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

Optimal. Leaf size=27 \[ -2+\frac {\sqrt [4]{2}}{e^3}-e^x+e^{4+e^5+x}-x \]

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Rubi [A]  time = 0.01, antiderivative size = 17, normalized size of antiderivative = 0.63, number of steps used = 3, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {2194} \begin {gather*} -x-e^x+e^{x+e^5+4} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1 - E^x + E^(4 + E^5 + x),x]

[Out]

-E^x + E^(4 + E^5 + x) - x

Rule 2194

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

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Mathematica [A]  time = 0.01, size = 17, normalized size = 0.63 \begin {gather*} -e^x+e^{4+e^5+x}-x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-E^x + E^(4 + E^5 + x) - x

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fricas [A]  time = 0.88, size = 31, normalized size = 1.15 \begin {gather*} {\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 )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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giac [A]  time = 0.36, size = 14, normalized size = 0.52 \begin {gather*} -x + e^{\left (x + e^{5} + 4\right )} - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x + e^(x + e^5 + 4) - e^x

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maple [A]  time = 0.02, size = 15, normalized size = 0.56

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.48, size = 14, normalized size = 0.52 \begin {gather*} -x + e^{\left (x + e^{5} + 4\right )} - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x + e^(x + e^5 + 4) - e^x

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mupad [B]  time = 0.06, size = 14, normalized size = 0.52 \begin {gather*} {\mathrm {e}}^x\,\left ({\mathrm {e}}^{{\mathrm {e}}^5+4}-1\right )-x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(x)*(exp(exp(5) + 4) - 1) - x

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sympy [A]  time = 0.09, size = 14, normalized size = 0.52 \begin {gather*} - x + \left (-1 + e^{4} e^{e^{5}}\right ) e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x + (-1 + exp(4)*exp(exp(5)))*exp(x)

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