3.46.28 \(\int (1+e^2 (-4-4 x)) \, dx\)

Optimal. Leaf size=13 \[ x-2 e^2 x (2+x)+\log (7) \]

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Rubi [A]  time = 0.00, antiderivative size = 12, normalized size of antiderivative = 0.92, number of steps used = 1, number of rules used = 0, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x-2 e^2 (x+1)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 + E^2*(-4 - 4*x),x]

[Out]

x - 2*E^2*(1 + x)^2

Rubi steps

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

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Mathematica [A]  time = 0.00, size = 16, normalized size = 1.23 \begin {gather*} x-4 e^2 x-2 e^2 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 + E^2*(-4 - 4*x),x]

[Out]

x - 4*E^2*x - 2*E^2*x^2

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fricas [A]  time = 0.58, size = 13, normalized size = 1.00 \begin {gather*} -2 \, {\left (x^{2} + 2 \, x\right )} e^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2*(x^2 + 2*x)*e^2 + x

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giac [A]  time = 0.15, size = 13, normalized size = 1.00 \begin {gather*} -2 \, {\left (x^{2} + 2 \, x\right )} e^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2*(x^2 + 2*x)*e^2 + x

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maple [A]  time = 0.02, size = 15, normalized size = 1.15

method	result	size
gosper	\(-x \left (2 \,{\mathrm e}^{2} x +4 \,{\mathrm e}^{2}-1\right )\)	\(15\)
default	\({\mathrm e}^{2} \left (-2 x^{2}-4 x \right )+x\)	\(15\)
risch	\(-2 x^{2} {\mathrm e}^{2}-4 \,{\mathrm e}^{2} x +x\)	\(15\)
norman	\(\left (-4 \,{\mathrm e}^{2}+1\right ) x -2 x^{2} {\mathrm e}^{2}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x*(2*exp(2)*x+4*exp(2)-1)

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maxima [A]  time = 0.40, size = 13, normalized size = 1.00 \begin {gather*} -2 \, {\left (x^{2} + 2 \, x\right )} e^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2*(x^2 + 2*x)*e^2 + x

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mupad [B]  time = 3.14, size = 17, normalized size = 1.31 \begin {gather*} -\frac {\left (4\,x+4\right )\,\left ({\mathrm {e}}^2\,\left (4\,x+4\right )-2\right )}{8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1 - exp(2)*(4*x + 4),x)

[Out]

-((4*x + 4)*(exp(2)*(4*x + 4) - 2))/8

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sympy [A]  time = 0.05, size = 15, normalized size = 1.15 \begin {gather*} - 2 x^{2} e^{2} + x \left (1 - 4 e^{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2*x**2*exp(2) + x*(1 - 4*exp(2))

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