Optimal. Leaf size=102 \[ -\frac{a^8}{4 x^4}-\frac{8 a^7 b}{x}+14 a^6 b^2 x^2+\frac{56}{5} a^5 b^3 x^5+\frac{35}{4} a^4 b^4 x^8+\frac{56}{11} a^3 b^5 x^{11}+2 a^2 b^6 x^{14}+\frac{8}{17} a b^7 x^{17}+\frac{b^8 x^{20}}{20} \]
[Out]
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Rubi [A] time = 0.0973903, antiderivative size = 102, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{a^8}{4 x^4}-\frac{8 a^7 b}{x}+14 a^6 b^2 x^2+\frac{56}{5} a^5 b^3 x^5+\frac{35}{4} a^4 b^4 x^8+\frac{56}{11} a^3 b^5 x^{11}+2 a^2 b^6 x^{14}+\frac{8}{17} a b^7 x^{17}+\frac{b^8 x^{20}}{20} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^8/x^5,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{8}}{4 x^{4}} - \frac{8 a^{7} b}{x} + 28 a^{6} b^{2} \int x\, dx + \frac{56 a^{5} b^{3} x^{5}}{5} + \frac{35 a^{4} b^{4} x^{8}}{4} + \frac{56 a^{3} b^{5} x^{11}}{11} + 2 a^{2} b^{6} x^{14} + \frac{8 a b^{7} x^{17}}{17} + \frac{b^{8} x^{20}}{20} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**8/x**5,x)
[Out]
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Mathematica [A] time = 0.00835476, size = 102, normalized size = 1. \[ -\frac{a^8}{4 x^4}-\frac{8 a^7 b}{x}+14 a^6 b^2 x^2+\frac{56}{5} a^5 b^3 x^5+\frac{35}{4} a^4 b^4 x^8+\frac{56}{11} a^3 b^5 x^{11}+2 a^2 b^6 x^{14}+\frac{8}{17} a b^7 x^{17}+\frac{b^8 x^{20}}{20} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^8/x^5,x]
[Out]
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Maple [A] time = 0.008, size = 91, normalized size = 0.9 \[ -{\frac{{a}^{8}}{4\,{x}^{4}}}-8\,{\frac{{a}^{7}b}{x}}+14\,{a}^{6}{b}^{2}{x}^{2}+{\frac{56\,{a}^{5}{b}^{3}{x}^{5}}{5}}+{\frac{35\,{a}^{4}{b}^{4}{x}^{8}}{4}}+{\frac{56\,{a}^{3}{b}^{5}{x}^{11}}{11}}+2\,{a}^{2}{b}^{6}{x}^{14}+{\frac{8\,a{b}^{7}{x}^{17}}{17}}+{\frac{{b}^{8}{x}^{20}}{20}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^8/x^5,x)
[Out]
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Maxima [A] time = 1.43346, size = 123, normalized size = 1.21 \[ \frac{1}{20} \, b^{8} x^{20} + \frac{8}{17} \, a b^{7} x^{17} + 2 \, a^{2} b^{6} x^{14} + \frac{56}{11} \, a^{3} b^{5} x^{11} + \frac{35}{4} \, a^{4} b^{4} x^{8} + \frac{56}{5} \, a^{5} b^{3} x^{5} + 14 \, a^{6} b^{2} x^{2} - \frac{32 \, a^{7} b x^{3} + a^{8}}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8/x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206897, size = 124, normalized size = 1.22 \[ \frac{187 \, b^{8} x^{24} + 1760 \, a b^{7} x^{21} + 7480 \, a^{2} b^{6} x^{18} + 19040 \, a^{3} b^{5} x^{15} + 32725 \, a^{4} b^{4} x^{12} + 41888 \, a^{5} b^{3} x^{9} + 52360 \, a^{6} b^{2} x^{6} - 29920 \, a^{7} b x^{3} - 935 \, a^{8}}{3740 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8/x^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.59148, size = 102, normalized size = 1. \[ 14 a^{6} b^{2} x^{2} + \frac{56 a^{5} b^{3} x^{5}}{5} + \frac{35 a^{4} b^{4} x^{8}}{4} + \frac{56 a^{3} b^{5} x^{11}}{11} + 2 a^{2} b^{6} x^{14} + \frac{8 a b^{7} x^{17}}{17} + \frac{b^{8} x^{20}}{20} - \frac{a^{8} + 32 a^{7} b x^{3}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**8/x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.219807, size = 123, normalized size = 1.21 \[ \frac{1}{20} \, b^{8} x^{20} + \frac{8}{17} \, a b^{7} x^{17} + 2 \, a^{2} b^{6} x^{14} + \frac{56}{11} \, a^{3} b^{5} x^{11} + \frac{35}{4} \, a^{4} b^{4} x^{8} + \frac{56}{5} \, a^{5} b^{3} x^{5} + 14 \, a^{6} b^{2} x^{2} - \frac{32 \, a^{7} b x^{3} + a^{8}}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8/x^5,x, algorithm="giac")
[Out]