Optimal. Leaf size=85 \[ \frac{2}{5} a^3 A x^{5/2}+\frac{2}{7} a^2 x^{7/2} (a B+3 A b)+\frac{2}{11} b^2 x^{11/2} (3 a B+A b)+\frac{2}{3} a b x^{9/2} (a B+A b)+\frac{2}{13} b^3 B x^{13/2} \]
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Rubi [A] time = 0.104972, antiderivative size = 85, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ \frac{2}{5} a^3 A x^{5/2}+\frac{2}{7} a^2 x^{7/2} (a B+3 A b)+\frac{2}{11} b^2 x^{11/2} (3 a B+A b)+\frac{2}{3} a b x^{9/2} (a B+A b)+\frac{2}{13} b^3 B x^{13/2} \]
Antiderivative was successfully verified.
[In] Int[x^(3/2)*(a + b*x)^3*(A + B*x),x]
[Out]
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Rubi in Sympy [A] time = 12.5153, size = 85, normalized size = 1. \[ \frac{2 A a^{3} x^{\frac{5}{2}}}{5} + \frac{2 B b^{3} x^{\frac{13}{2}}}{13} + \frac{2 a^{2} x^{\frac{7}{2}} \left (3 A b + B a\right )}{7} + \frac{2 a b x^{\frac{9}{2}} \left (A b + B a\right )}{3} + \frac{2 b^{2} x^{\frac{11}{2}} \left (A b + 3 B a\right )}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(3/2)*(b*x+a)**3*(B*x+A),x)
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Mathematica [A] time = 0.0361539, size = 71, normalized size = 0.84 \[ \frac{2 x^{5/2} \left (429 a^3 (7 A+5 B x)+715 a^2 b x (9 A+7 B x)+455 a b^2 x^2 (11 A+9 B x)+105 b^3 x^3 (13 A+11 B x)\right )}{15015} \]
Antiderivative was successfully verified.
[In] Integrate[x^(3/2)*(a + b*x)^3*(A + B*x),x]
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Maple [A] time = 0.007, size = 76, normalized size = 0.9 \[{\frac{2310\,B{b}^{3}{x}^{4}+2730\,A{b}^{3}{x}^{3}+8190\,B{x}^{3}a{b}^{2}+10010\,aA{b}^{2}{x}^{2}+10010\,B{x}^{2}{a}^{2}b+12870\,{a}^{2}Abx+4290\,{a}^{3}Bx+6006\,{a}^{3}A}{15015}{x}^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(3/2)*(b*x+a)^3*(B*x+A),x)
[Out]
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Maxima [A] time = 1.34545, size = 99, normalized size = 1.16 \[ \frac{2}{13} \, B b^{3} x^{\frac{13}{2}} + \frac{2}{5} \, A a^{3} x^{\frac{5}{2}} + \frac{2}{11} \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{\frac{11}{2}} + \frac{2}{3} \,{\left (B a^{2} b + A a b^{2}\right )} x^{\frac{9}{2}} + \frac{2}{7} \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3*x^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208591, size = 105, normalized size = 1.24 \[ \frac{2}{15015} \,{\left (1155 \, B b^{3} x^{6} + 3003 \, A a^{3} x^{2} + 1365 \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{5} + 5005 \,{\left (B a^{2} b + A a b^{2}\right )} x^{4} + 2145 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x^{3}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3*x^(3/2),x, algorithm="fricas")
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Sympy [A] time = 5.27254, size = 114, normalized size = 1.34 \[ \frac{2 A a^{3} x^{\frac{5}{2}}}{5} + \frac{6 A a^{2} b x^{\frac{7}{2}}}{7} + \frac{2 A a b^{2} x^{\frac{9}{2}}}{3} + \frac{2 A b^{3} x^{\frac{11}{2}}}{11} + \frac{2 B a^{3} x^{\frac{7}{2}}}{7} + \frac{2 B a^{2} b x^{\frac{9}{2}}}{3} + \frac{6 B a b^{2} x^{\frac{11}{2}}}{11} + \frac{2 B b^{3} x^{\frac{13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(3/2)*(b*x+a)**3*(B*x+A),x)
[Out]
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GIAC/XCAS [A] time = 0.278187, size = 104, normalized size = 1.22 \[ \frac{2}{13} \, B b^{3} x^{\frac{13}{2}} + \frac{6}{11} \, B a b^{2} x^{\frac{11}{2}} + \frac{2}{11} \, A b^{3} x^{\frac{11}{2}} + \frac{2}{3} \, B a^{2} b x^{\frac{9}{2}} + \frac{2}{3} \, A a b^{2} x^{\frac{9}{2}} + \frac{2}{7} \, B a^{3} x^{\frac{7}{2}} + \frac{6}{7} \, A a^{2} b x^{\frac{7}{2}} + \frac{2}{5} \, A a^{3} x^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3*x^(3/2),x, algorithm="giac")
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