3.88.69 \(\int (1-2 x-8 x^3-6 x^5) \, dx\)

Optimal. Leaf size=18 \[ -20+x-\left (x+x^3\right )^2+\frac {10}{\log ^2(5)} \]

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Rubi [A]  time = 0.00, antiderivative size = 17, normalized size of antiderivative = 0.94, number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -x^6-2 x^4-x^2+x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 - 2*x - 8*x^3 - 6*x^5,x]

[Out]

x - x^2 - 2*x^4 - x^6

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x-x^2-2 x^4-x^6\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 17, normalized size = 0.94 \begin {gather*} x-x^2-2 x^4-x^6 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 - 2*x - 8*x^3 - 6*x^5,x]

[Out]

x - x^2 - 2*x^4 - x^6

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fricas [A]  time = 0.47, size = 17, normalized size = 0.94 \begin {gather*} -x^{6} - 2 \, x^{4} - x^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-6*x^5-8*x^3-2*x+1,x, algorithm="fricas")

[Out]

-x^6 - 2*x^4 - x^2 + x

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giac [A]  time = 0.18, size = 17, normalized size = 0.94 \begin {gather*} -x^{6} - 2 \, x^{4} - x^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-6*x^5-8*x^3-2*x+1,x, algorithm="giac")

[Out]

-x^6 - 2*x^4 - x^2 + x

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maple [A]  time = 0.01, size = 15, normalized size = 0.83

method	result	size
gosper	\(-x \left (x^{5}+2 x^{3}+x -1\right )\)	\(15\)
default	\(-x^{6}-2 x^{4}-x^{2}+x\)	\(18\)
norman	\(-x^{6}-2 x^{4}-x^{2}+x\)	\(18\)
risch	\(-x^{6}-2 x^{4}-x^{2}+x\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-6*x^5-8*x^3-2*x+1,x,method=_RETURNVERBOSE)

[Out]

-x*(x^5+2*x^3+x-1)

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maxima [A]  time = 0.34, size = 17, normalized size = 0.94 \begin {gather*} -x^{6} - 2 \, x^{4} - x^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-6*x^5-8*x^3-2*x+1,x, algorithm="maxima")

[Out]

-x^6 - 2*x^4 - x^2 + x

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mupad [B]  time = 0.03, size = 17, normalized size = 0.94 \begin {gather*} -x^6-2\,x^4-x^2+x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1 - 8*x^3 - 6*x^5 - 2*x,x)

[Out]

x - x^2 - 2*x^4 - x^6

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sympy [A]  time = 0.05, size = 12, normalized size = 0.67 \begin {gather*} - x^{6} - 2 x^{4} - x^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-6*x**5-8*x**3-2*x+1,x)

[Out]

-x**6 - 2*x**4 - x**2 + x

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