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

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 = 0.0018788, 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., Rules used = {} \[ -\frac{x^6}{2}-\frac{x^3}{3}+x \]

Antiderivative was successfully verified.

[In]

Int[1 - x^2 - 3*x^5,x]

[Out]

x - x^3/3 - x^6/2

Rubi steps

\begin{align*} \int \left (1-x^2-3 x^5\right ) \, dx &=x-\frac{x^3}{3}-\frac{x^6}{2}\\ \end{align*}

Mathematica [A]  time = 0.0000448, 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 \begin{align*} x-{\frac{{x}^{3}}{3}}-{\frac{{x}^{6}}{2}} \end{align*}

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 = 0.98298, size = 16, normalized size = 1. \begin{align*} -\frac{1}{2} \, x^{6} - \frac{1}{3} \, x^{3} + x \end{align*}

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 = 1.69309, size = 32, normalized size = 2. \begin{align*} -\frac{1}{2} x^{6} - \frac{1}{3} x^{3} + x \end{align*}

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 = 0.052106, size = 10, normalized size = 0.62 \begin{align*} - \frac{x^{6}}{2} - \frac{x^{3}}{3} + x \end{align*}

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 [A]  time = 1.05034, size = 16, normalized size = 1. \begin{align*} -\frac{1}{2} \, x^{6} - \frac{1}{3} \, x^{3} + x \end{align*}

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