Optimal. Leaf size=72 \[ -\frac{a^3 \left (a+b x^3\right )^6}{18 b^4}+\frac{a^2 \left (a+b x^3\right )^7}{7 b^4}+\frac{\left (a+b x^3\right )^9}{27 b^4}-\frac{a \left (a+b x^3\right )^8}{8 b^4} \]
[Out]
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Rubi [A] time = 0.189253, antiderivative size = 72, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{a^3 \left (a+b x^3\right )^6}{18 b^4}+\frac{a^2 \left (a+b x^3\right )^7}{7 b^4}+\frac{\left (a+b x^3\right )^9}{27 b^4}-\frac{a \left (a+b x^3\right )^8}{8 b^4} \]
Antiderivative was successfully verified.
[In] Int[x^11*(a + b*x^3)^5,x]
[Out]
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Rubi in Sympy [A] time = 15.0275, size = 65, normalized size = 0.9 \[ \frac{a^{5} x^{12}}{12} + \frac{a^{4} b x^{15}}{3} + \frac{5 a^{3} b^{2} x^{18}}{9} + \frac{10 a^{2} b^{3} x^{21}}{21} + \frac{5 a b^{4} x^{24}}{24} + \frac{b^{5} x^{27}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**11*(b*x**3+a)**5,x)
[Out]
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Mathematica [A] time = 0.00385388, size = 69, normalized size = 0.96 \[ \frac{a^5 x^{12}}{12}+\frac{1}{3} a^4 b x^{15}+\frac{5}{9} a^3 b^2 x^{18}+\frac{10}{21} a^2 b^3 x^{21}+\frac{5}{24} a b^4 x^{24}+\frac{b^5 x^{27}}{27} \]
Antiderivative was successfully verified.
[In] Integrate[x^11*(a + b*x^3)^5,x]
[Out]
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Maple [A] time = 0.001, size = 58, normalized size = 0.8 \[{\frac{{b}^{5}{x}^{27}}{27}}+{\frac{5\,a{b}^{4}{x}^{24}}{24}}+{\frac{10\,{a}^{2}{b}^{3}{x}^{21}}{21}}+{\frac{5\,{a}^{3}{b}^{2}{x}^{18}}{9}}+{\frac{{a}^{4}b{x}^{15}}{3}}+{\frac{{a}^{5}{x}^{12}}{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^11*(b*x^3+a)^5,x)
[Out]
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Maxima [A] time = 1.43417, size = 77, normalized size = 1.07 \[ \frac{1}{27} \, b^{5} x^{27} + \frac{5}{24} \, a b^{4} x^{24} + \frac{10}{21} \, a^{2} b^{3} x^{21} + \frac{5}{9} \, a^{3} b^{2} x^{18} + \frac{1}{3} \, a^{4} b x^{15} + \frac{1}{12} \, a^{5} x^{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5*x^11,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.192928, size = 1, normalized size = 0.01 \[ \frac{1}{27} x^{27} b^{5} + \frac{5}{24} x^{24} b^{4} a + \frac{10}{21} x^{21} b^{3} a^{2} + \frac{5}{9} x^{18} b^{2} a^{3} + \frac{1}{3} x^{15} b a^{4} + \frac{1}{12} x^{12} a^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5*x^11,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.122263, size = 65, normalized size = 0.9 \[ \frac{a^{5} x^{12}}{12} + \frac{a^{4} b x^{15}}{3} + \frac{5 a^{3} b^{2} x^{18}}{9} + \frac{10 a^{2} b^{3} x^{21}}{21} + \frac{5 a b^{4} x^{24}}{24} + \frac{b^{5} x^{27}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**11*(b*x**3+a)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.215621, size = 77, normalized size = 1.07 \[ \frac{1}{27} \, b^{5} x^{27} + \frac{5}{24} \, a b^{4} x^{24} + \frac{10}{21} \, a^{2} b^{3} x^{21} + \frac{5}{9} \, a^{3} b^{2} x^{18} + \frac{1}{3} \, a^{4} b x^{15} + \frac{1}{12} \, a^{5} x^{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5*x^11,x, algorithm="giac")
[Out]