A c+3 b B)+\frac{2}{5} b c x^{15/2} (A c+b B)+\frac{2}{19} B c^3 x^{19/2} \]
Antiderivative was successfully verified.
[In] Int[x^(3/2)*(A + B*x)*(b*x + c*x^2)^3,x]
[Out]
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Rubi in Sympy [A] time = 13.7658, size = 85, normalized size = 1. \[ \frac{2 A b^{3} x^{\frac{11}{2}}}{11} + \frac{2 B c^{3} x^{\frac{19}{2}}}{19} + \frac{2 b^{2} x^{\frac{13}{2}} \left (3 A c + B b\right )}{13} + \frac{2 b c x^{\frac{15}{2}} \left (A c + B b\right )}{5} + \frac{2 c^{2} x^{\frac{17}{2}} \left (A c + 3 B b\right )}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(3/2)*(B*x+A)*(c*x**2+b*x)**3,x)
[Out]
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Mathematica [A] time = 0.0394312, size = 85, normalized size = 1. \[ \frac{2}{11} A b^3 x^{11/2}+\frac{2}{13} b^2 x^{13/2} (3 A c+b B)+\frac{2}{17} c^2 x^{17/2} (A c+3 b B)+\frac{2}{5} b c x^{15/2} (A c+b B)+\frac{2}{19} B c^3 x^{19/2} \]
Antiderivative was successfully verified.
[In] Integrate[x^(3/2)*(A + B*x)*(b*x + c*x^2)^3,x]
[Out]
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Maple [A] time = 0.01, size = 76, normalized size = 0.9 \[{\frac{24310\,B{c}^{3}{x}^{4}+27170\,A{c}^{3}{x}^{3}+81510\,B{x}^{3}b{c}^{2}+92378\,Ab{c}^{2}{x}^{2}+92378\,B{x}^{2}{b}^{2}c+106590\,A{b}^{2}cx+35530\,Bx{b}^{3}+41990\,A{b}^{3}}{230945}{x}^{{\frac{11}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(3/2)*(B*x+A)*(c*x^2+b*x)^3,x)
[Out]
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Maxima [A] time = 0.679924, size = 99, normalized size = 1.16 \[ \frac{2}{19} \, B c^{3} x^{\frac{19}{2}} + \frac{2}{11} \, A b^{3} x^{\frac{11}{2}} + \frac{2}{17} \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{\frac{17}{2}} + \frac{2}{5} \,{\left (B b^{2} c + A b c^{2}\right )} x^{\frac{15}{2}} + \frac{2}{13} \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x^{\frac{13}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)*x^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.30556, size = 105, normalized size = 1.24 \[ \frac{2}{230945} \,{\left (12155 \, B c^{3} x^{9} + 20995 \, A b^{3} x^{5} + 13585 \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{8} + 46189 \,{\left (B b^{2} c + A b c^{2}\right )} x^{7} + 17765 \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x^{6}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)*x^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 23.4263, size = 114, normalized size = 1.34 \[ \frac{2 A b^{3} x^{\frac{11}{2}}}{11} + \frac{6 A b^{2} c x^{\frac{13}{2}}}{13} + \frac{2 A b c^{2} x^{\frac{15}{2}}}{5} + \frac{2 A c^{3} x^{\frac{17}{2}}}{17} + \frac{2 B b^{3} x^{\frac{13}{2}}}{13} + \frac{2 B b^{2} c x^{\frac{15}{2}}}{5} + \frac{6 B b c^{2} x^{\frac{17}{2}}}{17} + \frac{2 B c^{3} x^{\frac{19}{2}}}{19} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(3/2)*(B*x+A)*(c*x**2+b*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.267355, size = 104, normalized size = 1.22 \[ \frac{2}{19} \, B c^{3} x^{\frac{19}{2}} + \frac{6}{17} \, B b c^{2} x^{\frac{17}{2}} + \frac{2}{17} \, A c^{3} x^{\frac{17}{2}} + \frac{2}{5} \, B b^{2} c x^{\frac{15}{2}} + \frac{2}{5} \, A b c^{2} x^{\frac{15}{2}} + \frac{2}{13} \, B b^{3} x^{\frac{13}{2}} + \frac{6}{13} \, A b^{2} c x^{\frac{13}{2}} + \frac{2}{11} \, A b^{3} x^{\frac{11}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)*x^(3/2),x, algorithm="giac")
[Out]