3.35.39 \(\int (-16-16 x+e^{2+5 e^5} (4+4 x)) \, dx\)

Optimal. Leaf size=18 \[ 2 \left (-4+e^{2+5 e^5}\right ) (1+x)^2 \]

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Rubi [A]  time = 0.01, antiderivative size = 25, normalized size of antiderivative = 1.39, number of steps used = 1, number of rules used = 0, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -8 x^2-16 x+2 e^{2+5 e^5} (x+1)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-16 - 16*x + E^(2 + 5*E^5)*(4 + 4*x),x]

[Out]

-16*x - 8*x^2 + 2*E^(2 + 5*E^5)*(1 + x)^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-16 x-8 x^2+2 e^{2+5 e^5} (1+x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 22, normalized size = 1.22 \begin {gather*} 4 \left (-4+e^{2+5 e^5}\right ) \left (x+\frac {x^2}{2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-16 - 16*x + E^(2 + 5*E^5)*(4 + 4*x),x]

[Out]

4*(-4 + E^(2 + 5*E^5))*(x + x^2/2)

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fricas [A]  time = 0.45, size = 25, normalized size = 1.39 \begin {gather*} -8 \, x^{2} + 2 \, {\left (x^{2} + 2 \, x\right )} e^{\left (5 \, e^{5} + 2\right )} - 16 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x+4)*exp(5*exp(5)+2)-16*x-16,x, algorithm="fricas")

[Out]

-8*x^2 + 2*(x^2 + 2*x)*e^(5*e^5 + 2) - 16*x

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giac [A]  time = 0.16, size = 25, normalized size = 1.39 \begin {gather*} -8 \, x^{2} + 2 \, {\left (x^{2} + 2 \, x\right )} e^{\left (5 \, e^{5} + 2\right )} - 16 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x+4)*exp(5*exp(5)+2)-16*x-16,x, algorithm="giac")

[Out]

-8*x^2 + 2*(x^2 + 2*x)*e^(5*e^5 + 2) - 16*x

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maple [A]  time = 0.02, size = 16, normalized size = 0.89

method	result	size
gosper	\(2 \left ({\mathrm e}^{5 \,{\mathrm e}^{5}+2}-4\right ) x \left (2+x \right )\)	\(16\)
default	\({\mathrm e}^{5 \,{\mathrm e}^{5}+2} \left (2 x^{2}+4 x \right )-8 x^{2}-16 x\)	\(27\)
norman	\(\left (2 \,{\mathrm e}^{5 \,{\mathrm e}^{5}} {\mathrm e}^{2}-8\right ) x^{2}+\left (4 \,{\mathrm e}^{5 \,{\mathrm e}^{5}} {\mathrm e}^{2}-16\right ) x\)	\(30\)
risch	\(2 x^{2} {\mathrm e}^{5 \,{\mathrm e}^{5}+2}+4 x \,{\mathrm e}^{5 \,{\mathrm e}^{5}+2}-8 x^{2}-16 x\)	\(32\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*x+4)*exp(5*exp(5)+2)-16*x-16,x,method=_RETURNVERBOSE)

[Out]

2*(exp(5*exp(5)+2)-4)*x*(2+x)

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maxima [A]  time = 0.48, size = 25, normalized size = 1.39 \begin {gather*} -8 \, x^{2} + 2 \, {\left (x^{2} + 2 \, x\right )} e^{\left (5 \, e^{5} + 2\right )} - 16 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x+4)*exp(5*exp(5)+2)-16*x-16,x, algorithm="maxima")

[Out]

-8*x^2 + 2*(x^2 + 2*x)*e^(5*e^5 + 2) - 16*x

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mupad [B]  time = 0.06, size = 15, normalized size = 0.83 \begin {gather*} 2\,x\,\left (x+2\right )\,\left ({\mathrm {e}}^{5\,{\mathrm {e}}^5+2}-4\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(5*exp(5) + 2)*(4*x + 4) - 16*x - 16,x)

[Out]

2*x*(x + 2)*(exp(5*exp(5) + 2) - 4)

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sympy [B]  time = 0.06, size = 31, normalized size = 1.72 \begin {gather*} x^{2} \left (-8 + 2 e^{2} e^{5 e^{5}}\right ) + x \left (-16 + 4 e^{2} e^{5 e^{5}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x+4)*exp(5*exp(5)+2)-16*x-16,x)

[Out]

x**2*(-8 + 2*exp(2)*exp(5*exp(5))) + x*(-16 + 4*exp(2)*exp(5*exp(5)))

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