3.13.47 \(\int \frac {1+e^4 (-11-10 x)}{e^4} \, dx\)

Optimal. Leaf size=21 \[ -x+\frac {x}{e^4}-4 x^2-(5+x)^2 \]

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Rubi [A]  time = 0.01, antiderivative size = 17, normalized size of antiderivative = 0.81, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12} \begin {gather*} \frac {x}{e^4}-\frac {1}{20} (10 x+11)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 + E^4*(-11 - 10*x))/E^4,x]

[Out]

x/E^4 - (11 + 10*x)^2/20

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (1+e^4 (-11-10 x)\right ) \, dx}{e^4}\\ &=\frac {x}{e^4}-\frac {1}{20} (11+10 x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 0.67 \begin {gather*} -11 x+\frac {x}{e^4}-5 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 + E^4*(-11 - 10*x))/E^4,x]

[Out]

-11*x + x/E^4 - 5*x^2

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fricas [A]  time = 0.66, size = 20, normalized size = 0.95 \begin {gather*} -{\left ({\left (5 \, x^{2} + 11 \, x\right )} e^{4} - x\right )} e^{\left (-4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-10*x-11)*exp(4)+1)/exp(4),x, algorithm="fricas")

[Out]

-((5*x^2 + 11*x)*e^4 - x)*e^(-4)

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giac [A]  time = 0.24, size = 20, normalized size = 0.95 \begin {gather*} -{\left ({\left (5 \, x^{2} + 11 \, x\right )} e^{4} - x\right )} e^{\left (-4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-10*x-11)*exp(4)+1)/exp(4),x, algorithm="giac")

[Out]

-((5*x^2 + 11*x)*e^4 - x)*e^(-4)

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maple [A]  time = 0.02, size = 14, normalized size = 0.67

method	result	size
risch	\(-5 x^{2}-11 x +x \,{\mathrm e}^{-4}\)	\(14\)
gosper	\(-x \left (5 x \,{\mathrm e}^{4}+11 \,{\mathrm e}^{4}-1\right ) {\mathrm e}^{-4}\)	\(19\)
default	\({\mathrm e}^{-4} \left ({\mathrm e}^{4} \left (-5 x^{2}-11 x \right )+x \right )\)	\(20\)
norman	\(-5 x^{2}-{\mathrm e}^{-4} \left (11 \,{\mathrm e}^{4}-1\right ) x\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-10*x-11)*exp(4)+1)/exp(4),x,method=_RETURNVERBOSE)

[Out]

-5*x^2-11*x+x*exp(-4)

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maxima [A]  time = 0.36, size = 20, normalized size = 0.95 \begin {gather*} -{\left ({\left (5 \, x^{2} + 11 \, x\right )} e^{4} - x\right )} e^{\left (-4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-10*x-11)*exp(4)+1)/exp(4),x, algorithm="maxima")

[Out]

-((5*x^2 + 11*x)*e^4 - x)*e^(-4)

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mupad [B]  time = 0.39, size = 16, normalized size = 0.76 \begin {gather*} -\frac {{\mathrm {e}}^{-8}\,{\left ({\mathrm {e}}^4\,\left (10\,x+11\right )-1\right )}^2}{20} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(-4)*(exp(4)*(10*x + 11) - 1),x)

[Out]

-(exp(-8)*(exp(4)*(10*x + 11) - 1)^2)/20

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sympy [A]  time = 0.05, size = 15, normalized size = 0.71 \begin {gather*} - 5 x^{2} + \frac {x \left (1 - 11 e^{4}\right )}{e^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-10*x-11)*exp(4)+1)/exp(4),x)

[Out]

-5*x**2 + x*(1 - 11*exp(4))*exp(-4)

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