3.99.7 \(\int (2-e^3+6 x-64 x^3) \, dx\)

Optimal. Leaf size=20 \[ 2 x-16 x^4+x \left (-e^3+3 x\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.00, 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*} -16 x^4+3 x^2+\left (2-e^3\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2 - E^3 + 6*x - 64*x^3,x]

[Out]

(2 - E^3)*x + 3*x^2 - 16*x^4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\left (2-e^3\right ) x+3 x^2-16 x^4\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 20, normalized size = 1.00 \begin {gather*} 2 x-e^3 x+3 x^2-16 x^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2 - E^3 + 6*x - 64*x^3,x]

[Out]

2*x - E^3*x + 3*x^2 - 16*x^4

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fricas [A]  time = 0.71, size = 19, normalized size = 0.95 \begin {gather*} -16 \, x^{4} + 3 \, x^{2} - x e^{3} + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(3)-64*x^3+6*x+2,x, algorithm="fricas")

[Out]

-16*x^4 + 3*x^2 - x*e^3 + 2*x

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giac [A]  time = 0.14, size = 19, normalized size = 0.95 \begin {gather*} -16 \, x^{4} + 3 \, x^{2} - x e^{3} + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(3)-64*x^3+6*x+2,x, algorithm="giac")

[Out]

-16*x^4 + 3*x^2 - x*e^3 + 2*x

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maple [A]  time = 0.02, size = 16, normalized size = 0.80

method	result	size
gosper	\(-x \left (16 x^{3}+{\mathrm e}^{3}-3 x -2\right )\)	\(16\)
default	\(-x \,{\mathrm e}^{3}-16 x^{4}+3 x^{2}+2 x\)	\(20\)
norman	\(\left (2-{\mathrm e}^{3}\right ) x +3 x^{2}-16 x^{4}\)	\(20\)
risch	\(-x \,{\mathrm e}^{3}-16 x^{4}+3 x^{2}+2 x\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(3)-64*x^3+6*x+2,x,method=_RETURNVERBOSE)

[Out]

-x*(16*x^3+exp(3)-3*x-2)

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maxima [A]  time = 0.35, size = 19, normalized size = 0.95 \begin {gather*} -16 \, x^{4} + 3 \, x^{2} - x e^{3} + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(3)-64*x^3+6*x+2,x, algorithm="maxima")

[Out]

-16*x^4 + 3*x^2 - x*e^3 + 2*x

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mupad [B]  time = 5.58, size = 18, normalized size = 0.90 \begin {gather*} -16\,x^4+3\,x^2+\left (2-{\mathrm {e}}^3\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(6*x - exp(3) - 64*x^3 + 2,x)

[Out]

3*x^2 - x*(exp(3) - 2) - 16*x^4

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sympy [A]  time = 0.05, size = 15, normalized size = 0.75 \begin {gather*} - 16 x^{4} + 3 x^{2} + x \left (2 - e^{3}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(3)-64*x**3+6*x+2,x)

[Out]

-16*x**4 + 3*x**2 + x*(2 - exp(3))

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