\(\int (-1+e^{e^4}-8 x) \, dx\) [3259]

Optimal result

Integrand size = 10, antiderivative size = 24 \[ \int \left (-1+e^{e^4}-8 x\right ) \, dx=3+e^4-x+e^{e^4} x-4 x^2-\log (4) \]

[Out]

exp(4)-4*x^2+3+x*exp(exp(4))-x-2*ln(2)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.75, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (-1+e^{e^4}-8 x\right ) \, dx=-4 x^2-\left (1-e^{e^4}\right ) x \]

[In]

Int[-1 + E^E^4 - 8*x,x]

[Out]

-((1 - E^E^4)*x) - 4*x^2

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

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.67 \[ \int \left (-1+e^{e^4}-8 x\right ) \, dx=-x+e^{e^4} x-4 x^2 \]

[In]

Integrate[-1 + E^E^4 - 8*x,x]

[Out]

-x + E^E^4*x - 4*x^2

Maple [A] (verified)

Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.58

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

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.58 \[ \int \left (-1+e^{e^4}-8 x\right ) \, dx=-4 \, x^{2} + x e^{\left (e^{4}\right )} - x \]

[In]

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

[Out]

-4*x^2 + x*e^(e^4) - x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.50 \[ \int \left (-1+e^{e^4}-8 x\right ) \, dx=- 4 x^{2} + x \left (-1 + e^{e^{4}}\right ) \]

[In]

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

[Out]

-4*x**2 + x*(-1 + exp(exp(4)))

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.58 \[ \int \left (-1+e^{e^4}-8 x\right ) \, dx=-4 \, x^{2} + x e^{\left (e^{4}\right )} - x \]

[In]

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

[Out]

-4*x^2 + x*e^(e^4) - x

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.58 \[ \int \left (-1+e^{e^4}-8 x\right ) \, dx=-4 \, x^{2} + x e^{\left (e^{4}\right )} - x \]

[In]

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

[Out]

-4*x^2 + x*e^(e^4) - x

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.54 \[ \int \left (-1+e^{e^4}-8 x\right ) \, dx=x\,\left ({\mathrm {e}}^{{\mathrm {e}}^4}-1\right )-4\,x^2 \]

[In]

int(exp(exp(4)) - 8*x - 1,x)

[Out]

x*(exp(exp(4)) - 1) - 4*x^2