3.3.43 \(\int (-e^e+e^5 (-1-2 x)) \, dx\)

Optimal. Leaf size=22 \[ e^5 \left (-x-x \left (e^{-5+e}+x\right )+16 \log (4)\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 21, normalized size of antiderivative = 0.95, number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -\frac {1}{4} e^5 (2 x+1)^2-e^e x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-E^E + E^5*(-1 - 2*x),x]

[Out]

-(E^E*x) - (E^5*(1 + 2*x)^2)/4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-e^e x-\frac {1}{4} e^5 (1+2 x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 21, normalized size = 0.95 \begin {gather*} -e^5 x-e^e x-e^5 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-E^E + E^5*(-1 - 2*x),x]

[Out]

-(E^5*x) - E^E*x - E^5*x^2

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fricas [A]  time = 0.54, size = 16, normalized size = 0.73 \begin {gather*} -{\left (x^{2} + x\right )} e^{5} - x e^{e} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(x^2 + x)*e^5 - x*e^e

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giac [A]  time = 0.34, size = 16, normalized size = 0.73 \begin {gather*} -{\left (x^{2} + x\right )} e^{5} - x e^{e} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(x^2 + x)*e^5 - x*e^e

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maple [A]  time = 0.07, size = 14, normalized size = 0.64

method	result	size
gosper	\(-{\mathrm e}^{5} x \left (x +{\mathrm e}^{{\mathrm e}-5}+1\right )\)	\(14\)
risch	\(-x \,{\mathrm e}^{{\mathrm e}}-x^{2} {\mathrm e}^{5}-x \,{\mathrm e}^{5}\)	\(20\)
default	\(-{\mathrm e}^{5} {\mathrm e}^{{\mathrm e}-5} x +\left (-x^{2}-x \right ) {\mathrm e}^{5}\)	\(24\)
norman	\(\left (-{\mathrm e}^{5} {\mathrm e}^{{\mathrm e}} {\mathrm e}^{-5}-{\mathrm e}^{5}\right ) x -x^{2} {\mathrm e}^{5}\)	\(25\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.52, size = 16, normalized size = 0.73 \begin {gather*} -{\left (x^{2} + x\right )} e^{5} - x e^{e} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(x^2 + x)*e^5 - x*e^e

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mupad [B]  time = 0.09, size = 18, normalized size = 0.82 \begin {gather*} -\frac {{\mathrm {e}}^5\,{\left (2\,x+1\right )}^2}{4}-x\,{\mathrm {e}}^{\mathrm {e}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.06, size = 17, normalized size = 0.77 \begin {gather*} - x^{2} e^{5} + x \left (- e^{5} - e^{e}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x**2*exp(5) + x*(-exp(5) - exp(E))

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