3.48.57 \(\int (-1+e^{e^5}+2 x) \, dx\)

Optimal. Leaf size=24 \[ -2+\left (-2+e^{e^5}-x\right ) x+x^2+\left (\frac {1}{2}+x\right )^2 \]

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Rubi [A]  time = 0.00, antiderivative size = 16, normalized size of antiderivative = 0.67, 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*} x^2-\left (1-e^{e^5}\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1 + E^E^5 + 2*x,x]

[Out]

-((1 - E^E^5)*x) + x^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (1-e^{e^5}\right ) x\right )+x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 0.58 \begin {gather*} -x+e^{e^5} x+x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 + E^E^5 + 2*x,x]

[Out]

-x + E^E^5*x + x^2

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fricas [A]  time = 0.85, size = 12, normalized size = 0.50 \begin {gather*} x^{2} + x e^{\left (e^{5}\right )} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(exp(5))+2*x-1,x, algorithm="fricas")

[Out]

x^2 + x*e^(e^5) - x

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giac [A]  time = 0.17, size = 12, normalized size = 0.50 \begin {gather*} x^{2} + x e^{\left (e^{5}\right )} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(exp(5))+2*x-1,x, algorithm="giac")

[Out]

x^2 + x*e^(e^5) - x

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maple [A]  time = 0.02, size = 12, normalized size = 0.50

method	result	size
norman	\(x^{2}+\left ({\mathrm e}^{{\mathrm e}^{5}}-1\right ) x\)	\(12\)
gosper	\(x \,{\mathrm e}^{{\mathrm e}^{5}}+x^{2}-x\)	\(13\)
default	\(x \,{\mathrm e}^{{\mathrm e}^{5}}+x^{2}-x\)	\(13\)
risch	\(x \,{\mathrm e}^{{\mathrm e}^{5}}+x^{2}-x\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(exp(5))+2*x-1,x,method=_RETURNVERBOSE)

[Out]

x^2+(exp(exp(5))-1)*x

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maxima [A]  time = 0.36, size = 12, normalized size = 0.50 \begin {gather*} x^{2} + x e^{\left (e^{5}\right )} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(exp(5))+2*x-1,x, algorithm="maxima")

[Out]

x^2 + x*e^(e^5) - x

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mupad [B]  time = 3.30, size = 11, normalized size = 0.46 \begin {gather*} x^2+\left ({\mathrm {e}}^{{\mathrm {e}}^5}-1\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x + exp(exp(5)) - 1,x)

[Out]

x*(exp(exp(5)) - 1) + x^2

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sympy [A]  time = 0.05, size = 10, normalized size = 0.42 \begin {gather*} x^{2} + x \left (-1 + e^{e^{5}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(exp(5))+2*x-1,x)

[Out]

x**2 + x*(-1 + exp(exp(5)))

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