3.1900 \(\int \left (1-x^2-3 x^5\right ) \, dx\)

Optimal. Leaf size=16 \[ -\frac{x^6}{2}-\frac{x^3}{3}+x \]

[Out]

x - x^3/3 - x^6/2

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Rubi [A]  time = 0.00701179, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ -\frac{x^6}{2}-\frac{x^3}{3}+x \]

Antiderivative was successfully verified.

[In]  Int[1 - x^2 - 3*x^5,x]

[Out]

x - x^3/3 - x^6/2

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Rubi in Sympy [A]  time = 1.44201, size = 10, normalized size = 0.62 \[ - \frac{x^{6}}{2} - \frac{x^{3}}{3} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(-3*x**5-x**2+1,x)

[Out]

-x**6/2 - x**3/3 + x

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Mathematica [A]  time = 0.0000601568, size = 16, normalized size = 1. \[ -\frac{x^6}{2}-\frac{x^3}{3}+x \]

Antiderivative was successfully verified.

[In]  Integrate[1 - x^2 - 3*x^5,x]

[Out]

x - x^3/3 - x^6/2

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Maple [A]  time = 0.001, size = 13, normalized size = 0.8 \[ x-{\frac{{x}^{3}}{3}}-{\frac{{x}^{6}}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(-3*x^5-x^2+1,x)

[Out]

x-1/3*x^3-1/2*x^6

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Maxima [A]  time = 1.34163, size = 16, normalized size = 1. \[ -\frac{1}{2} \, x^{6} - \frac{1}{3} \, x^{3} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-3*x^5 - x^2 + 1,x, algorithm="maxima")

[Out]

-1/2*x^6 - 1/3*x^3 + x

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Fricas [A]  time = 0.177979, size = 1, normalized size = 0.06 \[ -\frac{1}{2} x^{6} - \frac{1}{3} x^{3} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-3*x^5 - x^2 + 1,x, algorithm="fricas")

[Out]

-1/2*x^6 - 1/3*x^3 + x

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Sympy [A]  time = 0.033107, size = 10, normalized size = 0.62 \[ - \frac{x^{6}}{2} - \frac{x^{3}}{3} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-3*x**5-x**2+1,x)

[Out]

-x**6/2 - x**3/3 + x

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GIAC/XCAS [A]  time = 0.228001, size = 16, normalized size = 1. \[ -\frac{1}{2} \, x^{6} - \frac{1}{3} \, x^{3} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-3*x^5 - x^2 + 1,x, algorithm="giac")

[Out]

-1/2*x^6 - 1/3*x^3 + x