Optimal. Leaf size=81 \[ \frac{a^4 (a+b x)^8}{8 b^5}-\frac{4 a^3 (a+b x)^9}{9 b^5}+\frac{3 a^2 (a+b x)^{10}}{5 b^5}+\frac{(a+b x)^{12}}{12 b^5}-\frac{4 a (a+b x)^{11}}{11 b^5} \]
[Out]
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Rubi [A] time = 0.0830989, antiderivative size = 81, 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 \[ \frac{a^4 (a+b x)^8}{8 b^5}-\frac{4 a^3 (a+b x)^9}{9 b^5}+\frac{3 a^2 (a+b x)^{10}}{5 b^5}+\frac{(a+b x)^{12}}{12 b^5}-\frac{4 a (a+b x)^{11}}{11 b^5} \]
Antiderivative was successfully verified.
[In] Int[x^4*(a + b*x)^7,x]
[Out]
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Rubi in Sympy [A] time = 18.218, size = 75, normalized size = 0.93 \[ \frac{a^{4} \left (a + b x\right )^{8}}{8 b^{5}} - \frac{4 a^{3} \left (a + b x\right )^{9}}{9 b^{5}} + \frac{3 a^{2} \left (a + b x\right )^{10}}{5 b^{5}} - \frac{4 a \left (a + b x\right )^{11}}{11 b^{5}} + \frac{\left (a + b x\right )^{12}}{12 b^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4*(b*x+a)**7,x)
[Out]
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Mathematica [A] time = 0.00329103, size = 93, normalized size = 1.15 \[ \frac{a^7 x^5}{5}+\frac{7}{6} a^6 b x^6+3 a^5 b^2 x^7+\frac{35}{8} a^4 b^3 x^8+\frac{35}{9} a^3 b^4 x^9+\frac{21}{10} a^2 b^5 x^{10}+\frac{7}{11} a b^6 x^{11}+\frac{b^7 x^{12}}{12} \]
Antiderivative was successfully verified.
[In] Integrate[x^4*(a + b*x)^7,x]
[Out]
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Maple [A] time = 0.003, size = 80, normalized size = 1. \[{\frac{{b}^{7}{x}^{12}}{12}}+{\frac{7\,a{b}^{6}{x}^{11}}{11}}+{\frac{21\,{a}^{2}{b}^{5}{x}^{10}}{10}}+{\frac{35\,{a}^{3}{b}^{4}{x}^{9}}{9}}+{\frac{35\,{a}^{4}{b}^{3}{x}^{8}}{8}}+3\,{a}^{5}{b}^{2}{x}^{7}+{\frac{7\,{a}^{6}b{x}^{6}}{6}}+{\frac{{a}^{7}{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4*(b*x+a)^7,x)
[Out]
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Maxima [A] time = 1.34667, size = 107, normalized size = 1.32 \[ \frac{1}{12} \, b^{7} x^{12} + \frac{7}{11} \, a b^{6} x^{11} + \frac{21}{10} \, a^{2} b^{5} x^{10} + \frac{35}{9} \, a^{3} b^{4} x^{9} + \frac{35}{8} \, a^{4} b^{3} x^{8} + 3 \, a^{5} b^{2} x^{7} + \frac{7}{6} \, a^{6} b x^{6} + \frac{1}{5} \, a^{7} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^7*x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.176396, size = 1, normalized size = 0.01 \[ \frac{1}{12} x^{12} b^{7} + \frac{7}{11} x^{11} b^{6} a + \frac{21}{10} x^{10} b^{5} a^{2} + \frac{35}{9} x^{9} b^{4} a^{3} + \frac{35}{8} x^{8} b^{3} a^{4} + 3 x^{7} b^{2} a^{5} + \frac{7}{6} x^{6} b a^{6} + \frac{1}{5} x^{5} a^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^7*x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.135242, size = 92, normalized size = 1.14 \[ \frac{a^{7} x^{5}}{5} + \frac{7 a^{6} b x^{6}}{6} + 3 a^{5} b^{2} x^{7} + \frac{35 a^{4} b^{3} x^{8}}{8} + \frac{35 a^{3} b^{4} x^{9}}{9} + \frac{21 a^{2} b^{5} x^{10}}{10} + \frac{7 a b^{6} x^{11}}{11} + \frac{b^{7} x^{12}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4*(b*x+a)**7,x)
[Out]
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GIAC/XCAS [A] time = 0.207633, size = 107, normalized size = 1.32 \[ \frac{1}{12} \, b^{7} x^{12} + \frac{7}{11} \, a b^{6} x^{11} + \frac{21}{10} \, a^{2} b^{5} x^{10} + \frac{35}{9} \, a^{3} b^{4} x^{9} + \frac{35}{8} \, a^{4} b^{3} x^{8} + 3 \, a^{5} b^{2} x^{7} + \frac{7}{6} \, a^{6} b x^{6} + \frac{1}{5} \, a^{7} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^7*x^4,x, algorithm="giac")
[Out]