3.58.13 \(\int \frac {-4 e^{258}+4 e^{258+e^2}+4 e^3 x}{e} \, dx\)

Optimal. Leaf size=20 \[ 2 e^2 x \left (2 e^{255} \left (-1+e^{e^2}\right )+x\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 24, normalized size of antiderivative = 1.20, number of steps used = 1, number of rules used = 1, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {9} \begin {gather*} 2 e^2 \left (e^{255} \left (1-e^{e^2}\right )-x\right )^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-4*E^258 + 4*E^(258 + E^2) + 4*E^3*x)/E,x]

[Out]

2*E^2*(E^255*(1 - E^E^2) - x)^2

Rule 9

Int[(a_)*((b_) + (c_.)*(x_)), x_Symbol] :> Simp[(a*(b + c*x)^2)/(2*c), x] /; FreeQ[{a, b, c}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=2 e^2 \left (e^{255} \left (1-e^{e^2}\right )-x\right )^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 28, normalized size = 1.40 \begin {gather*} 4 e^2 \left (-e^{255} x+e^{255+e^2} x+\frac {x^2}{2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-4*E^258 + 4*E^(258 + E^2) + 4*E^3*x)/E,x]

[Out]

4*E^2*(-(E^255*x) + E^(255 + E^2)*x + x^2/2)

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fricas [A]  time = 0.88, size = 24, normalized size = 1.20 \begin {gather*} 2 \, {\left (x^{2} e^{3} - 2 \, x e^{258} + 2 \, x e^{\left (e^{2} + 258\right )}\right )} e^{\left (-1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*exp(2)*exp(256)*exp(exp(2))-4*exp(2)*exp(256)+4*x*exp(1)*exp(2))/exp(1),x, algorithm="fricas")

[Out]

2*(x^2*e^3 - 2*x*e^258 + 2*x*e^(e^2 + 258))*e^(-1)

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giac [A]  time = 0.18, size = 24, normalized size = 1.20 \begin {gather*} 2 \, {\left (x^{2} e^{3} - 2 \, x e^{258} + 2 \, x e^{\left (e^{2} + 258\right )}\right )} e^{\left (-1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*exp(2)*exp(256)*exp(exp(2))-4*exp(2)*exp(256)+4*x*exp(1)*exp(2))/exp(1),x, algorithm="giac")

[Out]

2*(x^2*e^3 - 2*x*e^258 + 2*x*e^(e^2 + 258))*e^(-1)

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maple [A]  time = 0.04, size = 25, normalized size = 1.25

method	result	size
norman	\(2 x^{2} {\mathrm e}^{2}+4 \,{\mathrm e}^{2} {\mathrm e}^{256} \left ({\mathrm e}^{{\mathrm e}^{2}}-1\right ) {\mathrm e}^{-1} x\)	\(25\)
gosper	\(2 \,{\mathrm e}^{2} x \left (x \,{\mathrm e}+2 \,{\mathrm e}^{256} {\mathrm e}^{{\mathrm e}^{2}}-2 \,{\mathrm e}^{256}\right ) {\mathrm e}^{-1}\)	\(26\)
risch	\(4 \,{\mathrm e}^{2} x \,{\mathrm e}^{{\mathrm e}^{2}+255}-4 \,{\mathrm e}^{2} {\mathrm e}^{255} x +2 x^{2} {\mathrm e}^{2}\)	\(26\)
default	\({\mathrm e}^{-1} \left (4 \,{\mathrm e}^{2} {\mathrm e}^{256} {\mathrm e}^{{\mathrm e}^{2}} x -4 \,{\mathrm e}^{2} {\mathrm e}^{256} x +2 x^{2} {\mathrm e} \,{\mathrm e}^{2}\right )\)	\(33\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*exp(2)*exp(256)*exp(exp(2))-4*exp(2)*exp(256)+4*x*exp(1)*exp(2))/exp(1),x,method=_RETURNVERBOSE)

[Out]

2*x^2*exp(2)+4*exp(2)*exp(256)*(exp(exp(2))-1)/exp(1)*x

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maxima [A]  time = 0.35, size = 24, normalized size = 1.20 \begin {gather*} 2 \, {\left (x^{2} e^{3} - 2 \, x e^{258} + 2 \, x e^{\left (e^{2} + 258\right )}\right )} e^{\left (-1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*exp(2)*exp(256)*exp(exp(2))-4*exp(2)*exp(256)+4*x*exp(1)*exp(2))/exp(1),x, algorithm="maxima")

[Out]

2*(x^2*e^3 - 2*x*e^258 + 2*x*e^(e^2 + 258))*e^(-1)

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mupad [B]  time = 0.24, size = 23, normalized size = 1.15 \begin {gather*} \frac {{\mathrm {e}}^{-4}\,{\left (4\,{\mathrm {e}}^{{\mathrm {e}}^2+258}-4\,{\mathrm {e}}^{258}+4\,x\,{\mathrm {e}}^3\right )}^2}{8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(-1)*(4*x*exp(3) - 4*exp(258) + 4*exp(258)*exp(exp(2))),x)

[Out]

(exp(-4)*(4*exp(exp(2) + 258) - 4*exp(258) + 4*x*exp(3))^2)/8

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sympy [A]  time = 0.06, size = 24, normalized size = 1.20 \begin {gather*} 2 x^{2} e^{2} + x \left (- 4 e^{257} + 4 e^{257} e^{e^{2}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*exp(2)*exp(256)*exp(exp(2))-4*exp(2)*exp(256)+4*x*exp(1)*exp(2))/exp(1),x)

[Out]

2*x**2*exp(2) + x*(-4*exp(257) + 4*exp(257)*exp(exp(2)))

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