Optimal. Leaf size=105 \[ -\frac{a^8}{3 x^3}+8 a^7 b \log (x)+\frac{28}{3} a^6 b^2 x^3+\frac{28}{3} a^5 b^3 x^6+\frac{70}{9} a^4 b^4 x^9+\frac{14}{3} a^3 b^5 x^{12}+\frac{28}{15} a^2 b^6 x^{15}+\frac{4}{9} a b^7 x^{18}+\frac{b^8 x^{21}}{21} \]
[Out]
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Rubi [A] time = 0.155611, antiderivative size = 105, 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 \[ -\frac{a^8}{3 x^3}+8 a^7 b \log (x)+\frac{28}{3} a^6 b^2 x^3+\frac{28}{3} a^5 b^3 x^6+\frac{70}{9} a^4 b^4 x^9+\frac{14}{3} a^3 b^5 x^{12}+\frac{28}{15} a^2 b^6 x^{15}+\frac{4}{9} a b^7 x^{18}+\frac{b^8 x^{21}}{21} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^8/x^4,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{8}}{3 x^{3}} + \frac{8 a^{7} b \log{\left (x^{3} \right )}}{3} + \frac{28 a^{6} b^{2} x^{3}}{3} + \frac{56 a^{5} b^{3} \int ^{x^{3}} x\, dx}{3} + \frac{70 a^{4} b^{4} x^{9}}{9} + \frac{14 a^{3} b^{5} x^{12}}{3} + \frac{28 a^{2} b^{6} x^{15}}{15} + \frac{4 a b^{7} x^{18}}{9} + \frac{b^{8} x^{21}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**8/x**4,x)
[Out]
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Mathematica [A] time = 0.0166772, size = 105, normalized size = 1. \[ -\frac{a^8}{3 x^3}+8 a^7 b \log (x)+\frac{28}{3} a^6 b^2 x^3+\frac{28}{3} a^5 b^3 x^6+\frac{70}{9} a^4 b^4 x^9+\frac{14}{3} a^3 b^5 x^{12}+\frac{28}{15} a^2 b^6 x^{15}+\frac{4}{9} a b^7 x^{18}+\frac{b^8 x^{21}}{21} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^8/x^4,x]
[Out]
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Maple [A] time = 0.009, size = 90, normalized size = 0.9 \[ -{\frac{{a}^{8}}{3\,{x}^{3}}}+{\frac{28\,{a}^{6}{b}^{2}{x}^{3}}{3}}+{\frac{28\,{a}^{5}{b}^{3}{x}^{6}}{3}}+{\frac{70\,{a}^{4}{b}^{4}{x}^{9}}{9}}+{\frac{14\,{a}^{3}{b}^{5}{x}^{12}}{3}}+{\frac{28\,{a}^{2}{b}^{6}{x}^{15}}{15}}+{\frac{4\,a{b}^{7}{x}^{18}}{9}}+{\frac{{b}^{8}{x}^{21}}{21}}+8\,{a}^{7}b\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^8/x^4,x)
[Out]
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Maxima [A] time = 1.4256, size = 123, normalized size = 1.17 \[ \frac{1}{21} \, b^{8} x^{21} + \frac{4}{9} \, a b^{7} x^{18} + \frac{28}{15} \, a^{2} b^{6} x^{15} + \frac{14}{3} \, a^{3} b^{5} x^{12} + \frac{70}{9} \, a^{4} b^{4} x^{9} + \frac{28}{3} \, a^{5} b^{3} x^{6} + \frac{28}{3} \, a^{6} b^{2} x^{3} + \frac{8}{3} \, a^{7} b \log \left (x^{3}\right ) - \frac{a^{8}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210162, size = 127, normalized size = 1.21 \[ \frac{15 \, b^{8} x^{24} + 140 \, a b^{7} x^{21} + 588 \, a^{2} b^{6} x^{18} + 1470 \, a^{3} b^{5} x^{15} + 2450 \, a^{4} b^{4} x^{12} + 2940 \, a^{5} b^{3} x^{9} + 2940 \, a^{6} b^{2} x^{6} + 2520 \, a^{7} b x^{3} \log \left (x\right ) - 105 \, a^{8}}{315 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.52058, size = 105, normalized size = 1. \[ - \frac{a^{8}}{3 x^{3}} + 8 a^{7} b \log{\left (x \right )} + \frac{28 a^{6} b^{2} x^{3}}{3} + \frac{28 a^{5} b^{3} x^{6}}{3} + \frac{70 a^{4} b^{4} x^{9}}{9} + \frac{14 a^{3} b^{5} x^{12}}{3} + \frac{28 a^{2} b^{6} x^{15}}{15} + \frac{4 a b^{7} x^{18}}{9} + \frac{b^{8} x^{21}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**8/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.224818, size = 135, normalized size = 1.29 \[ \frac{1}{21} \, b^{8} x^{21} + \frac{4}{9} \, a b^{7} x^{18} + \frac{28}{15} \, a^{2} b^{6} x^{15} + \frac{14}{3} \, a^{3} b^{5} x^{12} + \frac{70}{9} \, a^{4} b^{4} x^{9} + \frac{28}{3} \, a^{5} b^{3} x^{6} + \frac{28}{3} \, a^{6} b^{2} x^{3} + 8 \, a^{7} b{\rm ln}\left ({\left | x \right |}\right ) - \frac{8 \, a^{7} b x^{3} + a^{8}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8/x^4,x, algorithm="giac")
[Out]