3.33.59 \(\int (-1+e^{e^4}-8 x) \, dx\)

Optimal. Leaf size=24 \[ 3+e^4-x+e^{e^4} x-4 x^2-\log (4) \]

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Rubi [A]  time = 0.01, antiderivative size = 18, normalized size of antiderivative = 0.75, number of steps used = 1, number of rules used = 0, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -4 x^2-\left (1-e^{e^4}\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1 + E^E^4 - 8*x,x]

[Out]

-((1 - E^E^4)*x) - 4*x^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (1-e^{e^4}\right ) x\right )-4 x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 16, normalized size = 0.67 \begin {gather*} -x+e^{e^4} x-4 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 + E^E^4 - 8*x,x]

[Out]

-x + E^E^4*x - 4*x^2

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fricas [A]  time = 0.58, size = 14, normalized size = 0.58 \begin {gather*} -4 \, x^{2} + x e^{\left (e^{4}\right )} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(exp(4))-8*x-1,x, algorithm="fricas")

[Out]

-4*x^2 + x*e^(e^4) - x

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giac [A]  time = 0.50, size = 14, normalized size = 0.58 \begin {gather*} -4 \, x^{2} + x e^{\left (e^{4}\right )} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(exp(4))-8*x-1,x, algorithm="giac")

[Out]

-4*x^2 + x*e^(e^4) - x

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maple [A]  time = 0.02, size = 14, normalized size = 0.58

method	result	size
norman	\(-4 x^{2}+\left ({\mathrm e}^{{\mathrm e}^{4}}-1\right ) x\)	\(14\)
gosper	\(x \,{\mathrm e}^{{\mathrm e}^{4}}-4 x^{2}-x\)	\(15\)
default	\(x \,{\mathrm e}^{{\mathrm e}^{4}}-4 x^{2}-x\)	\(15\)
risch	\(x \,{\mathrm e}^{{\mathrm e}^{4}}-4 x^{2}-x\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(exp(4))-8*x-1,x,method=_RETURNVERBOSE)

[Out]

-4*x^2+(exp(exp(4))-1)*x

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maxima [A]  time = 0.35, size = 14, normalized size = 0.58 \begin {gather*} -4 \, x^{2} + x e^{\left (e^{4}\right )} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(exp(4))-8*x-1,x, algorithm="maxima")

[Out]

-4*x^2 + x*e^(e^4) - x

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mupad [B]  time = 0.04, size = 13, normalized size = 0.54 \begin {gather*} x\,\left ({\mathrm {e}}^{{\mathrm {e}}^4}-1\right )-4\,x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(exp(4)) - 8*x - 1,x)

[Out]

x*(exp(exp(4)) - 1) - 4*x^2

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sympy [A]  time = 0.06, size = 12, normalized size = 0.50 \begin {gather*} - 4 x^{2} + x \left (-1 + e^{e^{4}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(exp(4))-8*x-1,x)

[Out]

-4*x**2 + x*(-1 + exp(exp(4)))

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