3.19.100 \(\int (1-x^2-3 x^5) \, dx\) [1900]

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

[Out]

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

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Rubi [A]
time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -\frac {x^6}{2}-\frac {x^3}{3}+x \end {gather*}

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*}

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Mathematica [A]
time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} x-\frac {x^3}{3}-\frac {x^6}{2} \end {gather*}

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 = 0.01, size = 13, normalized size = 0.81

method	result	size
default	\(x -\frac {1}{3} x^{3}-\frac {1}{2} x^{6}\)	\(13\)
norman	\(x -\frac {1}{3} x^{3}-\frac {1}{2} x^{6}\)	\(13\)
risch	\(x -\frac {1}{3} x^{3}-\frac {1}{2} x^{6}\)	\(13\)
gosper	\(-\frac {x \left (3 x^{5}+2 x^{2}-6\right )}{6}\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-3*x^5-x^2+1,x,method=_RETURNVERBOSE)

[Out]

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

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Maxima [A]
time = 0.28, size = 12, normalized size = 0.75 \begin {gather*} -\frac {1}{2} \, x^{6} - \frac {1}{3} \, x^{3} + x \end {gather*}

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 = 0.63, size = 12, normalized size = 0.75 \begin {gather*} -\frac {1}{2} \, x^{6} - \frac {1}{3} \, x^{3} + x \end {gather*}

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 = 0.01, size = 10, normalized size = 0.62 \begin {gather*} - \frac {x^{6}}{2} - \frac {x^{3}}{3} + x \end {gather*}

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 = 2.44, size = 12, normalized size = 0.75 \begin {gather*} -\frac {1}{2} \, x^{6} - \frac {1}{3} \, x^{3} + x \end {gather*}

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

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Mupad [B]
time = 0.02, size = 12, normalized size = 0.75 \begin {gather*} -\frac {x^6}{2}-\frac {x^3}{3}+x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1 - 3*x^5 - x^2,x)

[Out]

x - x^3/3 - x^6/2

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