Optimal. Leaf size=46 \[ -\frac{5}{63} \left (1-x^3\right )^{21/5}+\frac{5}{24} \left (1-x^3\right )^{16/5}-\frac{5}{33} \left (1-x^3\right )^{11/5} \]
[Out]
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Rubi [A] time = 0.0516766, antiderivative size = 46, 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 \[ -\frac{5}{63} \left (1-x^3\right )^{21/5}+\frac{5}{24} \left (1-x^3\right )^{16/5}-\frac{5}{33} \left (1-x^3\right )^{11/5} \]
Antiderivative was successfully verified.
[In] Int[x^8*(1 - x^3)^(6/5),x]
[Out]
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Rubi in Sympy [A] time = 5.07063, size = 34, normalized size = 0.74 \[ - \frac{5 \left (- x^{3} + 1\right )^{\frac{21}{5}}}{63} + \frac{5 \left (- x^{3} + 1\right )^{\frac{16}{5}}}{24} - \frac{5 \left (- x^{3} + 1\right )^{\frac{11}{5}}}{33} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**8*(-x**3+1)**(6/5),x)
[Out]
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Mathematica [A] time = 0.0240797, size = 27, normalized size = 0.59 \[ -\frac{5 \left (1-x^3\right )^{11/5} \left (88 x^6+55 x^3+25\right )}{5544} \]
Antiderivative was successfully verified.
[In] Integrate[x^8*(1 - x^3)^(6/5),x]
[Out]
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Maple [A] time = 0.006, size = 33, normalized size = 0.7 \[{\frac{ \left ( -5+5\,x \right ) \left ({x}^{2}+x+1 \right ) \left ( 88\,{x}^{6}+55\,{x}^{3}+25 \right ) }{5544} \left ( -{x}^{3}+1 \right ) ^{{\frac{6}{5}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^8*(-x^3+1)^(6/5),x)
[Out]
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Maxima [A] time = 1.43625, size = 46, normalized size = 1. \[ -\frac{5}{63} \,{\left (-x^{3} + 1\right )}^{\frac{21}{5}} + \frac{5}{24} \,{\left (-x^{3} + 1\right )}^{\frac{16}{5}} - \frac{5}{33} \,{\left (-x^{3} + 1\right )}^{\frac{11}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x^3 + 1)^(6/5)*x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.240264, size = 45, normalized size = 0.98 \[ -\frac{5}{5544} \,{\left (88 \, x^{12} - 121 \, x^{9} + 3 \, x^{6} + 5 \, x^{3} + 25\right )}{\left (-x^{3} + 1\right )}^{\frac{1}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x^3 + 1)^(6/5)*x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 34.0241, size = 71, normalized size = 1.54 \[ - \frac{5 x^{12} \sqrt [5]{- x^{3} + 1}}{63} + \frac{55 x^{9} \sqrt [5]{- x^{3} + 1}}{504} - \frac{5 x^{6} \sqrt [5]{- x^{3} + 1}}{1848} - \frac{25 x^{3} \sqrt [5]{- x^{3} + 1}}{5544} - \frac{125 \sqrt [5]{- x^{3} + 1}}{5544} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**8*(-x**3+1)**(6/5),x)
[Out]
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GIAC/XCAS [A] time = 0.322967, size = 74, normalized size = 1.61 \[ -\frac{5}{63} \,{\left (x^{3} - 1\right )}^{4}{\left (-x^{3} + 1\right )}^{\frac{1}{5}} - \frac{5}{24} \,{\left (x^{3} - 1\right )}^{3}{\left (-x^{3} + 1\right )}^{\frac{1}{5}} - \frac{5}{33} \,{\left (x^{3} - 1\right )}^{2}{\left (-x^{3} + 1\right )}^{\frac{1}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x^3 + 1)^(6/5)*x^8,x, algorithm="giac")
[Out]