3.48 \(\int x \left (-1+x^2\right )^9 \, dx\)

Optimal. Leaf size=13 \[ \frac{1}{20} \left (1-x^2\right )^{10} \]

[Out]

(1 - x^2)^10/20

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Rubi [A]  time = 0.00727161, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{1}{20} \left (1-x^2\right )^{10} \]

Antiderivative was successfully verified.

[In]  Int[x*(-1 + x^2)^9,x]

[Out]

(1 - x^2)^10/20

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Rubi in Sympy [A]  time = 0.718554, size = 7, normalized size = 0.54 \[ \frac{\left (- x^{2} + 1\right )^{10}}{20} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x*(x**2-1)**9,x)

[Out]

(-x**2 + 1)**10/20

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Mathematica [A]  time = 0.00273841, size = 11, normalized size = 0.85 \[ \frac{1}{20} \left (x^2-1\right )^{10} \]

Antiderivative was successfully verified.

[In]  Integrate[x*(-1 + x^2)^9,x]

[Out]

(-1 + x^2)^10/20

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Maple [B]  time = 0.026, size = 52, normalized size = 4. \[{\frac{{x}^{20}}{20}}-{\frac{{x}^{18}}{2}}+{\frac{9\,{x}^{16}}{4}}-6\,{x}^{14}+{\frac{21\,{x}^{12}}{2}}-{\frac{63\,{x}^{10}}{5}}+{\frac{21\,{x}^{8}}{2}}-6\,{x}^{6}+{\frac{9\,{x}^{4}}{4}}-{\frac{{x}^{2}}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x*(x^2-1)^9,x)

[Out]

1/20*x^20-1/2*x^18+9/4*x^16-6*x^14+21/2*x^12-63/5*x^10+21/2*x^8-6*x^6+9/4*x^4-1/
2*x^2

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Maxima [A]  time = 1.36909, size = 12, normalized size = 0.92 \[ \frac{1}{20} \,{\left (x^{2} - 1\right )}^{10} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - 1)^9*x,x, algorithm="maxima")

[Out]

1/20*(x^2 - 1)^10

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Fricas [A]  time = 0.194271, size = 1, normalized size = 0.08 \[ \frac{1}{20} x^{20} - \frac{1}{2} x^{18} + \frac{9}{4} x^{16} - 6 x^{14} + \frac{21}{2} x^{12} - \frac{63}{5} x^{10} + \frac{21}{2} x^{8} - 6 x^{6} + \frac{9}{4} x^{4} - \frac{1}{2} x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - 1)^9*x,x, algorithm="fricas")

[Out]

1/20*x^20 - 1/2*x^18 + 9/4*x^16 - 6*x^14 + 21/2*x^12 - 63/5*x^10 + 21/2*x^8 - 6*
x^6 + 9/4*x^4 - 1/2*x^2

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Sympy [A]  time = 0.038316, size = 58, normalized size = 4.46 \[ \frac{x^{20}}{20} - \frac{x^{18}}{2} + \frac{9 x^{16}}{4} - 6 x^{14} + \frac{21 x^{12}}{2} - \frac{63 x^{10}}{5} + \frac{21 x^{8}}{2} - 6 x^{6} + \frac{9 x^{4}}{4} - \frac{x^{2}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*(x**2-1)**9,x)

[Out]

x**20/20 - x**18/2 + 9*x**16/4 - 6*x**14 + 21*x**12/2 - 63*x**10/5 + 21*x**8/2 -
6*x**6 + 9*x**4/4 - x**2/2

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GIAC/XCAS [A]  time = 0.228086, size = 12, normalized size = 0.92 \[ \frac{1}{20} \,{\left (x^{2} - 1\right )}^{10} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - 1)^9*x,x, algorithm="giac")

[Out]

1/20*(x^2 - 1)^10