Optimal. Leaf size=66 \[ \frac{a^5 x^7}{7}+\frac{5}{8} a^4 b x^8+\frac{10}{9} a^3 b^2 x^9+a^2 b^3 x^{10}+\frac{5}{11} a b^4 x^{11}+\frac{b^5 x^{12}}{12} \]
[Out]
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Rubi [A] time = 0.0728336, antiderivative size = 66, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{a^5 x^7}{7}+\frac{5}{8} a^4 b x^8+\frac{10}{9} a^3 b^2 x^9+a^2 b^3 x^{10}+\frac{5}{11} a b^4 x^{11}+\frac{b^5 x^{12}}{12} \]
Antiderivative was successfully verified.
[In] Int[x^6*(a + b*x)^5,x]
[Out]
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Rubi in Sympy [A] time = 12.3958, size = 63, normalized size = 0.95 \[ \frac{a^{5} x^{7}}{7} + \frac{5 a^{4} b x^{8}}{8} + \frac{10 a^{3} b^{2} x^{9}}{9} + a^{2} b^{3} x^{10} + \frac{5 a b^{4} x^{11}}{11} + \frac{b^{5} x^{12}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**6*(b*x+a)**5,x)
[Out]
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Mathematica [A] time = 0.00343054, size = 66, normalized size = 1. \[ \frac{a^5 x^7}{7}+\frac{5}{8} a^4 b x^8+\frac{10}{9} a^3 b^2 x^9+a^2 b^3 x^{10}+\frac{5}{11} a b^4 x^{11}+\frac{b^5 x^{12}}{12} \]
Antiderivative was successfully verified.
[In] Integrate[x^6*(a + b*x)^5,x]
[Out]
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Maple [A] time = 0.036, size = 57, normalized size = 0.9 \[{\frac{{a}^{5}{x}^{7}}{7}}+{\frac{5\,{a}^{4}b{x}^{8}}{8}}+{\frac{10\,{a}^{3}{b}^{2}{x}^{9}}{9}}+{a}^{2}{b}^{3}{x}^{10}+{\frac{5\,a{b}^{4}{x}^{11}}{11}}+{\frac{{b}^{5}{x}^{12}}{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^6*(b*x+a)^5,x)
[Out]
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Maxima [A] time = 1.45358, size = 76, normalized size = 1.15 \[ \frac{1}{12} \, b^{5} x^{12} + \frac{5}{11} \, a b^{4} x^{11} + a^{2} b^{3} x^{10} + \frac{10}{9} \, a^{3} b^{2} x^{9} + \frac{5}{8} \, a^{4} b x^{8} + \frac{1}{7} \, a^{5} x^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5*x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.181033, size = 1, normalized size = 0.02 \[ \frac{1}{12} x^{12} b^{5} + \frac{5}{11} x^{11} b^{4} a + x^{10} b^{3} a^{2} + \frac{10}{9} x^{9} b^{2} a^{3} + \frac{5}{8} x^{8} b a^{4} + \frac{1}{7} x^{7} a^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5*x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.122087, size = 63, normalized size = 0.95 \[ \frac{a^{5} x^{7}}{7} + \frac{5 a^{4} b x^{8}}{8} + \frac{10 a^{3} b^{2} x^{9}}{9} + a^{2} b^{3} x^{10} + \frac{5 a b^{4} x^{11}}{11} + \frac{b^{5} x^{12}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**6*(b*x+a)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.21146, size = 76, normalized size = 1.15 \[ \frac{1}{12} \, b^{5} x^{12} + \frac{5}{11} \, a b^{4} x^{11} + a^{2} b^{3} x^{10} + \frac{10}{9} \, a^{3} b^{2} x^{9} + \frac{5}{8} \, a^{4} b x^{8} + \frac{1}{7} \, a^{5} x^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5*x^6,x, algorithm="giac")
[Out]