Optimal. Leaf size=85 \[ \frac{2}{7} A b^3 x^{7/2}+\frac{2}{9} b^2 x^{9/2} (3 A c+b B)+\frac{2}{13} c^2 x^{13/2} (A c+3 b B)+\frac{6}{11} b c x^{11/2} (A c+b B)+\frac{2}{15} B c^3 x^{15/2} \]
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Rubi [A] time = 0.121031, 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 \[ \frac{2}{7} A b^3 x^{7/2}+\frac{2}{9} b^2 x^{9/2} (3 A c+b B)+\frac{2}{13} c^2 x^{13/2} (A c+3 b B)+\frac{6}{11} b c x^{11/2} (A c+b B)+\frac{2}{15} B c^3 x^{15/2} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(b*x + c*x^2)^3)/Sqrt[x],x]
[Out]
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Rubi in Sympy [A] time = 14.0927, size = 85, normalized size = 1. \[ \frac{2 A b^{3} x^{\frac{7}{2}}}{7} + \frac{2 B c^{3} x^{\frac{15}{2}}}{15} + \frac{2 b^{2} x^{\frac{9}{2}} \left (3 A c + B b\right )}{9} + \frac{6 b c x^{\frac{11}{2}} \left (A c + B b\right )}{11} + \frac{2 c^{2} x^{\frac{13}{2}} \left (A c + 3 B b\right )}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x)**3/x**(1/2),x)
[Out]
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Mathematica [A] time = 0.042344, size = 69, normalized size = 0.81 \[ \frac{2 x^{7/2} \left (6435 A b^3+5005 b^2 x (3 A c+b B)+3465 c^2 x^3 (A c+3 b B)+12285 b c x^2 (A c+b B)+3003 B c^3 x^4\right )}{45045} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(b*x + c*x^2)^3)/Sqrt[x],x]
[Out]
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Maple [A] time = 0.007, size = 76, normalized size = 0.9 \[{\frac{6006\,B{c}^{3}{x}^{4}+6930\,A{c}^{3}{x}^{3}+20790\,B{x}^{3}b{c}^{2}+24570\,Ab{c}^{2}{x}^{2}+24570\,B{x}^{2}{b}^{2}c+30030\,A{b}^{2}cx+10010\,Bx{b}^{3}+12870\,A{b}^{3}}{45045}{x}^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x)^3/x^(1/2),x)
[Out]
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Maxima [A] time = 0.687442, size = 99, normalized size = 1.16 \[ \frac{2}{15} \, B c^{3} x^{\frac{15}{2}} + \frac{2}{7} \, A b^{3} x^{\frac{7}{2}} + \frac{2}{13} \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{\frac{13}{2}} + \frac{6}{11} \,{\left (B b^{2} c + A b c^{2}\right )} x^{\frac{11}{2}} + \frac{2}{9} \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.280278, size = 105, normalized size = 1.24 \[ \frac{2}{45045} \,{\left (3003 \, B c^{3} x^{7} + 6435 \, A b^{3} x^{3} + 3465 \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{6} + 12285 \,{\left (B b^{2} c + A b c^{2}\right )} x^{5} + 5005 \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x^{4}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.40621, size = 114, normalized size = 1.34 \[ \frac{2 A b^{3} x^{\frac{7}{2}}}{7} + \frac{2 A b^{2} c x^{\frac{9}{2}}}{3} + \frac{6 A b c^{2} x^{\frac{11}{2}}}{11} + \frac{2 A c^{3} x^{\frac{13}{2}}}{13} + \frac{2 B b^{3} x^{\frac{9}{2}}}{9} + \frac{6 B b^{2} c x^{\frac{11}{2}}}{11} + \frac{6 B b c^{2} x^{\frac{13}{2}}}{13} + \frac{2 B c^{3} x^{\frac{15}{2}}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x)**3/x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.269046, size = 104, normalized size = 1.22 \[ \frac{2}{15} \, B c^{3} x^{\frac{15}{2}} + \frac{6}{13} \, B b c^{2} x^{\frac{13}{2}} + \frac{2}{13} \, A c^{3} x^{\frac{13}{2}} + \frac{6}{11} \, B b^{2} c x^{\frac{11}{2}} + \frac{6}{11} \, A b c^{2} x^{\frac{11}{2}} + \frac{2}{9} \, B b^{3} x^{\frac{9}{2}} + \frac{2}{3} \, A b^{2} c x^{\frac{9}{2}} + \frac{2}{7} \, A b^{3} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/sqrt(x),x, algorithm="giac")
[Out]