\(\int (-1-e^x+e^{4+e^5+x}) \, dx\) [1452]

Optimal result

Integrand size = 15, antiderivative size = 27 \[ \int \left (-1-e^x+e^{4+e^5+x}\right ) \, dx=-2+\frac {\sqrt [4]{2}}{e^3}-e^x+e^{4+e^5+x}-x \]

[Out]

exp(1/4*ln(2)-3)-exp(x)-2-x+exp(exp(5)+4+x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.63, number of steps used = 3, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {2225} \[ \int \left (-1-e^x+e^{4+e^5+x}\right ) \, dx=-x-e^x+e^{x+e^5+4} \]

[In]

Int[-1 - E^x + E^(4 + E^5 + x),x]

[Out]

-E^x + E^(4 + E^5 + x) - x

Rule 2225

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps \begin{align*} \text {integral}& = -x-\int e^x \, dx+\int e^{4+e^5+x} \, dx \\ & = -e^x+e^{4+e^5+x}-x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.63 \[ \int \left (-1-e^x+e^{4+e^5+x}\right ) \, dx=-e^x+e^{4+e^5+x}-x \]

[In]

Integrate[-1 - E^x + E^(4 + E^5 + x),x]

[Out]

-E^x + E^(4 + E^5 + x) - x

Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.56

method	result	size
default	\(-{\mathrm e}^{x}-x +{\mathrm e}^{{\mathrm e}^{5}+4+x}\)	\(15\)
risch	\(-{\mathrm e}^{x}-x +{\mathrm e}^{{\mathrm e}^{5}+4+x}\)	\(15\)
parallelrisch	\(-{\mathrm e}^{x}-x +{\mathrm e}^{{\mathrm e}^{5}+4+x}\)	\(15\)
parts	\(-{\mathrm e}^{x}-x +{\mathrm e}^{{\mathrm e}^{5}+4+x}\)	\(15\)
norman	\(\left ({\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{5}}-1\right ) {\mathrm e}^{x}-x\)	\(16\)

[In]

int(exp(exp(5)+4+x)-exp(x)-1,x,method=_RETURNVERBOSE)

[Out]

-exp(x)-x+exp(exp(5)+4+x)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.15 \[ \int \left (-1-e^x+e^{4+e^5+x}\right ) \, dx={\left ({\left (e^{\left (e^{5} + 4\right )} - 1\right )} e^{\left (x + e^{5} + 4\right )} - x e^{\left (e^{5} + 4\right )}\right )} e^{\left (-e^{5} - 4\right )} \]

[In]

integrate(exp(exp(5)+4+x)-exp(x)-1,x, algorithm="fricas")

[Out]

((e^(e^5 + 4) - 1)*e^(x + e^5 + 4) - x*e^(e^5 + 4))*e^(-e^5 - 4)

Sympy [A] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.52 \[ \int \left (-1-e^x+e^{4+e^5+x}\right ) \, dx=- x + \left (-1 + e^{4} e^{e^{5}}\right ) e^{x} \]

[In]

integrate(exp(exp(5)+4+x)-exp(x)-1,x)

[Out]

-x + (-1 + exp(4)*exp(exp(5)))*exp(x)

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.52 \[ \int \left (-1-e^x+e^{4+e^5+x}\right ) \, dx=-x + e^{\left (x + e^{5} + 4\right )} - e^{x} \]

[In]

integrate(exp(exp(5)+4+x)-exp(x)-1,x, algorithm="maxima")

[Out]

-x + e^(x + e^5 + 4) - e^x

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.52 \[ \int \left (-1-e^x+e^{4+e^5+x}\right ) \, dx=-x + e^{\left (x + e^{5} + 4\right )} - e^{x} \]

[In]

integrate(exp(exp(5)+4+x)-exp(x)-1,x, algorithm="giac")

[Out]

-x + e^(x + e^5 + 4) - e^x

Mupad [B] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.52 \[ \int \left (-1-e^x+e^{4+e^5+x}\right ) \, dx={\mathrm {e}}^x\,\left ({\mathrm {e}}^{{\mathrm {e}}^5+4}-1\right )-x \]

[In]

int(exp(x + exp(5) + 4) - exp(x) - 1,x)

[Out]

exp(x)*(exp(exp(5) + 4) - 1) - x