∫ −48−470x−378x2+30x3+50x4+(−48−16x+216x2−240x3−200x4) log(x)_______ −1728−33264x−181611x2−200033x3+5697x4+79731x5+10255x6−11475x7−1125x8+625x9 dx

3.94.75 \(\int \frac {-48-470 x-378 x^2+30 x^3+50 x^4+(-48-16 x+216 x^2-240 x^3-200 x^4) \log (x)}{-1728-33264 x-181611 x^2-200033 x^3+5697 x^4+79731 x^5+10255 x^6-11475 x^7-1125 x^8+625 x^9} \, dx\)

Optimal. Leaf size=28 \[ \frac {x \log (x)}{4 (-3+x)^2 \left (1+\frac {1}{8} x (9+5 x)^2\right )} \]

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Rubi [F] time = 63.00, 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 {gather*} \int \frac {-48-470 x-378 x^2+30 x^3+50 x^4+\left (-48-16 x+216 x^2-240 x^3-200 x^4\right ) \log (x)}{-1728-33264 x-181611 x^2-200033 x^3+5697 x^4+79731 x^5+10255 x^6-11475 x^7-1125 x^8+625 x^9} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(-48 - 470*x - 378*x^2 + 30*x^3 + 50*x^4 + (-48 - 16*x + 216*x^2 - 240*x^3 - 200*x^4)*Log[x])/(-1728 - 332

64*x - 181611*x^2 - 200033*x^3 + 5697*x^4 + 79731*x^5 + 10255*x^6 - 11475*x^7 - 1125*x^8 + 625*x^9),x]

[Out]

141597/(40873252*(8 + 81*x + 90*x^2 + 25*x^3)) - (20329965*(7 + (2*I)*Sqrt[170])^(1/3))/(2779381136*(9 + (7 +

(2*I)*Sqrt[170])^(2/3) - (7 + (2*I)*Sqrt[170])^(1/3)*(6 + 5*x))) - (10000*(7 + (2*I)*Sqrt[170])^(8/3))/(3*(9 -

21*(7 + (2*I)*Sqrt[170])^(1/3) + (7 + (2*I)*Sqrt[170])^(2/3))^3*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2

*I)*Sqrt[170])^(4/3))^2*(9 + (7 + (2*I)*Sqrt[170])^(2/3) - (7 + (2*I)*Sqrt[170])^(1/3)*(6 + 5*x))) - (((5*I)/6

53972032)*Sqrt[5/34]*(7 + (2*I)*Sqrt[170])^(1/3)*(204944508 + ((265390622 + (18948583*I)*Sqrt[170] + 9*(7 + (2

*I)*Sqrt[170])^(1/3)*(11385806 + (546147*I)*Sqrt[170]))*(6 + 5*x))/(7 + (2*I)*Sqrt[170])^(2/3)))/((9 - (7 + (2

*I)*Sqrt[170])^(2/3))*((3 - (7 + (2*I)*Sqrt[170])^(1/3))^2/(7 + (2*I)*Sqrt[170])^(1/3) - 5*x)*(9 - 81/(7 + (2*

I)*Sqrt[170])^(2/3) - (7 + (2*I)*Sqrt[170])^(2/3) - ((9 + (7 + (2*I)*Sqrt[170])^(2/3))*(6 + 5*x))/(7 + (2*I)*S

qrt[170])^(1/3) - (6 + 5*x)^2)) + (((235*I)/1961916096)*Sqrt[5/34]*(7 + (2*I)*Sqrt[170])^(1/3)*(86548780 + ((5

9339910 + (9087783*I)*Sqrt[170] + (7 + (2*I)*Sqrt[170])^(1/3)*(43274390 + (679819*I)*Sqrt[170]))*(6 + 5*x))/(7

+ (2*I)*Sqrt[170])^(2/3)))/((9 - (7 + (2*I)*Sqrt[170])^(2/3))*((3 - (7 + (2*I)*Sqrt[170])^(1/3))^2/(7 + (2*I)

*Sqrt[170])^(1/3) - 5*x)*(9 - 81/(7 + (2*I)*Sqrt[170])^(2/3) - (7 + (2*I)*Sqrt[170])^(2/3) - ((9 + (7 + (2*I)*

Sqrt[170])^(2/3))*(6 + 5*x))/(7 + (2*I)*Sqrt[170])^(1/3) - (6 + 5*x)^2)) - (((27*I)/93424576)*Sqrt[5/34]*(7 +

(2*I)*Sqrt[170])^(1/3)*(42531500 + ((43192590 + (4176993*I)*Sqrt[170] + (7 + (2*I)*Sqrt[170])^(1/3)*(21265750

+ (705509*I)*Sqrt[170]))*(6 + 5*x))/(7 + (2*I)*Sqrt[170])^(2/3)))/((9 - (7 + (2*I)*Sqrt[170])^(2/3))*((3 - (7

+ (2*I)*Sqrt[170])^(1/3))^2/(7 + (2*I)*Sqrt[170])^(1/3) - 5*x)*(9 - 81/(7 + (2*I)*Sqrt[170])^(2/3) - (7 + (2*I

)*Sqrt[170])^(2/3) - ((9 + (7 + (2*I)*Sqrt[170])^(2/3))*(6 + 5*x))/(7 + (2*I)*Sqrt[170])^(1/3) - (6 + 5*x)^2))

+ (((5*I)/1961916096)*Sqrt[5/34]*(7 + (2*I)*Sqrt[170])^(1/3)*(1760448292 + ((3*(924271726 + (50871029*I)*Sqrt

[170]) + (7 + (2*I)*Sqrt[170])^(1/3)*(880224146 + (55275787*I)*Sqrt[170]))*(6 + 5*x))/(7 + (2*I)*Sqrt[170])^(2

/3)))/((9 - (7 + (2*I)*Sqrt[170])^(2/3))*((3 - (7 + (2*I)*Sqrt[170])^(1/3))^2/(7 + (2*I)*Sqrt[170])^(1/3) - 5*

x)*(9 - 81/(7 + (2*I)*Sqrt[170])^(2/3) - (7 + (2*I)*Sqrt[170])^(2/3) - ((9 + (7 + (2*I)*Sqrt[170])^(2/3))*(6 +

5*x))/(7 + (2*I)*Sqrt[170])^(1/3) - (6 + 5*x)^2)) + (125*(7*I - 2*Sqrt[170])^3*((2*I)*(454238*(7 + (2*I)*Sqrt

[170])^(1/3)*(631*I + 28*Sqrt[170]) + 9*(7 + (2*I)*Sqrt[170])^(2/3)*(11753609*I + 765050*Sqrt[170]) + 9*(13055

3521*I + 3601726*Sqrt[170])) - (410661641 - (736526*I)*Sqrt[170] + 365022*(7 + (2*I)*Sqrt[170])^(1/3)*(631 - (

28*I)*Sqrt[170]) + 9*(7 + (2*I)*Sqrt[170])^(2/3)*(2629721 - (332570*I)*Sqrt[170]))*(6 + 5*x)))/(1632*(27*(4587

96979814*I - 691884067*Sqrt[170]) + 5764492*(7 + (2*I)*Sqrt[170])^(2/3)*(264881*I + 35336*Sqrt[170]) + 9*(7 +

(2*I)*Sqrt[170])^(1/3)*(316680017234*I + 25470838571*Sqrt[170]))*(81 - 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2

*I)*Sqrt[170])^(4/3) + (7 + (2*I)*Sqrt[170] + 9*(7 + (2*I)*Sqrt[170])^(1/3))*(6 + 5*x) + (7 + (2*I)*Sqrt[170])

^(2/3)*(6 + 5*x)^2)) - (135*(51435930 + (27846411*I)*Sqrt[170] + (7 + (2*I)*Sqrt[170])^(2/3)*(15255730 + (2897

621*I)*Sqrt[170]))*ArcTan[(7 + (2*I)*Sqrt[170] + 9*(7 + (2*I)*Sqrt[170])^(1/3) + 2*(7 + (2*I)*Sqrt[170])^(2/3)

*(6 + 5*x))/Sqrt[3*(-631 + (28*I)*Sqrt[170] + 81*(7 + (2*I)*Sqrt[170])^(2/3) - 18*(7 + (2*I)*Sqrt[170])^(4/3))

]])/(141911930944*Sqrt[(-631 + (28*I)*Sqrt[170] + 81*(7 + (2*I)*Sqrt[170])^(2/3) - 18*(7 + (2*I)*Sqrt[170])^(4

/3))/3]*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3))) - (225*(464077460 + (67004701*I)*S

qrt[170] + (7 + (2*I)*Sqrt[170])^(2/3)*(3979500 + (8424651*I)*Sqrt[170]))*ArcTan[(7 + (2*I)*Sqrt[170] + 9*(7 +

(2*I)*Sqrt[170])^(1/3) + 2*(7 + (2*I)*Sqrt[170])^(2/3)*(6 + 5*x))/Sqrt[3*(-631 + (28*I)*Sqrt[170] + 81*(7 + (

2*I)*Sqrt[170])^(2/3) - 18*(7 + (2*I)*Sqrt[170])^(4/3))]])/(141911930944*Sqrt[(-631 + (28*I)*Sqrt[170] + 81*(7

+ (2*I)*Sqrt[170])^(2/3) - 18*(7 + (2*I)*Sqrt[170])^(4/3))/3]*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I

)*Sqrt[170])^(4/3))) - (27*(1408029280 + (120491111*I)*Sqrt[170] - (7 + (2*I)*Sqrt[170])^(2/3)*(48000120 - (17

597121*I)*Sqrt[170]))*ArcTan[(7 + (2*I)*Sqrt[170] + 9*(7 + (2*I)*Sqrt[170])^(1/3) + 2*(7 + (2*I)*Sqrt[170])^(2

/3)*(6 + 5*x))/Sqrt[3*(-631 + (28*I)*Sqrt[170] + 81*(7 + (2*I)*Sqrt[170])^(2/3) - 18*(7 + (2*I)*Sqrt[170])^(4/

3))]])/(20273132992*Sqrt[(-631 + (28*I)*Sqrt[170] + 81*(7 + (2*I)*Sqrt[170])^(2/3) - 18*(7 + (2*I)*Sqrt[170])^

(4/3))/3]*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3))) - (235*(4222933750 + (545086331*

I)*Sqrt[170] - (7 + (2*I)*Sqrt[170])^(2/3)*(10678290 - (70445301*I)*Sqrt[170]))*ArcTan[(7 + (2*I)*Sqrt[170] +

9*(7 + (2*I)*Sqrt[170])^(1/3) + 2*(7 + (2*I)*Sqrt[170])^(2/3)*(6 + 5*x))/Sqrt[3*(-631 + (28*I)*Sqrt[170] + 81*

(7 + (2*I)*Sqrt[170])^(2/3) - 18*(7 + (2*I)*Sqrt[170])^(4/3))]])/(141911930944*Sqrt[3*(-631 + (28*I)*Sqrt[170]

+ 81*(7 + (2*I)*Sqrt[170])^(2/3) - 18*(7 + (2*I)*Sqrt[170])^(4/3))]*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7

+ (2*I)*Sqrt[170])^(4/3))) - (2500*(7*I - 2*Sqrt[170])^3*(410661641*I + 736526*Sqrt[170] + 365022*(7 + (2*I)*S

qrt[170])^(1/3)*(631*I + 28*Sqrt[170]) + 9*(7 + (2*I)*Sqrt[170])^(2/3)*(2629721*I + 332570*Sqrt[170]))*ArcTan[

(7 + (2*I)*Sqrt[170] + 9*(7 + (2*I)*Sqrt[170])^(1/3) + 2*(7 + (2*I)*Sqrt[170])^(2/3)*(6 + 5*x))/Sqrt[3*(-631 +

(28*I)*Sqrt[170] + 81*(7 + (2*I)*Sqrt[170])^(2/3) - 18*(7 + (2*I)*Sqrt[170])^(4/3))]])/(3*Sqrt[3]*(-631 + (28

*I)*Sqrt[170] + 81*(7 + (2*I)*Sqrt[170])^(2/3) - 18*(7 + (2*I)*Sqrt[170])^(4/3))^(3/2)*(81 + 9*(7 + (2*I)*Sqrt

[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3))^2*((98 + I*Sqrt[170])*(7 + (2*I)*Sqrt[170])^(1/3) + 216*(7 + (2*I)

*Sqrt[170])^(2/3) + 3*(38 + (7*I)*Sqrt[170]))^3) - (((25000*I)/3)*(7 + (2*I)*Sqrt[170])^(1/3)*(18163194*(13868

407*I - 282410*Sqrt[170]) + 9*(7 + (2*I)*Sqrt[170])^(2/3)*(2407459997653*I + 121880867668*Sqrt[170]) + (7 + (2

*I)*Sqrt[170])^(1/3)*(76237740850691*I + 1222256614970*Sqrt[170]))*ArcTan[(7 + (2*I)*Sqrt[170] + 9*(7 + (2*I)*

Sqrt[170])^(1/3) + 2*(7 + (2*I)*Sqrt[170])^(2/3)*(6 + 5*x))/Sqrt[3*(-631 + (28*I)*Sqrt[170] + 81*(7 + (2*I)*Sq

rt[170])^(2/3) - 18*(7 + (2*I)*Sqrt[170])^(4/3))]])/(Sqrt[3*(-631 + (28*I)*Sqrt[170] + 81*(7 + (2*I)*Sqrt[170]

)^(2/3) - 18*(7 + (2*I)*Sqrt[170])^(4/3))]*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3))^

3*((98 + I*Sqrt[170])*(7 + (2*I)*Sqrt[170])^(1/3) + 216*(7 + (2*I)*Sqrt[170])^(2/3) + 3*(38 + (7*I)*Sqrt[170])

)^4) + (225*(520265915719*I - 158022595892*Sqrt[170] + (229086400191*I - 4385588088*Sqrt[170])*(7 + (2*I)*Sqrt

[170])^(2/3))*ArcTanh[(7*I - 2*Sqrt[170] + (9*I)*(7 + (2*I)*Sqrt[170])^(1/3) + (2*I)*(7 + (2*I)*Sqrt[170])^(2/

3)*(6 + 5*x))/Sqrt[3*(-631 + (28*I)*Sqrt[170] + 81*(7 + (2*I)*Sqrt[170])^(2/3) - 18*(7 + (2*I)*Sqrt[170])^(4/3

))]])/(5839036*(9 - (7 + (2*I)*Sqrt[170])^(2/3))^2*Sqrt[(-631 + (28*I)*Sqrt[170] + 81*(7 + (2*I)*Sqrt[170])^(2

/3) - 18*(7 + (2*I)*Sqrt[170])^(4/3))/3]*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3))^3)

- (25*(231225200213761*I - 42154189029260*Sqrt[170] + (61139293298889*I - 1957646798184*Sqrt[170])*(7 + (2*I)

*Sqrt[170])^(2/3))*ArcTanh[(7*I - 2*Sqrt[170] + (9*I)*(7 + (2*I)*Sqrt[170])^(1/3) + (2*I)*(7 + (2*I)*Sqrt[170]

)^(2/3)*(6 + 5*x))/Sqrt[3*(-631 + (28*I)*Sqrt[170] + 81*(7 + (2*I)*Sqrt[170])^(2/3) - 18*(7 + (2*I)*Sqrt[170])

^(4/3))]])/(122619756*(9 - (7 + (2*I)*Sqrt[170])^(2/3))^2*Sqrt[3*(-631 + (28*I)*Sqrt[170] + 81*(7 + (2*I)*Sqrt

[170])^(2/3) - 18*(7 + (2*I)*Sqrt[170])^(4/3))]*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4

/3))^3) + (25*(19717265333439*I - 4356637411140*Sqrt[170] + (6317478785911*I - 166702867016*Sqrt[170])*(7 + (2

*I)*Sqrt[170])^(2/3))*ArcTanh[(7*I - 2*Sqrt[170] + (9*I)*(7 + (2*I)*Sqrt[170])^(1/3) + (2*I)*(7 + (2*I)*Sqrt[1

70])^(2/3)*(6 + 5*x))/Sqrt[3*(-631 + (28*I)*Sqrt[170] + 81*(7 + (2*I)*Sqrt[170])^(2/3) - 18*(7 + (2*I)*Sqrt[17

0])^(4/3))]])/(40873252*(9 - (7 + (2*I)*Sqrt[170])^(2/3))^2*Sqrt[3*(-631 + (28*I)*Sqrt[170] + 81*(7 + (2*I)*Sq

rt[170])^(2/3) - 18*(7 + (2*I)*Sqrt[170])^(4/3))]*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^

(4/3))^3) - (5875*(342380216447*I - 266775803812*Sqrt[170] + (386583799863*I - 2836637160*Sqrt[170])*(7 + (2*I

)*Sqrt[170])^(2/3))*ArcTanh[(7*I - 2*Sqrt[170] + (9*I)*(7 + (2*I)*Sqrt[170])^(1/3) + (2*I)*(7 + (2*I)*Sqrt[170

])^(2/3)*(6 + 5*x))/Sqrt[3*(-631 + (28*I)*Sqrt[170] + 81*(7 + (2*I)*Sqrt[170])^(2/3) - 18*(7 + (2*I)*Sqrt[170]

)^(4/3))]])/(122619756*(9 - (7 + (2*I)*Sqrt[170])^(2/3))^2*Sqrt[3*(-631 + (28*I)*Sqrt[170] + 81*(7 + (2*I)*Sqr

t[170])^(2/3) - 18*(7 + (2*I)*Sqrt[170])^(4/3))]*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(

4/3))^3) - Log[x]/2604 + (3*Log[x])/(868*(3 - x)^2) + (269*x*Log[x])/(565068*(3 - x)) - (135*(7 + (2*I)*Sqrt[1

70])^(1/3)*(1136457 - 2897621*(7 + (2*I)*Sqrt[170])^(1/3) + 126273*(7 + (2*I)*Sqrt[170])^(2/3))*Log[-(3 - (7 +

(2*I)*Sqrt[170])^(1/3))^2 + 5*(7 + (2*I)*Sqrt[170])^(1/3)*x])/(283823861888*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/

3) + (7 + (2*I)*Sqrt[170])^(4/3))) + (225*(7 + (2*I)*Sqrt[170])^(1/3)*(5668173 + 8424651*(7 + (2*I)*Sqrt[170])

^(1/3) + 629797*(7 + (2*I)*Sqrt[170])^(2/3))*Log[-(3 - (7 + (2*I)*Sqrt[170])^(1/3))^2 + 5*(7 + (2*I)*Sqrt[170]

)^(1/3)*x])/(283823861888*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3))) + (27*(7 + (2*I)

*Sqrt[170])^(1/3)*(24353343 + 17597121*(7 + (2*I)*Sqrt[170])^(1/3) + 2705927*(7 + (2*I)*Sqrt[170])^(2/3))*Log[

-(3 - (7 + (2*I)*Sqrt[170])^(1/3))^2 + 5*(7 + (2*I)*Sqrt[170])^(1/3)*x])/(40546265984*(81 + 9*(7 + (2*I)*Sqrt[

170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3))) + (235*(7 + (2*I)*Sqrt[170])^(1/3)*(57163743 + 70445301*(7 + (2*I)

*Sqrt[170])^(1/3) + 6351527*(7 + (2*I)*Sqrt[170])^(2/3))*Log[-(3 - (7 + (2*I)*Sqrt[170])^(1/3))^2 + 5*(7 + (2*

I)*Sqrt[170])^(1/3)*x])/(851471585664*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3))) + (1

0000*(7 + (2*I)*Sqrt[170])^(8/3)*(111 - (84*I)*Sqrt[170] + 63*(7 + (2*I)*Sqrt[170])^(2/3) - (7 + (2*I)*Sqrt[17

0])^(1/3)*(343 - (10*I)*Sqrt[170]))*Log[-(3 - (7 + (2*I)*Sqrt[170])^(1/3))^2 + 5*(7 + (2*I)*Sqrt[170])^(1/3)*x

])/(3*(9 - 21*(7 + (2*I)*Sqrt[170])^(1/3) + (7 + (2*I)*Sqrt[170])^(2/3))^4*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3)

+ (7 + (2*I)*Sqrt[170])^(4/3))^3) + (25*(7*I - 2*Sqrt[170])*(3961008657*(7*I - 2*Sqrt[170])*(7 + (2*I)*Sqrt[1

70])^(1/3) - 2772815178*(7*I - 2*Sqrt[170])*(7 + (2*I)*Sqrt[170])^(2/3) - 440112073*(631*I + 28*Sqrt[170]))*Lo

g[-(3 - (7 + (2*I)*Sqrt[170])^(1/3))^2 + 5*(7 + (2*I)*Sqrt[170])^(1/3)*x])/(367859268*(9 - (7 + (2*I)*Sqrt[170

])^(2/3))^2*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3))^3) - (25*(7*I - 2*Sqrt[170])*(4

61125143*(7*I - 2*Sqrt[170])*(7 + (2*I)*Sqrt[170])^(1/3) - 265390622*(7*I - 2*Sqrt[170])*(7 + (2*I)*Sqrt[170])

^(2/3) - 51236127*(631*I + 28*Sqrt[170]))*Log[-(3 - (7 + (2*I)*Sqrt[170])^(1/3))^2 + 5*(7 + (2*I)*Sqrt[170])^(

1/3)*x])/(122619756*(9 - (7 + (2*I)*Sqrt[170])^(2/3))^2*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[

170])^(4/3))^3) + (5875*(7*I - 2*Sqrt[170])*(38946951*(7*I - 2*Sqrt[170])*(7 + (2*I)*Sqrt[170])^(1/3) - 118679

82*(7*I - 2*Sqrt[170])*(7 + (2*I)*Sqrt[170])^(2/3) - 4327439*(631*I + 28*Sqrt[170]))*Log[-(3 - (7 + (2*I)*Sqrt

[170])^(1/3))^2 + 5*(7 + (2*I)*Sqrt[170])^(1/3)*x])/(367859268*(9 - (7 + (2*I)*Sqrt[170])^(2/3))^2*(81 + 9*(7

+ (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3))^3) - (225*(7*I - 2*Sqrt[170])*(19139175*(7*I - 2*Sqrt[

170])*(7 + (2*I)*Sqrt[170])^(1/3) - 8638518*(7*I - 2*Sqrt[170])*(7 + (2*I)*Sqrt[170])^(2/3) - 2126575*(631*I +

28*Sqrt[170]))*Log[-(3 - (7 + (2*I)*Sqrt[170])^(1/3))^2 + 5*(7 + (2*I)*Sqrt[170])^(1/3)*x])/(5839036*(9 - (7

+ (2*I)*Sqrt[170])^(2/3))^2*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3))^3) + (9924651*L

og[8 + 81*x + 90*x^2 + 25*x^3])/35477982736 + (225*(19139175*(7 + (2*I)*Sqrt[170])^(1/3)*(631 - (28*I)*Sqrt[17

0]) + 2126575*(13937 + (1066*I)*Sqrt[170]) + (8638518*I)*(7 + (2*I)*Sqrt[170])^(2/3)*(631*I + 28*Sqrt[170]))*L

og[81*I + (7*I - 2*Sqrt[170])*(7 + (2*I)*Sqrt[170])^(1/3) - (9*I)*(7 + (2*I)*Sqrt[170])^(2/3) + (7*I - 2*Sqrt[

170] + (9*I)*(7 + (2*I)*Sqrt[170])^(1/3))*(6 + 5*x) + I*(7 + (2*I)*Sqrt[170])^(2/3)*(6 + 5*x)^2])/(11678072*(9

- (7 + (2*I)*Sqrt[170])^(2/3))^2*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3))^3) - (587

5*(38946951*(7 + (2*I)*Sqrt[170])^(1/3)*(631 - (28*I)*Sqrt[170]) + 4327439*(13937 + (1066*I)*Sqrt[170]) + (118

67982*I)*(7 + (2*I)*Sqrt[170])^(2/3)*(631*I + 28*Sqrt[170]))*Log[81*I + (7*I - 2*Sqrt[170])*(7 + (2*I)*Sqrt[17

0])^(1/3) - (9*I)*(7 + (2*I)*Sqrt[170])^(2/3) + (7*I - 2*Sqrt[170] + (9*I)*(7 + (2*I)*Sqrt[170])^(1/3))*(6 + 5

*x) + I*(7 + (2*I)*Sqrt[170])^(2/3)*(6 + 5*x)^2])/(735718536*(9 - (7 + (2*I)*Sqrt[170])^(2/3))^2*(81 + 9*(7 +

(2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3))^3) + (25*(461125143*(7 + (2*I)*Sqrt[170])^(1/3)*(631 - (

28*I)*Sqrt[170]) + 51236127*(13937 + (1066*I)*Sqrt[170]) + (265390622*I)*(7 + (2*I)*Sqrt[170])^(2/3)*(631*I +

28*Sqrt[170]))*Log[81*I + (7*I - 2*Sqrt[170])*(7 + (2*I)*Sqrt[170])^(1/3) - (9*I)*(7 + (2*I)*Sqrt[170])^(2/3)

+ (7*I - 2*Sqrt[170] + (9*I)*(7 + (2*I)*Sqrt[170])^(1/3))*(6 + 5*x) + I*(7 + (2*I)*Sqrt[170])^(2/3)*(6 + 5*x)^

2])/(245239512*(9 - (7 + (2*I)*Sqrt[170])^(2/3))^2*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])

^(4/3))^3) - (25*(3961008657*(7 + (2*I)*Sqrt[170])^(1/3)*(631 - (28*I)*Sqrt[170]) + 440112073*(13937 + (1066*I

)*Sqrt[170]) + (2772815178*I)*(7 + (2*I)*Sqrt[170])^(2/3)*(631*I + 28*Sqrt[170]))*Log[81*I + (7*I - 2*Sqrt[170

])*(7 + (2*I)*Sqrt[170])^(1/3) - (9*I)*(7 + (2*I)*Sqrt[170])^(2/3) + (7*I - 2*Sqrt[170] + (9*I)*(7 + (2*I)*Sqr

t[170])^(1/3))*(6 + 5*x) + I*(7 + (2*I)*Sqrt[170])^(2/3)*(6 + 5*x)^2])/(735718536*(9 - (7 + (2*I)*Sqrt[170])^(

2/3))^2*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3))^3) - (135*(7 + (2*I)*Sqrt[170])^(2/

3)*(2897621 - 1136457/(7 + (2*I)*Sqrt[170])^(1/3) - 126273*(7 + (2*I)*Sqrt[170])^(1/3))*Log[81 - 9*(7 + (2*I)*

Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3) + (7 + (2*I)*Sqrt[170] + 9*(7 + (2*I)*Sqrt[170])^(1/3))*(6 + 5*

x) + (7 + (2*I)*Sqrt[170])^(2/3)*(6 + 5*x)^2])/(567647723776*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*

Sqrt[170])^(4/3))) - (225*(7 + (2*I)*Sqrt[170])^(1/3)*(5668173 + 8424651*(7 + (2*I)*Sqrt[170])^(1/3) + 629797*

(7 + (2*I)*Sqrt[170])^(2/3))*Log[81 - 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3) + (7 + (2*I)

*Sqrt[170] + 9*(7 + (2*I)*Sqrt[170])^(1/3))*(6 + 5*x) + (7 + (2*I)*Sqrt[170])^(2/3)*(6 + 5*x)^2])/(56764772377

6*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3))) - (27*(7 + (2*I)*Sqrt[170])^(1/3)*(24353

343 + 17597121*(7 + (2*I)*Sqrt[170])^(1/3) + 2705927*(7 + (2*I)*Sqrt[170])^(2/3))*Log[81 - 9*(7 + (2*I)*Sqrt[1

70])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3) + (7 + (2*I)*Sqrt[170] + 9*(7 + (2*I)*Sqrt[170])^(1/3))*(6 + 5*x) + (

7 + (2*I)*Sqrt[170])^(2/3)*(6 + 5*x)^2])/(81092531968*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[17

0])^(4/3))) - (235*(7 + (2*I)*Sqrt[170])^(1/3)*(57163743 + 70445301*(7 + (2*I)*Sqrt[170])^(1/3) + 6351527*(7 +

(2*I)*Sqrt[170])^(2/3))*Log[81 - 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3) + (7 + (2*I)*Sqr

t[170] + 9*(7 + (2*I)*Sqrt[170])^(1/3))*(6 + 5*x) + (7 + (2*I)*Sqrt[170])^(2/3)*(6 + 5*x)^2])/(1702943171328*(

81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3))) - (12500*(7*I - 2*Sqrt[170])*((1458232*(264

881*I + 35336*Sqrt[170]))/(7 + (2*I)*Sqrt[170])^(1/3) + 9*(3811728361*I + 2331469822*Sqrt[170]) + (3*(65751801

2627*I + 38494811750*Sqrt[170]))/(7 + (2*I)*Sqrt[170])^(2/3))*Log[81 - 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2

*I)*Sqrt[170])^(4/3) + (7 + (2*I)*Sqrt[170] + 9*(7 + (2*I)*Sqrt[170])^(1/3))*(6 + 5*x) + (7 + (2*I)*Sqrt[170])

^(2/3)*(6 + 5*x)^2])/(3*(81 + 9*(7 + (2*I)*Sqrt[170])^(2/3) + (7 + (2*I)*Sqrt[170])^(4/3))^3*((98 + I*Sqrt[170

])*(7 + (2*I)*Sqrt[170])^(1/3) + 216*(7 + (2*I)*Sqrt[170])^(2/3) + 3*(38 + (7*I)*Sqrt[170]))^4) + (146484*Defe

r[Int][Log[x]/(8 + 81*x + 90*x^2 + 25*x^3)^2, x])/47089 + (1493745*Defer[Int][(x*Log[x])/(8 + 81*x + 90*x^2 +

25*x^3)^2, x])/94178 + (768825*Defer[Int][(x^2*Log[x])/(8 + 81*x + 90*x^2 + 25*x^3)^2, x])/94178 - (16005*Defe

r[Int][Log[x]/(8 + 81*x + 90*x^2 + 25*x^3), x])/94178 - (6725*Defer[Int][(x*Log[x])/(8 + 81*x + 90*x^2 + 25*x^

3), x])/188356

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {48+470 x+378 x^2-30 x^3-50 x^4-\left (-48-16 x+216 x^2-240 x^3-200 x^4\right ) \log (x)}{(3-x)^3 \left (8+81 x+90 x^2+25 x^3\right )^2} \, dx\\ &=\int \left (-\frac {48}{(-3+x)^3 \left (8+81 x+90 x^2+25 x^3\right )^2}-\frac {470 x}{(-3+x)^3 \left (8+81 x+90 x^2+25 x^3\right )^2}-\frac {378 x^2}{(-3+x)^3 \left (8+81 x+90 x^2+25 x^3\right )^2}+\frac {30 x^3}{(-3+x)^3 \left (8+81 x+90 x^2+25 x^3\right )^2}+\frac {50 x^4}{(-3+x)^3 \left (8+81 x+90 x^2+25 x^3\right )^2}-\frac {8 \left (6+2 x-27 x^2+30 x^3+25 x^4\right ) \log (x)}{(-3+x)^3 \left (8+81 x+90 x^2+25 x^3\right )^2}\right ) \, dx\\ &=-\left (8 \int \frac {\left (6+2 x-27 x^2+30 x^3+25 x^4\right ) \log (x)}{(-3+x)^3 \left (8+81 x+90 x^2+25 x^3\right )^2} \, dx\right )+30 \int \frac {x^3}{(-3+x)^3 \left (8+81 x+90 x^2+25 x^3\right )^2} \, dx-48 \int \frac {1}{(-3+x)^3 \left (8+81 x+90 x^2+25 x^3\right )^2} \, dx+50 \int \frac {x^4}{(-3+x)^3 \left (8+81 x+90 x^2+25 x^3\right )^2} \, dx-378 \int \frac {x^2}{(-3+x)^3 \left (8+81 x+90 x^2+25 x^3\right )^2} \, dx-470 \int \frac {x}{(-3+x)^3 \left (8+81 x+90 x^2+25 x^3\right )^2} \, dx\\ &=-\left (8 \int \left (\frac {3 \log (x)}{3472 (-3+x)^3}-\frac {269 \log (x)}{1506848 (-3+x)^2}-\frac {3 \left (97656+497915 x+256275 x^2\right ) \log (x)}{753424 \left (8+81 x+90 x^2+25 x^3\right )^2}+\frac {5 (6402+1345 x) \log (x)}{1506848 \left (8+81 x+90 x^2+25 x^3\right )}\right ) \, dx\right )+30 \int \left (\frac {27}{3013696 (-3+x)^3}-\frac {2889}{653972032 (-3+x)^2}+\frac {759411}{567647723776 (-3+x)}+\frac {-290456-1792395 x+9493425 x^2}{653972032 \left (8+81 x+90 x^2+25 x^3\right )^2}-\frac {9 \left (-4141716+6956835 x+2109475 x^2\right )}{567647723776 \left (8+81 x+90 x^2+25 x^3\right )}\right ) \, dx-48 \operatorname {Subst}\left (\int \frac {1}{\left (-\frac {21}{5}+x\right )^3 \left (-\frac {14}{5}-27 x+25 x^3\right )^2} \, dx,x,\frac {6}{5}+x\right )+50 \int \left (\frac {81}{3013696 (-3+x)^3}-\frac {351}{81746504 (-3+x)^2}-\frac {229419}{567647723776 (-3+x)}+\frac {-3037896-31049153 x-35968725 x^2}{653972032 \left (8+81 x+90 x^2+25 x^3\right )^2}+\frac {27 \left (12432852+3658805 x+212425 x^2\right )}{567647723776 \left (8+81 x+90 x^2+25 x^3\right )}\right ) \, dx-378 \int \left (\frac {9}{3013696 (-3+x)^3}-\frac {807}{326986016 (-3+x)^2}+\frac {720121}{567647723776 (-3+x)}+\frac {1148472+12761055 x+907675 x^2}{653972032 \left (8+81 x+90 x^2+25 x^3\right )^2}+\frac {-120941316-83796165 x-18003025 x^2}{567647723776 \left (8+81 x+90 x^2+25 x^3\right )}\right ) \, dx-470 \int \left (\frac {3}{3013696 (-3+x)^3}-\frac {755}{653972032 (-3+x)^2}+\frac {458487}{567647723776 (-3+x)}+\frac {1132776-12012635 x-3588975 x^2}{653972032 \left (8+81 x+90 x^2+25 x^3\right )^2}+\frac {-120933612-59266855 x-11462175 x^2}{567647723776 \left (8+81 x+90 x^2+25 x^3\right )}\right ) \, dx\\ &=-\frac {3}{376712 (3-x)^2}+\frac {46117}{40873252 (3-x)}-\frac {29773953 \log (3-x)}{35477982736}-\frac {135 \int \frac {-4141716+6956835 x+2109475 x^2}{8+81 x+90 x^2+25 x^3} \, dx}{283823861888}-\frac {27 \int \frac {-120941316-83796165 x-18003025 x^2}{8+81 x+90 x^2+25 x^3} \, dx}{40546265984}-\frac {235 \int \frac {-120933612-59266855 x-11462175 x^2}{8+81 x+90 x^2+25 x^3} \, dx}{283823861888}+\frac {675 \int \frac {12432852+3658805 x+212425 x^2}{8+81 x+90 x^2+25 x^3} \, dx}{283823861888}+\frac {15 \int \frac {-290456-1792395 x+9493425 x^2}{\left (8+81 x+90 x^2+25 x^3\right )^2} \, dx}{326986016}+\frac {25 \int \frac {-3037896-31049153 x-35968725 x^2}{\left (8+81 x+90 x^2+25 x^3\right )^2} \, dx}{326986016}-\frac {27 \int \frac {1148472+12761055 x+907675 x^2}{\left (8+81 x+90 x^2+25 x^3\right )^2} \, dx}{46712288}-\frac {235 \int \frac {1132776-12012635 x-3588975 x^2}{\left (8+81 x+90 x^2+25 x^3\right )^2} \, dx}{326986016}-\frac {5 \int \frac {(6402+1345 x) \log (x)}{8+81 x+90 x^2+25 x^3} \, dx}{188356}+\frac {3 \int \frac {\left (97656+497915 x+256275 x^2\right ) \log (x)}{\left (8+81 x+90 x^2+25 x^3\right )^2} \, dx}{94178}+\frac {269 \int \frac {\log (x)}{(-3+x)^2} \, dx}{188356}-\frac {3}{434} \int \frac {\log (x)}{(-3+x)^3} \, dx-18750000 \operatorname {Subst}\left (\int \frac {1}{\left (-\frac {21}{5}+x\right )^3 \left (-\frac {5 \left (9+\left (7+2 i \sqrt {170}\right )^{2/3}\right )}{\sqrt [3]{7+2 i \sqrt {170}}}+25 x\right )^2 \left (-25 \left (9-\frac {81}{\left (7+2 i \sqrt {170}\right )^{2/3}}-\left (7+2 i \sqrt {170}\right )^{2/3}\right )+\frac {125 \left (9+\left (7+2 i \sqrt {170}\right )^{2/3}\right ) x}{\sqrt [3]{7+2 i \sqrt {170}}}+625 x^2\right )^2} \, dx,x,\frac {6}{5}+x\right )\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A] time = 0.29, size = 27, normalized size = 0.96 \begin {gather*} \frac {2 x \log (x)}{(-3+x)^2 \left (8+81 x+90 x^2+25 x^3\right )} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(-48 - 470*x - 378*x^2 + 30*x^3 + 50*x^4 + (-48 - 16*x + 216*x^2 - 240*x^3 - 200*x^4)*Log[x])/(-1728

- 33264*x - 181611*x^2 - 200033*x^3 + 5697*x^4 + 79731*x^5 + 10255*x^6 - 11475*x^7 - 1125*x^8 + 625*x^9),x]

[Out]

(2*x*Log[x])/((-3 + x)^2*(8 + 81*x + 90*x^2 + 25*x^3))

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fricas [A] time = 0.82, size = 32, normalized size = 1.14 \begin {gather*} \frac {2 \, x \log \relax (x)}{25 \, x^{5} - 60 \, x^{4} - 234 \, x^{3} + 332 \, x^{2} + 681 \, x + 72} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-200*x^4-240*x^3+216*x^2-16*x-48)*log(x)+50*x^4+30*x^3-378*x^2-470*x-48)/(625*x^9-1125*x^8-11475*x

^7+10255*x^6+79731*x^5+5697*x^4-200033*x^3-181611*x^2-33264*x-1728),x, algorithm="fricas")

[Out]

2*x*log(x)/(25*x^5 - 60*x^4 - 234*x^3 + 332*x^2 + 681*x + 72)

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giac [B] time = 0.26, size = 50, normalized size = 1.79 \begin {gather*} \frac {1}{188356} \, {\left (\frac {6725 \, x^{2} + 28110 \, x - 1296}{25 \, x^{3} + 90 \, x^{2} + 81 \, x + 8} - \frac {269 \, x - 1458}{x^{2} - 6 \, x + 9}\right )} \log \relax (x) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-200*x^4-240*x^3+216*x^2-16*x-48)*log(x)+50*x^4+30*x^3-378*x^2-470*x-48)/(625*x^9-1125*x^8-11475*x

^7+10255*x^6+79731*x^5+5697*x^4-200033*x^3-181611*x^2-33264*x-1728),x, algorithm="giac")

[Out]

1/188356*((6725*x^2 + 28110*x - 1296)/(25*x^3 + 90*x^2 + 81*x + 8) - (269*x - 1458)/(x^2 - 6*x + 9))*log(x)

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maple [A] time = 0.12, size = 28, normalized size = 1.00


method	result	size

norman	\(\frac {2 x \ln \relax (x )}{\left (25 x^{3}+90 x^{2}+81 x +8\right ) \left (x -3\right )^{2}}\)	\(28\)
risch	\(\frac {2 x \ln \relax (x )}{25 x^{5}-60 x^{4}-234 x^{3}+332 x^{2}+681 x +72}\)	\(33\)
default	\(\frac {\left (\munderset {\textit {\_R} =\RootOf \left (25 \textit {\_Z}^{3}+90 \textit {\_Z}^{2}+81 \textit {\_Z} +8\right )}{\sum }\frac {\left (4050 \textit {\_R}^{2}+21305 \textit {\_R} +41232\right ) \ln \left (x -\textit {\_R} \right )}{25 \textit {\_R}^{2}+60 \textit {\_R} +27}\right )}{565068}-\frac {\ln \relax (x ) x \left (x -6\right )}{2604 \left (x -3\right )^{2}}-\frac {269 \ln \relax (x ) x}{565068 \left (x -3\right )}+\frac {\left (\munderset {\textit {\_R} =\RootOf \left (25 \textit {\_Z}^{3}+90 \textit {\_Z}^{2}+81 \textit {\_Z} +8\right )}{\sum }\frac {\left (-4050 \textit {\_R}^{2}-21305 \textit {\_R} -41232\right ) \ln \left (x -\textit {\_R} \right )}{25 \textit {\_R}^{2}+60 \textit {\_R} +27}\right )}{565068}+\frac {\ln \relax (x ) x \left (4050 x^{2}+21305 x +41232\right )}{4708900 x^{3}+16952040 x^{2}+15256836 x +1506848}\)	\(157\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((-200*x^4-240*x^3+216*x^2-16*x-48)*ln(x)+50*x^4+30*x^3-378*x^2-470*x-48)/(625*x^9-1125*x^8-11475*x^7+1025

5*x^6+79731*x^5+5697*x^4-200033*x^3-181611*x^2-33264*x-1728),x,method=_RETURNVERBOSE)

[Out]

2*x*ln(x)/(25*x^3+90*x^2+81*x+8)/(x-3)^2

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maxima [A] time = 0.35, size = 32, normalized size = 1.14 \begin {gather*} \frac {2 \, x \log \relax (x)}{25 \, x^{5} - 60 \, x^{4} - 234 \, x^{3} + 332 \, x^{2} + 681 \, x + 72} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-200*x^4-240*x^3+216*x^2-16*x-48)*log(x)+50*x^4+30*x^3-378*x^2-470*x-48)/(625*x^9-1125*x^8-11475*x

^7+10255*x^6+79731*x^5+5697*x^4-200033*x^3-181611*x^2-33264*x-1728),x, algorithm="maxima")

[Out]

2*x*log(x)/(25*x^5 - 60*x^4 - 234*x^3 + 332*x^2 + 681*x + 72)

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mupad [B] time = 9.21, size = 32, normalized size = 1.14 \begin {gather*} \frac {2\,x\,\ln \relax (x)}{25\,\left (x^5-\frac {12\,x^4}{5}-\frac {234\,x^3}{25}+\frac {332\,x^2}{25}+\frac {681\,x}{25}+\frac {72}{25}\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((470*x + log(x)*(16*x - 216*x^2 + 240*x^3 + 200*x^4 + 48) + 378*x^2 - 30*x^3 - 50*x^4 + 48)/(33264*x + 181

611*x^2 + 200033*x^3 - 5697*x^4 - 79731*x^5 - 10255*x^6 + 11475*x^7 + 1125*x^8 - 625*x^9 + 1728),x)

[Out]

(2*x*log(x))/(25*((681*x)/25 + (332*x^2)/25 - (234*x^3)/25 - (12*x^4)/5 + x^5 + 72/25))

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sympy [A] time = 0.23, size = 31, normalized size = 1.11 \begin {gather*} \frac {2 x \log {\relax (x )}}{25 x^{5} - 60 x^{4} - 234 x^{3} + 332 x^{2} + 681 x + 72} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-200*x**4-240*x**3+216*x**2-16*x-48)*ln(x)+50*x**4+30*x**3-378*x**2-470*x-48)/(625*x**9-1125*x**8-

11475*x**7+10255*x**6+79731*x**5+5697*x**4-200033*x**3-181611*x**2-33264*x-1728),x)

[Out]

2*x*log(x)/(25*x**5 - 60*x**4 - 234*x**3 + 332*x**2 + 681*x + 72)

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