3.27.18 \(\int \frac {50 x^3 \log (-4+x)+(-200 x-50 x^2+25 x^3) \log ^2(-4+x)+(8 x^3-2 x^4) \log ^3(-4+x)+(100 x^2 \log (-4+x)+(-200+50 x) \log ^2(-4+x)+(24 x^2-2 x^3-x^4) \log ^3(-4+x)) \log (x)+(50 x \log (-4+x)+(100-25 x) \log ^2(-4+x)+(24 x+6 x^2-3 x^3) \log ^3(-4+x)) \log ^2(x)+(8+10 x-3 x^2) \log ^3(-4+x) \log ^3(x)+(4-x) \log ^3(-4+x) \log ^4(x)}{-62500 x^2+15625 x^3+(-7500 x^3+1875 x^4) \log (-4+x) \log (x)+((-7500 x^2+1875 x^3) \log (-4+x)+(-300 x^4+75 x^5) \log ^2(-4+x)) \log ^2(x)+((-600 x^3+150 x^4) \log ^2(-4+x)+(-4 x^5+x^6) \log ^3(-4+x)) \log ^3(x)+((-300 x^2+75 x^3) \log ^2(-4+x)+(-12 x^4+3 x^5) \log ^3(-4+x)) \log ^4(x)+(-12 x^3+3 x^4) \log ^3(-4+x) \log ^5(x)+(-4 x^2+x^3) \log ^3(-4+x) \log ^6(x)} \, dx\)

Optimal. Leaf size=23 \[ \frac {1}{x \left (\log (x)+\frac {25}{\log (-4+x) (x+\log (x))}\right )^2} \]

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Rubi [F]  time = 161.20, 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 {50 x^3 \log (-4+x)+\left (-200 x-50 x^2+25 x^3\right ) \log ^2(-4+x)+\left (8 x^3-2 x^4\right ) \log ^3(-4+x)+\left (100 x^2 \log (-4+x)+(-200+50 x) \log ^2(-4+x)+\left (24 x^2-2 x^3-x^4\right ) \log ^3(-4+x)\right ) \log (x)+\left (50 x \log (-4+x)+(100-25 x) \log ^2(-4+x)+\left (24 x+6 x^2-3 x^3\right ) \log ^3(-4+x)\right ) \log ^2(x)+\left (8+10 x-3 x^2\right ) \log ^3(-4+x) \log ^3(x)+(4-x) \log ^3(-4+x) \log ^4(x)}{-62500 x^2+15625 x^3+\left (-7500 x^3+1875 x^4\right ) \log (-4+x) \log (x)+\left (\left (-7500 x^2+1875 x^3\right ) \log (-4+x)+\left (-300 x^4+75 x^5\right ) \log ^2(-4+x)\right ) \log ^2(x)+\left (\left (-600 x^3+150 x^4\right ) \log ^2(-4+x)+\left (-4 x^5+x^6\right ) \log ^3(-4+x)\right ) \log ^3(x)+\left (\left (-300 x^2+75 x^3\right ) \log ^2(-4+x)+\left (-12 x^4+3 x^5\right ) \log ^3(-4+x)\right ) \log ^4(x)+\left (-12 x^3+3 x^4\right ) \log ^3(-4+x) \log ^5(x)+\left (-4 x^2+x^3\right ) \log ^3(-4+x) \log ^6(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(50*x^3*Log[-4 + x] + (-200*x - 50*x^2 + 25*x^3)*Log[-4 + x]^2 + (8*x^3 - 2*x^4)*Log[-4 + x]^3 + (100*x^2*
Log[-4 + x] + (-200 + 50*x)*Log[-4 + x]^2 + (24*x^2 - 2*x^3 - x^4)*Log[-4 + x]^3)*Log[x] + (50*x*Log[-4 + x] +
(100 - 25*x)*Log[-4 + x]^2 + (24*x + 6*x^2 - 3*x^3)*Log[-4 + x]^3)*Log[x]^2 + (8 + 10*x - 3*x^2)*Log[-4 + x]^
3*Log[x]^3 + (4 - x)*Log[-4 + x]^3*Log[x]^4)/(-62500*x^2 + 15625*x^3 + (-7500*x^3 + 1875*x^4)*Log[-4 + x]*Log[
x] + ((-7500*x^2 + 1875*x^3)*Log[-4 + x] + (-300*x^4 + 75*x^5)*Log[-4 + x]^2)*Log[x]^2 + ((-600*x^3 + 150*x^4)
*Log[-4 + x]^2 + (-4*x^5 + x^6)*Log[-4 + x]^3)*Log[x]^3 + ((-300*x^2 + 75*x^3)*Log[-4 + x]^2 + (-12*x^4 + 3*x^
5)*Log[-4 + x]^3)*Log[x]^4 + (-12*x^3 + 3*x^4)*Log[-4 + x]^3*Log[x]^5 + (-4*x^2 + x^3)*Log[-4 + x]^3*Log[x]^6)
,x]

[Out]

(-625*Defer[Int][1/((-4 + x)*(25 + Log[-4 + x]*Log[x]*(x + Log[x]))^3), x])/2 + (625*Defer[Int][1/(x*(25 + Log
[-4 + x]*Log[x]*(x + Log[x]))^3), x])/2 + 50*Defer[Int][Log[-4 + x]/(25 + Log[-4 + x]*Log[x]*(x + Log[x]))^3,
x] + 200*Defer[Int][Log[-4 + x]/((-4 + x)*(25 + Log[-4 + x]*Log[x]*(x + Log[x]))^3), x] + 50*Defer[Int][Log[-4
+ x]^2/(25 + Log[-4 + x]*Log[x]*(x + Log[x]))^3, x] + 150*Defer[Int][Log[-4 + x]^2/(x*(25 + Log[-4 + x]*Log[x
]*(x + Log[x]))^3), x] - 2*Defer[Int][(x*Log[-4 + x]^3)/(25 + Log[-4 + x]*Log[x]*(x + Log[x]))^3, x] + 50*Defe
r[Int][(Log[-4 + x]*Log[x])/((-4 + x)*(25 + Log[-4 + x]*Log[x]*(x + Log[x]))^3), x] + 100*Defer[Int][(Log[-4 +
x]^2*Log[x])/(x^2*(25 + Log[-4 + x]*Log[x]*(x + Log[x]))^3), x] + 50*Defer[Int][(Log[-4 + x]^2*Log[x])/(x*(25
+ Log[-4 + x]*Log[x]*(x + Log[x]))^3), x] - 2*Defer[Int][(Log[-4 + x]^3*Log[x])/(25 + Log[-4 + x]*Log[x]*(x +
Log[x]))^3, x] + (25*Defer[Int][1/((-4 + x)*(25 + Log[-4 + x]*Log[x]*(x + Log[x]))^2), x])/2 - (25*Defer[Int]
[1/(x*(25 + Log[-4 + x]*Log[x]*(x + Log[x]))^2), x])/2 + 25*Defer[Int][Log[-4 + x]/(x^2*(25 + Log[-4 + x]*Log[
x]*(x + Log[x]))^2), x] - Defer[Int][Log[-4 + x]^2/(25 + Log[-4 + x]*Log[x]*(x + Log[x]))^2, x] - 4*Defer[Int]
[Log[-4 + x]^2/(x*(25 + Log[-4 + x]*Log[x]*(x + Log[x]))^2), x] - 2*Defer[Int][(Log[-4 + x]^2*Log[x])/(x^2*(25
+ Log[-4 + x]*Log[x]*(x + Log[x]))^2), x] - Defer[Int][(Log[-4 + x]^2*Log[x])/(x*(25 + Log[-4 + x]*Log[x]*(x
+ Log[x]))^2), x] - Defer[Int][Log[-4 + x]/(x^2*(25 + Log[-4 + x]*Log[x]*(x + Log[x]))), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\log (-4+x) (x+\log (x)) \left (-25 (-4+x) \log (-4+x) (2+x-\log (x))-50 x (x+\log (x))+(-4+x) \log ^2(-4+x) (2+\log (x)) (x+\log (x))^2\right )}{(4-x) x^2 (25+\log (-4+x) \log (x) (x+\log (x)))^3} \, dx\\ &=\int \left (-\frac {2 \left (625 x-25 x^3 \log (-4+x)+300 x \log ^2(-4+x)+25 x^2 \log ^2(-4+x)-25 x^3 \log ^2(-4+x)-4 x^3 \log ^3(-4+x)+x^4 \log ^3(-4+x)-25 x^2 \log (-4+x) \log (x)+200 \log ^2(-4+x) \log (x)+50 x \log ^2(-4+x) \log (x)-25 x^2 \log ^2(-4+x) \log (x)-4 x^2 \log ^3(-4+x) \log (x)+x^3 \log ^3(-4+x) \log (x)\right )}{(-4+x) x^2 \left (25+x \log (-4+x) \log (x)+\log (-4+x) \log ^2(x)\right )^3}+\frac {50 x-100 \log (-4+x)+25 x \log (-4+x)+16 x \log ^2(-4+x)-x^3 \log ^2(-4+x)+8 \log ^2(-4+x) \log (x)+2 x \log ^2(-4+x) \log (x)-x^2 \log ^2(-4+x) \log (x)}{(-4+x) x^2 \left (25+x \log (-4+x) \log (x)+\log (-4+x) \log ^2(x)\right )^2}-\frac {\log (-4+x)}{x^2 \left (25+x \log (-4+x) \log (x)+\log (-4+x) \log ^2(x)\right )}\right ) \, dx\\ &=-\left (2 \int \frac {625 x-25 x^3 \log (-4+x)+300 x \log ^2(-4+x)+25 x^2 \log ^2(-4+x)-25 x^3 \log ^2(-4+x)-4 x^3 \log ^3(-4+x)+x^4 \log ^3(-4+x)-25 x^2 \log (-4+x) \log (x)+200 \log ^2(-4+x) \log (x)+50 x \log ^2(-4+x) \log (x)-25 x^2 \log ^2(-4+x) \log (x)-4 x^2 \log ^3(-4+x) \log (x)+x^3 \log ^3(-4+x) \log (x)}{(-4+x) x^2 \left (25+x \log (-4+x) \log (x)+\log (-4+x) \log ^2(x)\right )^3} \, dx\right )+\int \frac {50 x-100 \log (-4+x)+25 x \log (-4+x)+16 x \log ^2(-4+x)-x^3 \log ^2(-4+x)+8 \log ^2(-4+x) \log (x)+2 x \log ^2(-4+x) \log (x)-x^2 \log ^2(-4+x) \log (x)}{(-4+x) x^2 \left (25+x \log (-4+x) \log (x)+\log (-4+x) \log ^2(x)\right )^2} \, dx-\int \frac {\log (-4+x)}{x^2 \left (25+x \log (-4+x) \log (x)+\log (-4+x) \log ^2(x)\right )} \, dx\\ &=-\left (2 \int \frac {-625 x+25 x^2 \log (-4+x) (x+\log (x))-(-4+x) x^2 \log ^3(-4+x) (x+\log (x))+25 (-4+x) \log ^2(-4+x) (x (3+x)+(2+x) \log (x))}{(4-x) x^2 (25+\log (-4+x) \log (x) (x+\log (x)))^3} \, dx\right )-\int \frac {\log (-4+x)}{x^2 (25+\log (-4+x) \log (x) (x+\log (x)))} \, dx+\int \frac {-50 x-25 (-4+x) \log (-4+x)+(-4+x) \log ^2(-4+x) (x (4+x)+(2+x) \log (x))}{(4-x) x^2 (25+\log (-4+x) \log (x) (x+\log (x)))^2} \, dx\\ &=-\left (2 \int \left (\frac {-625 x+25 x^3 \log (-4+x)-300 x \log ^2(-4+x)-25 x^2 \log ^2(-4+x)+25 x^3 \log ^2(-4+x)+4 x^3 \log ^3(-4+x)-x^4 \log ^3(-4+x)+25 x^2 \log (-4+x) \log (x)-200 \log ^2(-4+x) \log (x)-50 x \log ^2(-4+x) \log (x)+25 x^2 \log ^2(-4+x) \log (x)+4 x^2 \log ^3(-4+x) \log (x)-x^3 \log ^3(-4+x) \log (x)}{4 x^2 \left (25+x \log (-4+x) \log (x)+\log (-4+x) \log ^2(x)\right )^3}+\frac {-625 x+25 x^3 \log (-4+x)-300 x \log ^2(-4+x)-25 x^2 \log ^2(-4+x)+25 x^3 \log ^2(-4+x)+4 x^3 \log ^3(-4+x)-x^4 \log ^3(-4+x)+25 x^2 \log (-4+x) \log (x)-200 \log ^2(-4+x) \log (x)-50 x \log ^2(-4+x) \log (x)+25 x^2 \log ^2(-4+x) \log (x)+4 x^2 \log ^3(-4+x) \log (x)-x^3 \log ^3(-4+x) \log (x)}{16 x \left (25+x \log (-4+x) \log (x)+\log (-4+x) \log ^2(x)\right )^3}+\frac {625 x-25 x^3 \log (-4+x)+300 x \log ^2(-4+x)+25 x^2 \log ^2(-4+x)-25 x^3 \log ^2(-4+x)-4 x^3 \log ^3(-4+x)+x^4 \log ^3(-4+x)-25 x^2 \log (-4+x) \log (x)+200 \log ^2(-4+x) \log (x)+50 x \log ^2(-4+x) \log (x)-25 x^2 \log ^2(-4+x) \log (x)-4 x^2 \log ^3(-4+x) \log (x)+x^3 \log ^3(-4+x) \log (x)}{16 (-4+x) \left (25+x \log (-4+x) \log (x)+\log (-4+x) \log ^2(x)\right )^3}\right ) \, dx\right )-\int \frac {\log (-4+x)}{x^2 (25+\log (-4+x) \log (x) (x+\log (x)))} \, dx+\int \left (\frac {50 x-100 \log (-4+x)+25 x \log (-4+x)+16 x \log ^2(-4+x)-x^3 \log ^2(-4+x)+8 \log ^2(-4+x) \log (x)+2 x \log ^2(-4+x) \log (x)-x^2 \log ^2(-4+x) \log (x)}{16 (-4+x) \left (25+x \log (-4+x) \log (x)+\log (-4+x) \log ^2(x)\right )^2}+\frac {-50 x+100 \log (-4+x)-25 x \log (-4+x)-16 x \log ^2(-4+x)+x^3 \log ^2(-4+x)-8 \log ^2(-4+x) \log (x)-2 x \log ^2(-4+x) \log (x)+x^2 \log ^2(-4+x) \log (x)}{4 x^2 \left (25+x \log (-4+x) \log (x)+\log (-4+x) \log ^2(x)\right )^2}+\frac {-50 x+100 \log (-4+x)-25 x \log (-4+x)-16 x \log ^2(-4+x)+x^3 \log ^2(-4+x)-8 \log ^2(-4+x) \log (x)-2 x \log ^2(-4+x) \log (x)+x^2 \log ^2(-4+x) \log (x)}{16 x \left (25+x \log (-4+x) \log (x)+\log (-4+x) \log ^2(x)\right )^2}\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 5.19, size = 31, normalized size = 1.35 \begin {gather*} \frac {\log ^2(-4+x) (x+\log (x))^2}{x (25+\log (-4+x) \log (x) (x+\log (x)))^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(50*x^3*Log[-4 + x] + (-200*x - 50*x^2 + 25*x^3)*Log[-4 + x]^2 + (8*x^3 - 2*x^4)*Log[-4 + x]^3 + (10
0*x^2*Log[-4 + x] + (-200 + 50*x)*Log[-4 + x]^2 + (24*x^2 - 2*x^3 - x^4)*Log[-4 + x]^3)*Log[x] + (50*x*Log[-4
+ x] + (100 - 25*x)*Log[-4 + x]^2 + (24*x + 6*x^2 - 3*x^3)*Log[-4 + x]^3)*Log[x]^2 + (8 + 10*x - 3*x^2)*Log[-4
+ x]^3*Log[x]^3 + (4 - x)*Log[-4 + x]^3*Log[x]^4)/(-62500*x^2 + 15625*x^3 + (-7500*x^3 + 1875*x^4)*Log[-4 + x
]*Log[x] + ((-7500*x^2 + 1875*x^3)*Log[-4 + x] + (-300*x^4 + 75*x^5)*Log[-4 + x]^2)*Log[x]^2 + ((-600*x^3 + 15
0*x^4)*Log[-4 + x]^2 + (-4*x^5 + x^6)*Log[-4 + x]^3)*Log[x]^3 + ((-300*x^2 + 75*x^3)*Log[-4 + x]^2 + (-12*x^4
+ 3*x^5)*Log[-4 + x]^3)*Log[x]^4 + (-12*x^3 + 3*x^4)*Log[-4 + x]^3*Log[x]^5 + (-4*x^2 + x^3)*Log[-4 + x]^3*Log
[x]^6),x]

[Out]

(Log[-4 + x]^2*(x + Log[x])^2)/(x*(25 + Log[-4 + x]*Log[x]*(x + Log[x]))^2)

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fricas [B]  time = 0.70, size = 101, normalized size = 4.39 \begin {gather*} \frac {x^{2} \log \left (x - 4\right )^{2} + 2 \, x \log \left (x - 4\right )^{2} \log \relax (x) + \log \left (x - 4\right )^{2} \log \relax (x)^{2}}{2 \, x^{2} \log \left (x - 4\right )^{2} \log \relax (x)^{3} + x \log \left (x - 4\right )^{2} \log \relax (x)^{4} + 50 \, x^{2} \log \left (x - 4\right ) \log \relax (x) + {\left (x^{3} \log \left (x - 4\right )^{2} + 50 \, x \log \left (x - 4\right )\right )} \log \relax (x)^{2} + 625 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x+4)*log(x-4)^3*log(x)^4+(-3*x^2+10*x+8)*log(x-4)^3*log(x)^3+((-3*x^3+6*x^2+24*x)*log(x-4)^3+(-25
*x+100)*log(x-4)^2+50*x*log(x-4))*log(x)^2+((-x^4-2*x^3+24*x^2)*log(x-4)^3+(50*x-200)*log(x-4)^2+100*x^2*log(x
-4))*log(x)+(-2*x^4+8*x^3)*log(x-4)^3+(25*x^3-50*x^2-200*x)*log(x-4)^2+50*x^3*log(x-4))/((x^3-4*x^2)*log(x-4)^
3*log(x)^6+(3*x^4-12*x^3)*log(x-4)^3*log(x)^5+((3*x^5-12*x^4)*log(x-4)^3+(75*x^3-300*x^2)*log(x-4)^2)*log(x)^4
+((x^6-4*x^5)*log(x-4)^3+(150*x^4-600*x^3)*log(x-4)^2)*log(x)^3+((75*x^5-300*x^4)*log(x-4)^2+(1875*x^3-7500*x^
2)*log(x-4))*log(x)^2+(1875*x^4-7500*x^3)*log(x-4)*log(x)+15625*x^3-62500*x^2),x, algorithm="fricas")

[Out]

(x^2*log(x - 4)^2 + 2*x*log(x - 4)^2*log(x) + log(x - 4)^2*log(x)^2)/(2*x^2*log(x - 4)^2*log(x)^3 + x*log(x -
4)^2*log(x)^4 + 50*x^2*log(x - 4)*log(x) + (x^3*log(x - 4)^2 + 50*x*log(x - 4))*log(x)^2 + 625*x)

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giac [B]  time = 16.82, size = 107, normalized size = 4.65 \begin {gather*} -\frac {25 \, {\left (2 \, x \log \left (x - 4\right ) \log \relax (x) + 2 \, \log \left (x - 4\right ) \log \relax (x)^{2} + 25\right )}}{x^{3} \log \left (x - 4\right )^{2} \log \relax (x)^{4} + 2 \, x^{2} \log \left (x - 4\right )^{2} \log \relax (x)^{5} + x \log \left (x - 4\right )^{2} \log \relax (x)^{6} + 50 \, x^{2} \log \left (x - 4\right ) \log \relax (x)^{3} + 50 \, x \log \left (x - 4\right ) \log \relax (x)^{4} + 625 \, x \log \relax (x)^{2}} + \frac {1}{x \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x+4)*log(x-4)^3*log(x)^4+(-3*x^2+10*x+8)*log(x-4)^3*log(x)^3+((-3*x^3+6*x^2+24*x)*log(x-4)^3+(-25
*x+100)*log(x-4)^2+50*x*log(x-4))*log(x)^2+((-x^4-2*x^3+24*x^2)*log(x-4)^3+(50*x-200)*log(x-4)^2+100*x^2*log(x
-4))*log(x)+(-2*x^4+8*x^3)*log(x-4)^3+(25*x^3-50*x^2-200*x)*log(x-4)^2+50*x^3*log(x-4))/((x^3-4*x^2)*log(x-4)^
3*log(x)^6+(3*x^4-12*x^3)*log(x-4)^3*log(x)^5+((3*x^5-12*x^4)*log(x-4)^3+(75*x^3-300*x^2)*log(x-4)^2)*log(x)^4
+((x^6-4*x^5)*log(x-4)^3+(150*x^4-600*x^3)*log(x-4)^2)*log(x)^3+((75*x^5-300*x^4)*log(x-4)^2+(1875*x^3-7500*x^
2)*log(x-4))*log(x)^2+(1875*x^4-7500*x^3)*log(x-4)*log(x)+15625*x^3-62500*x^2),x, algorithm="giac")

[Out]

-25*(2*x*log(x - 4)*log(x) + 2*log(x - 4)*log(x)^2 + 25)/(x^3*log(x - 4)^2*log(x)^4 + 2*x^2*log(x - 4)^2*log(x
)^5 + x*log(x - 4)^2*log(x)^6 + 50*x^2*log(x - 4)*log(x)^3 + 50*x*log(x - 4)*log(x)^4 + 625*x*log(x)^2) + 1/(x
*log(x)^2)

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maple [B]  time = 0.06, size = 61, normalized size = 2.65

method	result	size
risch	\(\frac {1}{x \ln \relax (x )^{2}}-\frac {25 \left (2 x \ln \left (x -4\right ) \ln \relax (x )+2 \ln \relax (x )^{2} \ln \left (x -4\right )+25\right )}{\ln \relax (x )^{2} x \left (\ln \relax (x )^{2} \ln \left (x -4\right )+x \ln \left (x -4\right ) \ln \relax (x )+25\right )^{2}}\)	\(61\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-x+4)*ln(x-4)^3*ln(x)^4+(-3*x^2+10*x+8)*ln(x-4)^3*ln(x)^3+((-3*x^3+6*x^2+24*x)*ln(x-4)^3+(-25*x+100)*ln(
x-4)^2+50*x*ln(x-4))*ln(x)^2+((-x^4-2*x^3+24*x^2)*ln(x-4)^3+(50*x-200)*ln(x-4)^2+100*x^2*ln(x-4))*ln(x)+(-2*x^
4+8*x^3)*ln(x-4)^3+(25*x^3-50*x^2-200*x)*ln(x-4)^2+50*x^3*ln(x-4))/((x^3-4*x^2)*ln(x-4)^3*ln(x)^6+(3*x^4-12*x^
3)*ln(x-4)^3*ln(x)^5+((3*x^5-12*x^4)*ln(x-4)^3+(75*x^3-300*x^2)*ln(x-4)^2)*ln(x)^4+((x^6-4*x^5)*ln(x-4)^3+(150
*x^4-600*x^3)*ln(x-4)^2)*ln(x)^3+((75*x^5-300*x^4)*ln(x-4)^2+(1875*x^3-7500*x^2)*ln(x-4))*ln(x)^2+(1875*x^4-75
00*x^3)*ln(x-4)*ln(x)+15625*x^3-62500*x^2),x,method=_RETURNVERBOSE)

[Out]

1/x/ln(x)^2-25*(2*x*ln(x-4)*ln(x)+2*ln(x)^2*ln(x-4)+25)/ln(x)^2/x/(ln(x)^2*ln(x-4)+x*ln(x-4)*ln(x)+25)^2

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maxima [B]  time = 1.14, size = 76, normalized size = 3.30 \begin {gather*} \frac {{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2}\right )} \log \left (x - 4\right )^{2}}{{\left (x^{3} \log \relax (x)^{2} + 2 \, x^{2} \log \relax (x)^{3} + x \log \relax (x)^{4}\right )} \log \left (x - 4\right )^{2} + 50 \, {\left (x^{2} \log \relax (x) + x \log \relax (x)^{2}\right )} \log \left (x - 4\right ) + 625 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x+4)*log(x-4)^3*log(x)^4+(-3*x^2+10*x+8)*log(x-4)^3*log(x)^3+((-3*x^3+6*x^2+24*x)*log(x-4)^3+(-25
*x+100)*log(x-4)^2+50*x*log(x-4))*log(x)^2+((-x^4-2*x^3+24*x^2)*log(x-4)^3+(50*x-200)*log(x-4)^2+100*x^2*log(x
-4))*log(x)+(-2*x^4+8*x^3)*log(x-4)^3+(25*x^3-50*x^2-200*x)*log(x-4)^2+50*x^3*log(x-4))/((x^3-4*x^2)*log(x-4)^
3*log(x)^6+(3*x^4-12*x^3)*log(x-4)^3*log(x)^5+((3*x^5-12*x^4)*log(x-4)^3+(75*x^3-300*x^2)*log(x-4)^2)*log(x)^4
+((x^6-4*x^5)*log(x-4)^3+(150*x^4-600*x^3)*log(x-4)^2)*log(x)^3+((75*x^5-300*x^4)*log(x-4)^2+(1875*x^3-7500*x^
2)*log(x-4))*log(x)^2+(1875*x^4-7500*x^3)*log(x-4)*log(x)+15625*x^3-62500*x^2),x, algorithm="maxima")

[Out]

(x^2 + 2*x*log(x) + log(x)^2)*log(x - 4)^2/((x^3*log(x)^2 + 2*x^2*log(x)^3 + x*log(x)^4)*log(x - 4)^2 + 50*(x^
2*log(x) + x*log(x)^2)*log(x - 4) + 625*x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {50\,x^3\,\ln \left (x-4\right )-{\ln \left (x-4\right )}^2\,\left (-25\,x^3+50\,x^2+200\,x\right )+{\ln \left (x-4\right )}^3\,\left (8\,x^3-2\,x^4\right )+{\ln \relax (x)}^2\,\left (\left (-3\,x^3+6\,x^2+24\,x\right )\,{\ln \left (x-4\right )}^3+\left (100-25\,x\right )\,{\ln \left (x-4\right )}^2+50\,x\,\ln \left (x-4\right )\right )+\ln \relax (x)\,\left ({\ln \left (x-4\right )}^2\,\left (50\,x-200\right )+100\,x^2\,\ln \left (x-4\right )-{\ln \left (x-4\right )}^3\,\left (x^4+2\,x^3-24\,x^2\right )\right )-{\ln \left (x-4\right )}^3\,{\ln \relax (x)}^4\,\left (x-4\right )+{\ln \left (x-4\right )}^3\,{\ln \relax (x)}^3\,\left (-3\,x^2+10\,x+8\right )}{{\ln \relax (x)}^2\,\left (\left (300\,x^4-75\,x^5\right )\,{\ln \left (x-4\right )}^2+\left (7500\,x^2-1875\,x^3\right )\,\ln \left (x-4\right )\right )+{\ln \relax (x)}^4\,\left (\left (12\,x^4-3\,x^5\right )\,{\ln \left (x-4\right )}^3+\left (300\,x^2-75\,x^3\right )\,{\ln \left (x-4\right )}^2\right )+{\ln \relax (x)}^3\,\left (\left (4\,x^5-x^6\right )\,{\ln \left (x-4\right )}^3+\left (600\,x^3-150\,x^4\right )\,{\ln \left (x-4\right )}^2\right )+62500\,x^2-15625\,x^3+{\ln \left (x-4\right )}^3\,{\ln \relax (x)}^6\,\left (4\,x^2-x^3\right )+{\ln \left (x-4\right )}^3\,{\ln \relax (x)}^5\,\left (12\,x^3-3\,x^4\right )+\ln \left (x-4\right )\,\ln \relax (x)\,\left (7500\,x^3-1875\,x^4\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(50*x^3*log(x - 4) - log(x - 4)^2*(200*x + 50*x^2 - 25*x^3) + log(x - 4)^3*(8*x^3 - 2*x^4) + log(x)^2*(50
*x*log(x - 4) - log(x - 4)^2*(25*x - 100) + log(x - 4)^3*(24*x + 6*x^2 - 3*x^3)) + log(x)*(log(x - 4)^2*(50*x
- 200) + 100*x^2*log(x - 4) - log(x - 4)^3*(2*x^3 - 24*x^2 + x^4)) - log(x - 4)^3*log(x)^4*(x - 4) + log(x - 4
)^3*log(x)^3*(10*x - 3*x^2 + 8))/(log(x)^2*(log(x - 4)*(7500*x^2 - 1875*x^3) + log(x - 4)^2*(300*x^4 - 75*x^5)
) + log(x)^4*(log(x - 4)^3*(12*x^4 - 3*x^5) + log(x - 4)^2*(300*x^2 - 75*x^3)) + log(x)^3*(log(x - 4)^3*(4*x^5
- x^6) + log(x - 4)^2*(600*x^3 - 150*x^4)) + 62500*x^2 - 15625*x^3 + log(x - 4)^3*log(x)^6*(4*x^2 - x^3) + lo
g(x - 4)^3*log(x)^5*(12*x^3 - 3*x^4) + log(x - 4)*log(x)*(7500*x^3 - 1875*x^4)),x)

[Out]

int(-(50*x^3*log(x - 4) - log(x - 4)^2*(200*x + 50*x^2 - 25*x^3) + log(x - 4)^3*(8*x^3 - 2*x^4) + log(x)^2*(50
*x*log(x - 4) - log(x - 4)^2*(25*x - 100) + log(x - 4)^3*(24*x + 6*x^2 - 3*x^3)) + log(x)*(log(x - 4)^2*(50*x
- 200) + 100*x^2*log(x - 4) - log(x - 4)^3*(2*x^3 - 24*x^2 + x^4)) - log(x - 4)^3*log(x)^4*(x - 4) + log(x - 4
)^3*log(x)^3*(10*x - 3*x^2 + 8))/(log(x)^2*(log(x - 4)*(7500*x^2 - 1875*x^3) + log(x - 4)^2*(300*x^4 - 75*x^5)
) + log(x)^4*(log(x - 4)^3*(12*x^4 - 3*x^5) + log(x - 4)^2*(300*x^2 - 75*x^3)) + log(x)^3*(log(x - 4)^3*(4*x^5
- x^6) + log(x - 4)^2*(600*x^3 - 150*x^4)) + 62500*x^2 - 15625*x^3 + log(x - 4)^3*log(x)^6*(4*x^2 - x^3) + lo
g(x - 4)^3*log(x)^5*(12*x^3 - 3*x^4) + log(x - 4)*log(x)*(7500*x^3 - 1875*x^4)), x)

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sympy [B]  time = 0.81, size = 94, normalized size = 4.09 \begin {gather*} \frac {\left (- 50 x \log {\relax (x )} - 50 \log {\relax (x )}^{2}\right ) \log {\left (x - 4 \right )} - 625}{625 x \log {\relax (x )}^{2} + \left (50 x^{2} \log {\relax (x )}^{3} + 50 x \log {\relax (x )}^{4}\right ) \log {\left (x - 4 \right )} + \left (x^{3} \log {\relax (x )}^{4} + 2 x^{2} \log {\relax (x )}^{5} + x \log {\relax (x )}^{6}\right ) \log {\left (x - 4 \right )}^{2}} + \frac {1}{x \log {\relax (x )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x+4)*ln(x-4)**3*ln(x)**4+(-3*x**2+10*x+8)*ln(x-4)**3*ln(x)**3+((-3*x**3+6*x**2+24*x)*ln(x-4)**3+(
-25*x+100)*ln(x-4)**2+50*x*ln(x-4))*ln(x)**2+((-x**4-2*x**3+24*x**2)*ln(x-4)**3+(50*x-200)*ln(x-4)**2+100*x**2
*ln(x-4))*ln(x)+(-2*x**4+8*x**3)*ln(x-4)**3+(25*x**3-50*x**2-200*x)*ln(x-4)**2+50*x**3*ln(x-4))/((x**3-4*x**2)
*ln(x-4)**3*ln(x)**6+(3*x**4-12*x**3)*ln(x-4)**3*ln(x)**5+((3*x**5-12*x**4)*ln(x-4)**3+(75*x**3-300*x**2)*ln(x
-4)**2)*ln(x)**4+((x**6-4*x**5)*ln(x-4)**3+(150*x**4-600*x**3)*ln(x-4)**2)*ln(x)**3+((75*x**5-300*x**4)*ln(x-4
)**2+(1875*x**3-7500*x**2)*ln(x-4))*ln(x)**2+(1875*x**4-7500*x**3)*ln(x-4)*ln(x)+15625*x**3-62500*x**2),x)

[Out]

((-50*x*log(x) - 50*log(x)**2)*log(x - 4) - 625)/(625*x*log(x)**2 + (50*x**2*log(x)**3 + 50*x*log(x)**4)*log(x
- 4) + (x**3*log(x)**4 + 2*x**2*log(x)**5 + x*log(x)**6)*log(x - 4)**2) + 1/(x*log(x)**2)

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