Optimal. Leaf size=77 \[ -\frac{a^5}{5 x^5}-\frac{15 a^4 b}{14 x^{14/3}}-\frac{30 a^3 b^2}{13 x^{13/3}}-\frac{5 a^2 b^3}{2 x^4}-\frac{15 a b^4}{11 x^{11/3}}-\frac{3 b^5}{10 x^{10/3}} \]
[Out]
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Rubi [A] time = 0.0855027, antiderivative size = 77, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{a^5}{5 x^5}-\frac{15 a^4 b}{14 x^{14/3}}-\frac{30 a^3 b^2}{13 x^{13/3}}-\frac{5 a^2 b^3}{2 x^4}-\frac{15 a b^4}{11 x^{11/3}}-\frac{3 b^5}{10 x^{10/3}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))^5/x^6,x]
[Out]
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Rubi in Sympy [A] time = 14.6988, size = 76, normalized size = 0.99 \[ - \frac{a^{5}}{5 x^{5}} - \frac{15 a^{4} b}{14 x^{\frac{14}{3}}} - \frac{30 a^{3} b^{2}}{13 x^{\frac{13}{3}}} - \frac{5 a^{2} b^{3}}{2 x^{4}} - \frac{15 a b^{4}}{11 x^{\frac{11}{3}}} - \frac{3 b^{5}}{10 x^{\frac{10}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))**5/x**6,x)
[Out]
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Mathematica [A] time = 0.0233293, size = 67, normalized size = 0.87 \[ -\frac{2002 a^5+10725 a^4 b \sqrt [3]{x}+23100 a^3 b^2 x^{2/3}+25025 a^2 b^3 x+13650 a b^4 x^{4/3}+3003 b^5 x^{5/3}}{10010 x^5} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))^5/x^6,x]
[Out]
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Maple [A] time = 0.009, size = 58, normalized size = 0.8 \[ -{\frac{{a}^{5}}{5\,{x}^{5}}}-{\frac{15\,{a}^{4}b}{14}{x}^{-{\frac{14}{3}}}}-{\frac{30\,{a}^{3}{b}^{2}}{13}{x}^{-{\frac{13}{3}}}}-{\frac{5\,{a}^{2}{b}^{3}}{2\,{x}^{4}}}-{\frac{15\,a{b}^{4}}{11}{x}^{-{\frac{11}{3}}}}-{\frac{3\,{b}^{5}}{10}{x}^{-{\frac{10}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))^5/x^6,x)
[Out]
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Maxima [A] time = 1.44195, size = 77, normalized size = 1. \[ -\frac{3003 \, b^{5} x^{\frac{5}{3}} + 13650 \, a b^{4} x^{\frac{4}{3}} + 25025 \, a^{2} b^{3} x + 23100 \, a^{3} b^{2} x^{\frac{2}{3}} + 10725 \, a^{4} b x^{\frac{1}{3}} + 2002 \, a^{5}}{10010 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^5/x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.233553, size = 80, normalized size = 1.04 \[ -\frac{25025 \, a^{2} b^{3} x + 2002 \, a^{5} + 231 \,{\left (13 \, b^{5} x + 100 \, a^{3} b^{2}\right )} x^{\frac{2}{3}} + 975 \,{\left (14 \, a b^{4} x + 11 \, a^{4} b\right )} x^{\frac{1}{3}}}{10010 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^5/x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 25.3799, size = 76, normalized size = 0.99 \[ - \frac{a^{5}}{5 x^{5}} - \frac{15 a^{4} b}{14 x^{\frac{14}{3}}} - \frac{30 a^{3} b^{2}}{13 x^{\frac{13}{3}}} - \frac{5 a^{2} b^{3}}{2 x^{4}} - \frac{15 a b^{4}}{11 x^{\frac{11}{3}}} - \frac{3 b^{5}}{10 x^{\frac{10}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))**5/x**6,x)
[Out]
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GIAC/XCAS [A] time = 0.233085, size = 77, normalized size = 1. \[ -\frac{3003 \, b^{5} x^{\frac{5}{3}} + 13650 \, a b^{4} x^{\frac{4}{3}} + 25025 \, a^{2} b^{3} x + 23100 \, a^{3} b^{2} x^{\frac{2}{3}} + 10725 \, a^{4} b x^{\frac{1}{3}} + 2002 \, a^{5}}{10010 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^5/x^6,x, algorithm="giac")
[Out]