∫ e−x(12−12ex−x+x2+e3(13x−3x2+x3)+(1+e3x) log(3)+(−13x+3x2−x3−x log(3)) log(x))_______________________________________________________________

Optimal. Leaf size=32

(- 3 + e^{- x} (3 + \frac{1}{4} (- x + x^{2} + \log (3)))) (- e^{3} + \log (x))

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Rubi [B] time = 2.14, antiderivative size = 157, normalized size of antiderivative = 4.91, number of steps used = 21, number of rules used = 8, integrand size = 73,

\frac{number of rules}{integrand size}

= 0.110, Rules used = {12, 6742, 2199, 2176, 2194, 2178, 2196, 2554}

\begin{matrix} - \frac{1}{4} e^{3 - x} x^{2} + \frac{1}{4} e^{- x} x^{2} \log (x) - \frac{1}{2} e^{3 - x} x + \frac{e^{- x} x}{4} - \frac{1}{4} (1 - 3 e^{3}) e^{- x} x - \frac{e^{3 - x}}{2} - \frac{1}{4} (1 - 3 e^{3}) e^{- x} - \frac{1}{4} e^{- x} x \log (x) - \frac{1}{4} e^{- x} \log (x) + \frac{1}{4} e^{- x} (13 + \log (3)) \log (x) - 3 \log (x) + \frac{1}{4} e^{- x} (1 - e^{3} (13 + \log (3))) \end{matrix}

Int[(12 - 12*E^x - x + x^2 + E^3*(13*x - 3*x^2 + x^3) + (1 + E^3*x)*Log[3] + (-13*x + 3*x^2 - x^3 - x*Log[3])*

-1/2*E^(3 - x) - (1 - 3*E^3)/(4*E^x) - (E^(3 - x)*x)/2 + x/(4*E^x) - ((1 - 3*E^3)*x)/(4*E^x) - (E^(3 - x)*x^2)

/4 + (1 - E^3*(13 + Log[3]))/(4*E^x) - 3*Log[x] - Log[x]/(4*E^x) - (x*Log[x])/(4*E^x) + (x^2*Log[x])/(4*E^x) +

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_.), x_Symbol] :> Simp[((c + d*x)^m

*(b*F^(g*(e + f*x)))^n)/(f*g*n*Log[F]), x] - Dist[(d*m)/(f*g*n*Log[F]), Int[(c + d*x)^(m - 1)*(b*F^(g*(e + f*x

Int[(F_)^((g_.)*((e_.) + (f_.)*(x_)))/((c_.) + (d_.)*(x_)), x_Symbol] :> Simp[(F^(g*(e - (c*f)/d))*ExpIntegral

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre

Int[(F_)^((c_.)*(v_))*(u_), x_Symbol] :> Int[ExpandIntegrand[F^(c*ExpandToSum[v, x]), u, x], x] /; FreeQ[{F, c

Int[(F_)^((c_.)*(v_))*(u_)^(m_.)*(w_), x_Symbol] :> Int[ExpandIntegrand[F^(c*ExpandToSum[v, x]), w*NormalizePo

werOfLinear[u, x]^m, x], x] /; FreeQ[{F, c}, x] && PolynomialQ[w, x] && LinearQ[v, x] && PowerOfLinearQ[u, x]

Int[Log[u_]*(v_), x_Symbol] :> With[{w = IntHide[v, x]}, Dist[Log[u], w, x] - Int[SimplifyIntegrand[(w*D[u, x]

\begin{matrix} \begin{aligned} integral & = \frac{1}{4} \int \frac{e^{- x} (12 - 12 e^{x} - x + x^{2} + e^{3} (13 x - 3 x^{2} + x^{3}) + (1 + e^{3} x) \log (3) + (- 13 x + 3 x^{2} - x^{3} - x \log (3)) \log (x))}{x} d x \\ = \frac{1}{4} \int (- \frac{12}{x} + \frac{e^{- x} ((1 - 3 e^{3}) x^{2} + e^{3} x^{3} + 12 (1 + \frac{\log (3)}{12}) - x (1 - e^{3} (13 + \log (3))) + 3 x^{2} \log (x) - x^{3} \log (x) - 13 x (1 + \frac{\log (3)}{13}) \log (x))}{x}) d x \\ = - 3 \log (x) + \frac{1}{4} \int \frac{e^{- x} ((1 - 3 e^{3}) x^{2} + e^{3} x^{3} + 12 (1 + \frac{\log (3)}{12}) - x (1 - e^{3} (13 + \log (3))) + 3 x^{2} \log (x) - x^{3} \log (x) - 13 x (1 + \frac{\log (3)}{13}) \log (x))}{x} d x \\ = - 3 \log (x) + \frac{1}{4} \int (\frac{e^{- x} (12 + (1 - 3 e^{3}) x^{2} + e^{3} x^{3} + \log (3) - x (1 - e^{3} (13 + \log (3))))}{x} - e^{- x} (13 - 3 x + x^{2} + \log (3)) \log (x)) d x \\ = - 3 \log (x) + \frac{1}{4} \int \frac{e^{- x} (12 + (1 - 3 e^{3}) x^{2} + e^{3} x^{3} + \log (3) - x (1 - e^{3} (13 + \log (3))))}{x} d x - \frac{1}{4} \int e^{- x} (13 - 3 x + x^{2} + \log (3)) \log (x) d x \\ = - 3 \log (x) - \frac{1}{4} e^{- x} \log (x) - \frac{1}{4} e^{- x} x \log (x) + \frac{1}{4} e^{- x} x^{2} \log (x) + \frac{1}{4} e^{- x} (13 + \log (3)) \log (x) + \frac{1}{4} \int \frac{e^{- x} (- 12 + x - x^{2} - \log (3))}{x} d x + \frac{1}{4} \int (e^{- x} (1 - 3 e^{3}) x + e^{3 - x} x^{2} + \frac{e^{- x} (12 + \log (3))}{x} + e^{- x} (- 1 + e^{3} (13 + \log (3)))) d x \\ = - 3 \log (x) - \frac{1}{4} e^{- x} \log (x) - \frac{1}{4} e^{- x} x \log (x) + \frac{1}{4} e^{- x} x^{2} \log (x) + \frac{1}{4} e^{- x} (13 + \log (3)) \log (x) + \frac{1}{4} \int e^{3 - x} x^{2} d x + \frac{1}{4} \int (e^{- x} - e^{- x} x + \frac{e^{- x} (- 12 - \log (3))}{x}) d x + \frac{1}{4} (1 - 3 e^{3}) \int e^{- x} x d x + \frac{1}{4} (12 + \log (3)) \int \frac{e^{- x}}{x} d x + \frac{1}{4} (- 1 + e^{3} (13 + \log (3))) \int e^{- x} d x \\ = - \frac{1}{4} e^{- x} (1 - 3 e^{3}) x - \frac{1}{4} e^{3 - x} x^{2} + \frac{1}{4} Ei (- x) (12 + \log (3)) + \frac{1}{4} e^{- x} (1 - e^{3} (13 + \log (3))) - 3 \log (x) - \frac{1}{4} e^{- x} \log (x) - \frac{1}{4} e^{- x} x \log (x) + \frac{1}{4} e^{- x} x^{2} \log (x) + \frac{1}{4} e^{- x} (13 + \log (3)) \log (x) + \frac{1}{4} \int e^{- x} d x - \frac{1}{4} \int e^{- x} x d x + \frac{1}{2} \int e^{3 - x} x d x + \frac{1}{4} (1 - 3 e^{3}) \int e^{- x} d x + \frac{1}{4} (- 12 - \log (3)) \int \frac{e^{- x}}{x} d x \\ = - \frac{e^{- x}}{4} - \frac{1}{4} e^{- x} (1 - 3 e^{3}) - \frac{1}{2} e^{3 - x} x + \frac{e^{- x} x}{4} - \frac{1}{4} e^{- x} (1 - 3 e^{3}) x - \frac{1}{4} e^{3 - x} x^{2} + \frac{1}{4} e^{- x} (1 - e^{3} (13 + \log (3))) - 3 \log (x) - \frac{1}{4} e^{- x} \log (x) - \frac{1}{4} e^{- x} x \log (x) + \frac{1}{4} e^{- x} x^{2} \log (x) + \frac{1}{4} e^{- x} (13 + \log (3)) \log (x) - \frac{1}{4} \int e^{- x} d x + \frac{1}{2} \int e^{3 - x} d x \\ = - \frac{e^{3 - x}}{2} - \frac{1}{4} e^{- x} (1 - 3 e^{3}) - \frac{1}{2} e^{3 - x} x + \frac{e^{- x} x}{4} - \frac{1}{4} e^{- x} (1 - 3 e^{3}) x - \frac{1}{4} e^{3 - x} x^{2} + \frac{1}{4} e^{- x} (1 - e^{3} (13 + \log (3))) - 3 \log (x) - \frac{1}{4} e^{- x} \log (x) - \frac{1}{4} e^{- x} x \log (x) + \frac{1}{4} e^{- x} x^{2} \log (x) + \frac{1}{4} e^{- x} (13 + \log (3)) \log (x) \end{aligned} \end{matrix}

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Mathematica [A] time = 1.84, size = 43, normalized size = 1.34

\begin{matrix} \frac{1}{4} e^{- x} (- e^{3} (12 - x + x^{2} + \log (3)) + (12 - 12 e^{x} - x + x^{2} + \log (3)) \log (x)) \end{matrix}

Integrate[(12 - 12*E^x - x + x^2 + E^3*(13*x - 3*x^2 + x^3) + (1 + E^3*x)*Log[3] + (-13*x + 3*x^2 - x^3 - x*Lo

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fricas [A] time = 0.61, size = 41, normalized size = 1.28

\begin{matrix} - \frac{1}{4} ((x^{2} - x + 12) e^{3} + e^{3} \log (3) - (x^{2} - x - 12 e^{x} + \log (3) + 12) \log (x)) e^{(- x)} \end{matrix}

integrate(1/4*((-x*log(3)-x^3+3*x^2-13*x)*log(x)-12*exp(x)+(x*exp(3)+1)*log(3)+(x^3-3*x^2+13*x)*exp(3)+x^2-x+1

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giac [B] time = 0.19, size = 81, normalized size = 2.53

\begin{matrix} \frac{1}{4} x^{2} e^{(- x)} \log (x) - \frac{1}{4} x^{2} e^{(- x + 3)} - \frac{1}{4} x e^{(- x)} \log (x) + \frac{1}{4} e^{(- x)} \log (3) \log (x) + \frac{1}{4} x e^{(- x + 3)} - \frac{1}{4} e^{(- x + 3)} \log (3) + 3 e^{(- x)} \log (x) - 3 e^{(- x + 3)} - 3 \log (x) \end{matrix}

integrate(1/4*((-x*log(3)-x^3+3*x^2-13*x)*log(x)-12*exp(x)+(x*exp(3)+1)*log(3)+(x^3-3*x^2+13*x)*exp(3)+x^2-x+1

1/4*x^2*e^(-x)*log(x) - 1/4*x^2*e^(-x + 3) - 1/4*x*e^(-x)*log(x) + 1/4*e^(-x)*log(3)*log(x) + 1/4*x*e^(-x + 3)

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method	result	size

default	$\frac{(x e^{3} + x^{2} \ln (x) + (\ln (3) + 12) \ln (x) - x \ln (x) - x^{2} e^{3} - 12 e^{3} - e^{3} \ln (3)) e^{- x}}{4} - 3 \ln (x)$	$52$
risch	$\frac{(x^{2} + \ln (3) - x + 12) e^{- x} \ln (x)}{4} - \frac{(x^{2} e^{3} + 12 e^{x} \ln (x) + e^{3} \ln (3) - x e^{3} + 12 e^{3}) e^{- x}}{4}$	$53$
norman	$((\frac{\ln (3)}{4} + 3) \ln (x) - 3 e^{x} \ln (x) + \frac{x e^{3}}{4} - \frac{x \ln (x)}{4} - \frac{x^{2} e^{3}}{4} + \frac{x^{2} \ln (x)}{4} - 3 e^{3} - \frac{e^{3} \ln (3)}{4}) e^{- x}$	$56$

int(1/4*((-x*ln(3)-x^3+3*x^2-13*x)*ln(x)-12*exp(x)+(x*exp(3)+1)*ln(3)+(x^3-3*x^2+13*x)*exp(3)+x^2-x+12)/exp(x)

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maxima [F] time = 0.00, size = 0, normalized size = 0.00

\begin{matrix} \frac{1}{4} (x^{2} - x - 1) e^{(- x)} \log (x) + \frac{1}{4} e^{(- x)} \log (3) \log (x) - \frac{1}{4} (x^{2} e^{3} + 2 x e^{3} + 2 e^{3}) e^{(- x)} + \frac{3}{4} (x e^{3} + e^{3}) e^{(- x)} - \frac{1}{4} (x + 1) e^{(- x)} - \frac{1}{4} e^{(- x + 3)} \log (3) + \frac{13}{4} e^{(- x)} \log (x) - \frac{1}{4} E i (- x) + \frac{1}{4} e^{(- x)} - \frac{13}{4} e^{(- x + 3)} - \frac{1}{4} \int \frac{(x^{2} - x - 1) e^{(- x)}}{x} d x - 3 \log (x) \end{matrix}

integrate(1/4*((-x*log(3)-x^3+3*x^2-13*x)*log(x)-12*exp(x)+(x*exp(3)+1)*log(3)+(x^3-3*x^2+13*x)*exp(3)+x^2-x+1

1/4*(x^2 - x - 1)*e^(-x)*log(x) + 1/4*e^(-x)*log(3)*log(x) - 1/4*(x^2*e^3 + 2*x*e^3 + 2*e^3)*e^(-x) + 3/4*(x*e

^3 + e^3)*e^(-x) - 1/4*(x + 1)*e^(-x) - 1/4*e^(-x + 3)*log(3) + 13/4*e^(-x)*log(x) - 1/4*Ei(-x) + 1/4*e^(-x) -

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mupad [B] time = 2.13, size = 59, normalized size = 1.84

\begin{matrix} \frac{x e^{- x} (e^{3} - \ln (x))}{4} - \frac{e^{- x} (12 e^{x} \ln (x) - \ln (x) (\ln (3) + 12) + e^{3} (\ln (3) + 12))}{4} - \frac{x^{2} e^{- x} (e^{3} - \ln (x))}{4} \end{matrix}

int((exp(-x)*((exp(3)*(13*x - 3*x^2 + x^3))/4 - 3*exp(x) - x/4 + (log(3)*(x*exp(3) + 1))/4 - (log(x)*(13*x + x

(x*exp(-x)*(exp(3) - log(x)))/4 - (exp(-x)*(12*exp(x)*log(x) - log(x)*(log(3) + 12) + exp(3)*(log(3) + 12)))/4

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sympy [B] time = 0.60, size = 56, normalized size = 1.75

\begin{matrix} \frac{(x^{2} \log (x) - x^{2} e^{3} - x \log (x) + x e^{3} + \log (3) \log (x) + 12 \log (x) - 12 e^{3} - e^{3} \log (3)) e^{- x}}{4} - 3 \log (x) \end{matrix}

integrate(1/4*((-x*ln(3)-x**3+3*x**2-13*x)*ln(x)-12*exp(x)+(x*exp(3)+1)*ln(3)+(x**3-3*x**2+13*x)*exp(3)+x**2-x

(x**2*log(x) - x**2*exp(3) - x*log(x) + x*exp(3) + log(3)*log(x) + 12*log(x) - 12*exp(3) - exp(3)*log(3))*exp(

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3.33.87 ∫e−x(12−12ex−x+x2+e3(13x−3x2+x3)+(1+e3x)log⁡(3)+(−13x+3x2−x3−xlog⁡(3))log⁡(x))4xdx

3.33.87 $\int \frac{e^{- x} (12 - 12 e^{x} - x + x^{2} + e^{3} (13 x - 3 x^{2} + x^{3}) + (1 + e^{3} x) \log (3) + (- 13 x + 3 x^{2} - x^{3} - x \log (3)) \log (x))}{4 x} d x$