\(\int \frac {1+e^4 (-11-10 x)}{e^4} \, dx\) [1247]

Optimal result

Integrand size = 15, antiderivative size = 21 \[ \int \frac {1+e^4 (-11-10 x)}{e^4} \, dx=-x+\frac {x}{e^4}-4 x^2-(5+x)^2 \]

[Out]

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

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12} \[ \int \frac {1+e^4 (-11-10 x)}{e^4} \, dx=\frac {x}{e^4}-\frac {1}{20} (10 x+11)^2 \]

[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{align*} \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{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.67 \[ \int \frac {1+e^4 (-11-10 x)}{e^4} \, dx=-11 x+\frac {x}{e^4}-5 x^2 \]

[In]

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

[Out]

-11*x + x/E^4 - 5*x^2

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 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	\({\mathrm e}^{-4} \left (-5 x^{2} {\mathrm e}^{4}-11 x \,{\mathrm e}^{4}+x \right )\)	\(20\)
norman	\(-5 x^{2}-{\mathrm e}^{-4} \left (11 \,{\mathrm e}^{4}-1\right ) x\)	\(20\)
parallelrisch	\({\mathrm e}^{-4} \left ({\mathrm e}^{4} \left (-5 x^{2}-11 x \right )+x \right )\)	\(20\)

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95 \[ \int \frac {1+e^4 (-11-10 x)}{e^4} \, dx=-{\left ({\left (5 \, x^{2} + 11 \, x\right )} e^{4} - x\right )} e^{\left (-4\right )} \]

[In]

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

[Out]

-((5*x^2 + 11*x)*e^4 - x)*e^(-4)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.71 \[ \int \frac {1+e^4 (-11-10 x)}{e^4} \, dx=- 5 x^{2} + \frac {x \left (1 - 11 e^{4}\right )}{e^{4}} \]

[In]

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

[Out]

-5*x**2 + x*(1 - 11*exp(4))*exp(-4)

Maxima [A] (verification not implemented)

none

Time = 0.17 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95 \[ \int \frac {1+e^4 (-11-10 x)}{e^4} \, dx=-{\left ({\left (5 \, x^{2} + 11 \, x\right )} e^{4} - x\right )} e^{\left (-4\right )} \]

[In]

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

[Out]

-((5*x^2 + 11*x)*e^4 - x)*e^(-4)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95 \[ \int \frac {1+e^4 (-11-10 x)}{e^4} \, dx=-{\left ({\left (5 \, x^{2} + 11 \, x\right )} e^{4} - x\right )} e^{\left (-4\right )} \]

[In]

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

[Out]

-((5*x^2 + 11*x)*e^4 - x)*e^(-4)

Mupad [B] (verification not implemented)

Time = 8.39 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.76 \[ \int \frac {1+e^4 (-11-10 x)}{e^4} \, dx=-\frac {{\mathrm {e}}^{-8}\,{\left ({\mathrm {e}}^4\,\left (10\,x+11\right )-1\right )}^2}{20} \]

[In]

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

[Out]

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