3.73.87 $\int \frac{-400x+(-2800+e^5(1200-300x)+700x)\log (-4+x)+(-1600+400x)\log (-4+x)\log (\log (-4+x))}{(-4900-5495x-624x^2+576x^3+e^{10}(-900+225x)+e^5(4200+1830x-720x^2))\log (-4+x)+(-5600+e^5(2400-600x)-2440x+960x^2)\log (-4+x)\log (\log (-4+x))+(-1600+400x)\log (-4+x){\log }^2(\log (-4+x))}dx$

Optimal. Leaf size=27 $$\frac{x}{1+\frac{3}{4}(1-e^5)+\frac{6x}{5}+\log (\log (-4+x))}$$

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Rubi [F]  time = 2.10, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.000, Rules used = {} $$\begin{array}{c}\int \frac{-400x+(-2800+e^5(1200-300x)+700x)\log (-4+x)+(-1600+400x)\log (-4+x)\log (\log (-4+x))}{(-4900-5495x-624x^2+576x^3+e^{10}(-900+225x)+e^5(4200+1830x-720x^2))\log (-4+x)+(-5600+e^5(2400-600x)-2440x+960x^2)\log (-4+x)\log (\log (-4+x))+(-1600+400x)\log (-4+x){\log }^2(\log (-4+x))}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(-400*x + (-2800 + E^5*(1200 - 300*x) + 700*x)*Log[-4 + x] + (-1600 + 400*x)*Log[-4 + x]*Log[Log[-4 + x]])
/((-4900 - 5495*x - 624*x^2 + 576*x^3 + E^10*(-900 + 225*x) + E^5*(4200 + 1830*x - 720*x^2))*Log[-4 + x] + (-5
600 + E^5*(2400 - 600*x) - 2440*x + 960*x^2)*Log[-4 + x]*Log[Log[-4 + x]] + (-1600 + 400*x)*Log[-4 + x]*Log[Lo
g[-4 + x]]^2),x]

[Out]

80/(5*(7 - 3*E^5) + 24*x + 20*Log[Log[-4 + x]]) + 1920*Defer[Int][(35*(1 - (3*E^5)/7) + 24*x + 20*Log[Log[-4 +
x]])^(-2), x] - 480*Defer[Int][x/(35*(1 - (3*E^5)/7) + 24*x + 20*Log[Log[-4 + x]])^2, x] - 400*Defer[Int][1/(
Log[-4 + x]*(35*(1 - (3*E^5)/7) + 24*x + 20*Log[Log[-4 + x]])^2), x] + 20*Defer[Int][(35*(1 - (3*E^5)/7) + 24*
x + 20*Log[Log[-4 + x]])^(-1), x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{100(4x+(-4+x)\log (-4+x)(-7+3e^5-4\log (\log (-4+x))))}{(4-x)\log (-4+x){(35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x)))}^2}dx\\ & =100\int \frac{4x+(-4+x)\log (-4+x)(-7+3e^5-4\log (\log (-4+x)))}{(4-x)\log (-4+x){(35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x)))}^2}dx\\ & =100\int (\frac{4x(5-24\log (-4+x)+6x\log (-4+x))}{5(4-x)\log (-4+x){(35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x)))}^2}+\frac{1}{5(35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x)))})dx\\ & =20\int \frac{1}{35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x))}dx+80\int \frac{x(5-24\log (-4+x)+6x\log (-4+x))}{(4-x)\log (-4+x){(35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x)))}^2}dx\\ & =20\int \frac{1}{35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x))}dx+80\int \frac{x(5+6(-4+x)\log (-4+x))}{(4-x)\log (-4+x){(35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x)))}^2}dx\\ & =20\int \frac{1}{35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x))}dx+80\int (\frac{-5+24\log (-4+x)-6x\log (-4+x)}{\log (-4+x){(35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x)))}^2}+\frac{4(5-24\log (-4+x)+6x\log (-4+x))}{(4-x)\log (-4+x){(35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x)))}^2})dx\\ & =20\int \frac{1}{35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x))}dx+80\int \frac{-5+24\log (-4+x)-6x\log (-4+x)}{\log (-4+x){(35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x)))}^2}dx+320\int \frac{5-24\log (-4+x)+6x\log (-4+x)}{(4-x)\log (-4+x){(35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x)))}^2}dx\\ & =\frac{80}{5(7-3e^5)+24x+20\log (\log (-4+x))}+20\int \frac{1}{35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x))}dx+80\int \frac{-5-6(-4+x)\log (-4+x)}{\log (-4+x){(35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x)))}^2}dx\\ & =\frac{80}{5(7-3e^5)+24x+20\log (\log (-4+x))}+20\int \frac{1}{35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x))}dx+80\int (\frac{24}{{(35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x)))}^2}-\frac{6x}{{(35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x)))}^2}-\frac{5}{\log (-4+x){(35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x)))}^2})dx\\ & =\frac{80}{5(7-3e^5)+24x+20\log (\log (-4+x))}+20\int \frac{1}{35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x))}dx-400\int \frac{1}{\log (-4+x){(35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x)))}^2}dx-480\int \frac{x}{{(35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x)))}^2}dx+1920\int \frac{1}{{(35(1-\frac{3e^5}{7})+24x+20\log (\log (-4+x)))}^2}dx\end{array}\end{array}$$

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Mathematica [A]  time = 1.13, size = 22, normalized size = 0.81 $$\begin{array}{c}\frac{100x}{175-75e^5+120x+100\log (\log (-4+x))}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(-400*x + (-2800 + E^5*(1200 - 300*x) + 700*x)*Log[-4 + x] + (-1600 + 400*x)*Log[-4 + x]*Log[Log[-4
+ x]])/((-4900 - 5495*x - 624*x^2 + 576*x^3 + E^10*(-900 + 225*x) + E^5*(4200 + 1830*x - 720*x^2))*Log[-4 + x]
+ (-5600 + E^5*(2400 - 600*x) - 2440*x + 960*x^2)*Log[-4 + x]*Log[Log[-4 + x]] + (-1600 + 400*x)*Log[-4 + x]*
Log[Log[-4 + x]]^2),x]

[Out]

(100*x)/(175 - 75*E^5 + 120*x + 100*Log[Log[-4 + x]])

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fricas [A]  time = 0.61, size = 21, normalized size = 0.78 $$\begin{array}{c}\frac{20x}{24x-15e^5+20\log (\log (x-4))+35}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((400*x-1600)*log(x-4)*log(log(x-4))+((-300*x+1200)*exp(5)+700*x-2800)*log(x-4)-400*x)/((400*x-1600)
*log(x-4)*log(log(x-4))^2+((-600*x+2400)*exp(5)+960*x^2-2440*x-5600)*log(x-4)*log(log(x-4))+((225*x-900)*exp(5
)^2+(-720*x^2+1830*x+4200)*exp(5)+576*x^3-624*x^2-5495*x-4900)*log(x-4)),x, algorithm="fricas")

[Out]

20*x/(24*x - 15*e^5 + 20*log(log(x - 4)) + 35)

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giac [A]  time = 0.26, size = 21, normalized size = 0.78 $$\begin{array}{c}\frac{20x}{24x-15e^5+20\log (\log (x-4))+35}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((400*x-1600)*log(x-4)*log(log(x-4))+((-300*x+1200)*exp(5)+700*x-2800)*log(x-4)-400*x)/((400*x-1600)
*log(x-4)*log(log(x-4))^2+((-600*x+2400)*exp(5)+960*x^2-2440*x-5600)*log(x-4)*log(log(x-4))+((225*x-900)*exp(5
)^2+(-720*x^2+1830*x+4200)*exp(5)+576*x^3-624*x^2-5495*x-4900)*log(x-4)),x, algorithm="giac")

[Out]

20*x/(24*x - 15*e^5 + 20*log(log(x - 4)) + 35)

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maple [A]  time = 0.34, size = 22, normalized size = 0.81

method	result	size
risch	$-\frac{20x}{15{\mathrm{e}}^5-20\ln (\ln (x-4))-24x-35}$	$22$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((400*x-1600)*ln(x-4)*ln(ln(x-4))+((-300*x+1200)*exp(5)+700*x-2800)*ln(x-4)-400*x)/((400*x-1600)*ln(x-4)*l
n(ln(x-4))^2+((-600*x+2400)*exp(5)+960*x^2-2440*x-5600)*ln(x-4)*ln(ln(x-4))+((225*x-900)*exp(5)^2+(-720*x^2+18
30*x+4200)*exp(5)+576*x^3-624*x^2-5495*x-4900)*ln(x-4)),x,method=_RETURNVERBOSE)

[Out]

-20*x/(15*exp(5)-20*ln(ln(x-4))-24*x-35)

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maxima [A]  time = 0.42, size = 21, normalized size = 0.78 $$\begin{array}{c}\frac{20x}{24x-15e^5+20\log (\log (x-4))+35}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((400*x-1600)*log(x-4)*log(log(x-4))+((-300*x+1200)*exp(5)+700*x-2800)*log(x-4)-400*x)/((400*x-1600)
*log(x-4)*log(log(x-4))^2+((-600*x+2400)*exp(5)+960*x^2-2440*x-5600)*log(x-4)*log(log(x-4))+((225*x-900)*exp(5
)^2+(-720*x^2+1830*x+4200)*exp(5)+576*x^3-624*x^2-5495*x-4900)*log(x-4)),x, algorithm="maxima")

[Out]

20*x/(24*x - 15*e^5 + 20*log(log(x - 4)) + 35)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 $$\begin{array}{c}\int \frac{400x+\ln (x-4)({\mathrm{e}}^5(300x-1200)-700x+2800)-\ln (x-4)\ln (\ln (x-4))(400x-1600)}{-\ln (x-4)(400x-1600){\ln (\ln (x-4))}^2+\ln (x-4)(2440x-960x^2+{\mathrm{e}}^5(600x-2400)+5600)\ln (\ln (x-4))+\ln (x-4)(5495x-{\mathrm{e}}^5(-720x^2+1830x+4200)+624x^2-576x^3-{\mathrm{e}}^{10}(225x-900)+4900)}dx\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((400*x + log(x - 4)*(exp(5)*(300*x - 1200) - 700*x + 2800) - log(x - 4)*log(log(x - 4))*(400*x - 1600))/(l
og(x - 4)*(5495*x - exp(5)*(1830*x - 720*x^2 + 4200) + 624*x^2 - 576*x^3 - exp(10)*(225*x - 900) + 4900) + log
(x - 4)*log(log(x - 4))*(2440*x - 960*x^2 + exp(5)*(600*x - 2400) + 5600) - log(x - 4)*log(log(x - 4))^2*(400*
x - 1600)),x)

[Out]

int((400*x + log(x - 4)*(exp(5)*(300*x - 1200) - 700*x + 2800) - log(x - 4)*log(log(x - 4))*(400*x - 1600))/(l
og(x - 4)*(5495*x - exp(5)*(1830*x - 720*x^2 + 4200) + 624*x^2 - 576*x^3 - exp(10)*(225*x - 900) + 4900) + log
(x - 4)*log(log(x - 4))*(2440*x - 960*x^2 + exp(5)*(600*x - 2400) + 5600) - log(x - 4)*log(log(x - 4))^2*(400*
x - 1600)), x)

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sympy [A]  time = 0.41, size = 22, normalized size = 0.81 $$\begin{array}{c}\frac{x}{\frac{6x}{5}+\log (\log (x-4))-\frac{3e^5}{4}+\frac{7}{4}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((400*x-1600)*ln(x-4)*ln(ln(x-4))+((-300*x+1200)*exp(5)+700*x-2800)*ln(x-4)-400*x)/((400*x-1600)*ln(
x-4)*ln(ln(x-4))**2+((-600*x+2400)*exp(5)+960*x**2-2440*x-5600)*ln(x-4)*ln(ln(x-4))+((225*x-900)*exp(5)**2+(-7
20*x**2+1830*x+4200)*exp(5)+576*x**3-624*x**2-5495*x-4900)*ln(x-4)),x)

[Out]

x/(6*x/5 + log(log(x - 4)) - 3*exp(5)/4 + 7/4)

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