Optimal. Leaf size=105 \[ -\frac{a^8}{6 x^6}-\frac{8 a^7 b}{3 x^3}+28 a^6 b^2 \log (x)+\frac{56}{3} a^5 b^3 x^3+\frac{35}{3} a^4 b^4 x^6+\frac{56}{9} a^3 b^5 x^9+\frac{7}{3} a^2 b^6 x^{12}+\frac{8}{15} a b^7 x^{15}+\frac{b^8 x^{18}}{18} \]
[Out]
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Rubi [A] time = 0.133875, 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 \[ -\frac{a^8}{6 x^6}-\frac{8 a^7 b}{3 x^3}+28 a^6 b^2 \log (x)+\frac{56}{3} a^5 b^3 x^3+\frac{35}{3} a^4 b^4 x^6+\frac{56}{9} a^3 b^5 x^9+\frac{7}{3} a^2 b^6 x^{12}+\frac{8}{15} a b^7 x^{15}+\frac{b^8 x^{18}}{18} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^8/x^7,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{8}}{6 x^{6}} - \frac{8 a^{7} b}{3 x^{3}} + \frac{28 a^{6} b^{2} \log{\left (x^{3} \right )}}{3} + \frac{56 a^{5} b^{3} x^{3}}{3} + \frac{70 a^{4} b^{4} \int ^{x^{3}} x\, dx}{3} + \frac{56 a^{3} b^{5} x^{9}}{9} + \frac{7 a^{2} b^{6} x^{12}}{3} + \frac{8 a b^{7} x^{15}}{15} + \frac{b^{8} x^{18}}{18} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**8/x**7,x)
[Out]
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Mathematica [A] time = 0.00911952, size = 105, normalized size = 1. \[ -\frac{a^8}{6 x^6}-\frac{8 a^7 b}{3 x^3}+28 a^6 b^2 \log (x)+\frac{56}{3} a^5 b^3 x^3+\frac{35}{3} a^4 b^4 x^6+\frac{56}{9} a^3 b^5 x^9+\frac{7}{3} a^2 b^6 x^{12}+\frac{8}{15} a b^7 x^{15}+\frac{b^8 x^{18}}{18} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^8/x^7,x]
[Out]
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Maple [A] time = 0.009, size = 90, normalized size = 0.9 \[ -{\frac{{a}^{8}}{6\,{x}^{6}}}-{\frac{8\,{a}^{7}b}{3\,{x}^{3}}}+{\frac{56\,{a}^{5}{b}^{3}{x}^{3}}{3}}+{\frac{35\,{a}^{4}{b}^{4}{x}^{6}}{3}}+{\frac{56\,{a}^{3}{b}^{5}{x}^{9}}{9}}+{\frac{7\,{a}^{2}{b}^{6}{x}^{12}}{3}}+{\frac{8\,a{b}^{7}{x}^{15}}{15}}+{\frac{{b}^{8}{x}^{18}}{18}}+28\,{a}^{6}{b}^{2}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^8/x^7,x)
[Out]
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Maxima [A] time = 1.43207, size = 124, normalized size = 1.18 \[ \frac{1}{18} \, b^{8} x^{18} + \frac{8}{15} \, a b^{7} x^{15} + \frac{7}{3} \, a^{2} b^{6} x^{12} + \frac{56}{9} \, a^{3} b^{5} x^{9} + \frac{35}{3} \, a^{4} b^{4} x^{6} + \frac{56}{3} \, a^{5} b^{3} x^{3} + \frac{28}{3} \, a^{6} b^{2} \log \left (x^{3}\right ) - \frac{16 \, a^{7} b x^{3} + a^{8}}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8/x^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215054, size = 127, normalized size = 1.21 \[ \frac{5 \, b^{8} x^{24} + 48 \, a b^{7} x^{21} + 210 \, a^{2} b^{6} x^{18} + 560 \, a^{3} b^{5} x^{15} + 1050 \, a^{4} b^{4} x^{12} + 1680 \, a^{5} b^{3} x^{9} + 2520 \, a^{6} b^{2} x^{6} \log \left (x\right ) - 240 \, a^{7} b x^{3} - 15 \, a^{8}}{90 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8/x^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.75869, size = 104, normalized size = 0.99 \[ 28 a^{6} b^{2} \log{\left (x \right )} + \frac{56 a^{5} b^{3} x^{3}}{3} + \frac{35 a^{4} b^{4} x^{6}}{3} + \frac{56 a^{3} b^{5} x^{9}}{9} + \frac{7 a^{2} b^{6} x^{12}}{3} + \frac{8 a b^{7} x^{15}}{15} + \frac{b^{8} x^{18}}{18} - \frac{a^{8} + 16 a^{7} b x^{3}}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**8/x**7,x)
[Out]
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GIAC/XCAS [A] time = 0.216023, size = 138, normalized size = 1.31 \[ \frac{1}{18} \, b^{8} x^{18} + \frac{8}{15} \, a b^{7} x^{15} + \frac{7}{3} \, a^{2} b^{6} x^{12} + \frac{56}{9} \, a^{3} b^{5} x^{9} + \frac{35}{3} \, a^{4} b^{4} x^{6} + \frac{56}{3} \, a^{5} b^{3} x^{3} + 28 \, a^{6} b^{2}{\rm ln}\left ({\left | x \right |}\right ) - \frac{84 \, a^{6} b^{2} x^{6} + 16 \, a^{7} b x^{3} + a^{8}}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8/x^7,x, algorithm="giac")
[Out]