3.542 \(\int x^8 \left (1-x^3\right )^{6/5} \, dx\)

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]

(-5*(1 - x^3)^(11/5))/33 + (5*(1 - x^3)^(16/5))/24 - (5*(1 - x^3)^(21/5))/63

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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]

(-5*(1 - x^3)^(11/5))/33 + (5*(1 - x^3)^(16/5))/24 - (5*(1 - x^3)^(21/5))/63

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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]

-5*(-x**3 + 1)**(21/5)/63 + 5*(-x**3 + 1)**(16/5)/24 - 5*(-x**3 + 1)**(11/5)/33

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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]

(-5*(1 - x^3)^(11/5)*(25 + 55*x^3 + 88*x^6))/5544

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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]

5/5544*(-1+x)*(x^2+x+1)*(88*x^6+55*x^3+25)*(-x^3+1)^(6/5)

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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]

-5/63*(-x^3 + 1)^(21/5) + 5/24*(-x^3 + 1)^(16/5) - 5/33*(-x^3 + 1)^(11/5)

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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]

-5/5544*(88*x^12 - 121*x^9 + 3*x^6 + 5*x^3 + 25)*(-x^3 + 1)^(1/5)

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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]

-5*x**12*(-x**3 + 1)**(1/5)/63 + 55*x**9*(-x**3 + 1)**(1/5)/504 - 5*x**6*(-x**3
+ 1)**(1/5)/1848 - 25*x**3*(-x**3 + 1)**(1/5)/5544 - 125*(-x**3 + 1)**(1/5)/5544

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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]

-5/63*(x^3 - 1)^4*(-x^3 + 1)^(1/5) - 5/24*(x^3 - 1)^3*(-x^3 + 1)^(1/5) - 5/33*(x
^3 - 1)^2*(-x^3 + 1)^(1/5)