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

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

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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} $$\begin{array}{c}\frac{x}{e^4}-\frac{1}{20}(10x+11{)}^2\end{array}$$

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\frac{\int (1+e^4(-11-10x))dx}{e^4}\\ & =\frac{x}{e^4}-\frac{1}{20}(11+10x{)}^2\end{array}\end{array}$$

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

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 $$\begin{array}{c}-((5x^2+11x)e^4-x)e^{(-4)}\end{array}$$

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 $$\begin{array}{c}-((5x^2+11x)e^4-x)e^{(-4)}\end{array}$$

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	$-5x^2-11x+x{\mathrm{e}}^{-4}$	$14$
gosper	$-x(5x{\mathrm{e}}^4+11{\mathrm{e}}^4-1){\mathrm{e}}^{-4}$	$19$
default	${\mathrm{e}}^{-4}({\mathrm{e}}^4(-5x^2-11x)+x)$	$20$
norman	$-5x^2-{\mathrm{e}}^{-4}(11{\mathrm{e}}^4-1)x$	$20$

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 $$\begin{array}{c}-((5x^2+11x)e^4-x)e^{(-4)}\end{array}$$

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 $$\begin{array}{c}-\frac{{\mathrm{e}}^{-8}{({\mathrm{e}}^4(10x+11)-1)}^2}{20}\end{array}$$

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 $$\begin{array}{c}-5x^2+\frac{x(1-11e^4)}{e^4}\end{array}$$

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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