Optimal. Leaf size=95 \[ \frac{a^7 x^8}{8}+\frac{7}{9} a^6 b x^9+\frac{21}{10} a^5 b^2 x^{10}+\frac{35}{11} a^4 b^3 x^{11}+\frac{35}{12} a^3 b^4 x^{12}+\frac{21}{13} a^2 b^5 x^{13}+\frac{1}{2} a b^6 x^{14}+\frac{b^7 x^{15}}{15} \]
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Rubi [A] time = 0.0912505, antiderivative size = 95, 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 \[ \frac{a^7 x^8}{8}+\frac{7}{9} a^6 b x^9+\frac{21}{10} a^5 b^2 x^{10}+\frac{35}{11} a^4 b^3 x^{11}+\frac{35}{12} a^3 b^4 x^{12}+\frac{21}{13} a^2 b^5 x^{13}+\frac{1}{2} a b^6 x^{14}+\frac{b^7 x^{15}}{15} \]
Antiderivative was successfully verified.
[In] Int[x^7*(a + b*x)^7,x]
[Out]
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Rubi in Sympy [A] time = 17.8805, size = 92, normalized size = 0.97 \[ \frac{a^{7} x^{8}}{8} + \frac{7 a^{6} b x^{9}}{9} + \frac{21 a^{5} b^{2} x^{10}}{10} + \frac{35 a^{4} b^{3} x^{11}}{11} + \frac{35 a^{3} b^{4} x^{12}}{12} + \frac{21 a^{2} b^{5} x^{13}}{13} + \frac{a b^{6} x^{14}}{2} + \frac{b^{7} x^{15}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**7*(b*x+a)**7,x)
[Out]
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Mathematica [A] time = 0.00351693, size = 95, normalized size = 1. \[ \frac{a^7 x^8}{8}+\frac{7}{9} a^6 b x^9+\frac{21}{10} a^5 b^2 x^{10}+\frac{35}{11} a^4 b^3 x^{11}+\frac{35}{12} a^3 b^4 x^{12}+\frac{21}{13} a^2 b^5 x^{13}+\frac{1}{2} a b^6 x^{14}+\frac{b^7 x^{15}}{15} \]
Antiderivative was successfully verified.
[In] Integrate[x^7*(a + b*x)^7,x]
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Maple [A] time = 0.001, size = 80, normalized size = 0.8 \[{\frac{{a}^{7}{x}^{8}}{8}}+{\frac{7\,{a}^{6}b{x}^{9}}{9}}+{\frac{21\,{a}^{5}{b}^{2}{x}^{10}}{10}}+{\frac{35\,{a}^{4}{b}^{3}{x}^{11}}{11}}+{\frac{35\,{a}^{3}{b}^{4}{x}^{12}}{12}}+{\frac{21\,{a}^{2}{b}^{5}{x}^{13}}{13}}+{\frac{a{b}^{6}{x}^{14}}{2}}+{\frac{{b}^{7}{x}^{15}}{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^7*(b*x+a)^7,x)
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Maxima [A] time = 1.34719, size = 107, normalized size = 1.13 \[ \frac{1}{15} \, b^{7} x^{15} + \frac{1}{2} \, a b^{6} x^{14} + \frac{21}{13} \, a^{2} b^{5} x^{13} + \frac{35}{12} \, a^{3} b^{4} x^{12} + \frac{35}{11} \, a^{4} b^{3} x^{11} + \frac{21}{10} \, a^{5} b^{2} x^{10} + \frac{7}{9} \, a^{6} b x^{9} + \frac{1}{8} \, a^{7} x^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^7*x^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.174687, size = 1, normalized size = 0.01 \[ \frac{1}{15} x^{15} b^{7} + \frac{1}{2} x^{14} b^{6} a + \frac{21}{13} x^{13} b^{5} a^{2} + \frac{35}{12} x^{12} b^{4} a^{3} + \frac{35}{11} x^{11} b^{3} a^{4} + \frac{21}{10} x^{10} b^{2} a^{5} + \frac{7}{9} x^{9} b a^{6} + \frac{1}{8} x^{8} a^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^7*x^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.143411, size = 92, normalized size = 0.97 \[ \frac{a^{7} x^{8}}{8} + \frac{7 a^{6} b x^{9}}{9} + \frac{21 a^{5} b^{2} x^{10}}{10} + \frac{35 a^{4} b^{3} x^{11}}{11} + \frac{35 a^{3} b^{4} x^{12}}{12} + \frac{21 a^{2} b^{5} x^{13}}{13} + \frac{a b^{6} x^{14}}{2} + \frac{b^{7} x^{15}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**7*(b*x+a)**7,x)
[Out]
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GIAC/XCAS [A] time = 0.216858, size = 107, normalized size = 1.13 \[ \frac{1}{15} \, b^{7} x^{15} + \frac{1}{2} \, a b^{6} x^{14} + \frac{21}{13} \, a^{2} b^{5} x^{13} + \frac{35}{12} \, a^{3} b^{4} x^{12} + \frac{35}{11} \, a^{4} b^{3} x^{11} + \frac{21}{10} \, a^{5} b^{2} x^{10} + \frac{7}{9} \, a^{6} b x^{9} + \frac{1}{8} \, a^{7} x^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^7*x^7,x, algorithm="giac")
[Out]