3.85.42 $\int \frac{1}{9}{e}^{2-2x}(6{\log }^2(4)-2{\log }^2(4)\log (5))dx$

Optimal. Leaf size=22 $$(5+\frac{1}{9}{e}^{2-2x}{\log }^2(4))(-3+\log (5))$$

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Rubi [A]  time = 0.01, antiderivative size = 21, normalized size of antiderivative = 0.95, number of steps used = 2, number of rules used = 2, integrand size = 26, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.077, Rules used = {12, 2194} $$\begin{array}{c}-\frac{1}{9}{e}^{2-2x}{\log }^2(4)(3-\log (5))\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(E^(2 - 2*x)*(6*Log[4]^2 - 2*Log[4]^2*Log[5]))/9,x]

[Out]

-1/9*(E^(2 - 2*x)*Log[4]^2*(3 - Log[5]))

Rule 12

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

Rule 2194

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

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\frac{1}{9}(2{\log }^2(4)(3-\log (5)))\int e^{2-2x}dx\\ & =-\frac{1}{9}{e}^{2-2x}{\log }^2(4)(3-\log (5))\end{array}\end{array}$$

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Mathematica [A]  time = 0.01, size = 19, normalized size = 0.86 $$\begin{array}{c}\frac{1}{9}{e}^{2-2x}{\log }^2(4)(-3+\log (5))\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(E^(2 - 2*x)*(6*Log[4]^2 - 2*Log[4]^2*Log[5]))/9,x]

[Out]

(E^(2 - 2*x)*Log[4]^2*(-3 + Log[5]))/9

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fricas [A]  time = 1.16, size = 22, normalized size = 1.00 $$\begin{array}{c}\frac{4}{9}(\log (5)\log (2{)}^2-3\log (2{)}^2)e^{(-2x+2)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/9*(-8*log(2)^2*log(5)+24*log(2)^2)*exp(-x+1)^2,x, algorithm="fricas")

[Out]

4/9*(log(5)*log(2)^2 - 3*log(2)^2)*e^(-2*x + 2)

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giac [A]  time = 0.14, size = 22, normalized size = 1.00 $$\begin{array}{c}\frac{4}{9}(\log (5)\log (2{)}^2-3\log (2{)}^2)e^{(-2x+2)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/9*(-8*log(2)^2*log(5)+24*log(2)^2)*exp(-x+1)^2,x, algorithm="giac")

[Out]

4/9*(log(5)*log(2)^2 - 3*log(2)^2)*e^(-2*x + 2)

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maple [A]  time = 0.04, size = 19, normalized size = 0.86

method	result	size
gosper	$\frac{4\ln (2{)}^2(\ln (5)-3){\mathrm{e}}^{-2x+2}}{9}$	$19$
norman	$(\frac{4\ln (2{)}^2\ln (5)}{9}-\frac{4\ln (2{)}^2}{3}){\mathrm{e}}^{-2x+2}$	$25$
derivativedivides	$-\frac{(-8\ln (2{)}^2\ln (5)+24\ln (2{)}^2){\mathrm{e}}^{-2x+2}}{18}$	$26$
default	$-\frac{(-\frac{8\ln (2{)}^2\ln (5)}{9}+\frac{8\ln (2{)}^2}{3}){\mathrm{e}}^{-2x+2}}{2}$	$26$
risch	$\frac{4{\mathrm{e}}^{-2x+2}\ln (2{)}^2\ln (5)}{9}-\frac{4{\mathrm{e}}^{-2x+2}\ln (2{)}^2}{3}$	$28$
meijerg	$-\frac{4{\mathrm{e}}^{2{\mathrm{e}}^{2}x-2x}\ln (2{)}^2\ln (5)(1-{\mathrm{e}}^{-2{\mathrm{e}}^{2}x})}{9}+\frac{4{\mathrm{e}}^{2{\mathrm{e}}^{2}x-2x}\ln (2{)}^2(1-{\mathrm{e}}^{-2{\mathrm{e}}^{2}x})}{3}$	$56$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/9*(-8*ln(2)^2*ln(5)+24*ln(2)^2)*exp(1-x)^2,x,method=_RETURNVERBOSE)

[Out]

4/9*ln(2)^2*(ln(5)-3)*exp(1-x)^2

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maxima [A]  time = 0.39, size = 22, normalized size = 1.00 $$\begin{array}{c}\frac{4}{9}(\log (5)\log (2{)}^2-3\log (2{)}^2)e^{(-2x+2)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/9*(-8*log(2)^2*log(5)+24*log(2)^2)*exp(-x+1)^2,x, algorithm="maxima")

[Out]

4/9*(log(5)*log(2)^2 - 3*log(2)^2)*e^(-2*x + 2)

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mupad [B]  time = 5.16, size = 16, normalized size = 0.73 $$\begin{array}{c}\frac{4{\mathrm{e}}^{2-2x}{\ln (2)}^2(\ln (5)-3)}{9}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(2 - 2*x)*(8*log(2)^2*log(5) - 24*log(2)^2))/9,x)

[Out]

(4*exp(2 - 2*x)*log(2)^2*(log(5) - 3))/9

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sympy [A]  time = 0.11, size = 24, normalized size = 1.09 $$\begin{array}{c}\frac{(-12\log {(2)}^2+4\log {(2)}^2\log (5))e^{2-2x}}{9}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/9*(-8*ln(2)**2*ln(5)+24*ln(2)**2)*exp(-x+1)**2,x)

[Out]

(-12*log(2)**2 + 4*log(2)**2*log(5))*exp(2 - 2*x)/9

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