∫ (−10x3−2x4) log2(8)+(10+2x) log2(8) log(x)+(10−2x−30x3+6x4) log2(8) log( x______ 25−10x+x2 ) _______________________________________________________________________________________________________________________________________________________________________________________________________(45x10 −9x11) log3( x______ 25−10x+x2 )+(−135x7+27x8) log(x) log3( x______ 25−10x+x2 )+(135x4−27x5) log2(x) log3( x______ 25−10x+x2 )+(−45x+9x2) log3(x) log3( x_____

3.69.29 \(\int \frac {(-10 x^3-2 x^4) \log ^2(8)+(10+2 x) \log ^2(8) \log (x)+(10-2 x-30 x^3+6 x^4) \log ^2(8) \log (\frac {x}{25-10 x+x^2})}{(45 x^{10}-9 x^{11}) \log ^3(\frac {x}{25-10 x+x^2})+(-135 x^7+27 x^8) \log (x) \log ^3(\frac {x}{25-10 x+x^2})+(135 x^4-27 x^5) \log ^2(x) \log ^3(\frac {x}{25-10 x+x^2})+(-45 x+9 x^2) \log ^3(x) \log ^3(\frac {x}{25-10 x+x^2})} \, dx\)

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

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Rubi [F] time = 2.27, 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 {\left (-10 x^3-2 x^4\right ) \log ^2(8)+(10+2 x) \log ^2(8) \log (x)+\left (10-2 x-30 x^3+6 x^4\right ) \log ^2(8) \log \left (\frac {x}{25-10 x+x^2}\right )}{\left (45 x^{10}-9 x^{11}\right ) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (-135 x^7+27 x^8\right ) \log (x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (135 x^4-27 x^5\right ) \log ^2(x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )+\left (-45 x+9 x^2\right ) \log ^3(x) \log ^3\left (\frac {x}{25-10 x+x^2}\right )} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[((-10*x^3 - 2*x^4)*Log[8]^2 + (10 + 2*x)*Log[8]^2*Log[x] + (10 - 2*x - 30*x^3 + 6*x^4)*Log[8]^2*Log[x/(25

- 10*x + x^2)])/((45*x^10 - 9*x^11)*Log[x/(25 - 10*x + x^2)]^3 + (-135*x^7 + 27*x^8)*Log[x]*Log[x/(25 - 10*x +

x^2)]^3 + (135*x^4 - 27*x^5)*Log[x]^2*Log[x/(25 - 10*x + x^2)]^3 + (-45*x + 9*x^2)*Log[x]^3*Log[x/(25 - 10*x

+ x^2)]^3),x]

[Out]

(4*Log[8]^2*Defer[Int][1/((-5 + x)*(x^3 - Log[x])^2*Log[x/(-5 + x)^2]^3), x])/9 - (2*Log[8]^2*Defer[Int][1/(x*

(x^3 - Log[x])^2*Log[x/(-5 + x)^2]^3), x])/9 + (2*Log[8]^2*Defer[Int][1/(x*(x^3 - Log[x])^3*Log[x/(-5 + x)^2]^

2), x])/9 - (2*Log[8]^2*Defer[Int][x^2/((x^3 - Log[x])^3*Log[x/(-5 + x)^2]^2), x])/3

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \log ^2(8) \left (-x^3 (5+x)+(5+x) \log (x)+\left (5-x-15 x^3+3 x^4\right ) \log \left (\frac {x}{(-5+x)^2}\right )\right )}{9 (5-x) x \left (x^3-\log (x)\right )^3 \log ^3\left (\frac {x}{(-5+x)^2}\right )} \, dx\\ &=\frac {1}{9} \left (2 \log ^2(8)\right ) \int \frac {-x^3 (5+x)+(5+x) \log (x)+\left (5-x-15 x^3+3 x^4\right ) \log \left (\frac {x}{(-5+x)^2}\right )}{(5-x) x \left (x^3-\log (x)\right )^3 \log ^3\left (\frac {x}{(-5+x)^2}\right )} \, dx\\ &=\frac {1}{9} \left (2 \log ^2(8)\right ) \int \left (\frac {5+x}{(-5+x) x \left (x^3-\log (x)\right )^2 \log ^3\left (\frac {x}{(-5+x)^2}\right )}+\frac {1-3 x^3}{x \left (x^3-\log (x)\right )^3 \log ^2\left (\frac {x}{(-5+x)^2}\right )}\right ) \, dx\\ &=\frac {1}{9} \left (2 \log ^2(8)\right ) \int \frac {5+x}{(-5+x) x \left (x^3-\log (x)\right )^2 \log ^3\left (\frac {x}{(-5+x)^2}\right )} \, dx+\frac {1}{9} \left (2 \log ^2(8)\right ) \int \frac {1-3 x^3}{x \left (x^3-\log (x)\right )^3 \log ^2\left (\frac {x}{(-5+x)^2}\right )} \, dx\\ &=\frac {1}{9} \left (2 \log ^2(8)\right ) \int \left (\frac {2}{(-5+x) \left (x^3-\log (x)\right )^2 \log ^3\left (\frac {x}{(-5+x)^2}\right )}-\frac {1}{x \left (x^3-\log (x)\right )^2 \log ^3\left (\frac {x}{(-5+x)^2}\right )}\right ) \, dx+\frac {1}{9} \left (2 \log ^2(8)\right ) \int \left (\frac {1}{x \left (x^3-\log (x)\right )^3 \log ^2\left (\frac {x}{(-5+x)^2}\right )}-\frac {3 x^2}{\left (x^3-\log (x)\right )^3 \log ^2\left (\frac {x}{(-5+x)^2}\right )}\right ) \, dx\\ &=-\left (\frac {1}{9} \left (2 \log ^2(8)\right ) \int \frac {1}{x \left (x^3-\log (x)\right )^2 \log ^3\left (\frac {x}{(-5+x)^2}\right )} \, dx\right )+\frac {1}{9} \left (2 \log ^2(8)\right ) \int \frac {1}{x \left (x^3-\log (x)\right )^3 \log ^2\left (\frac {x}{(-5+x)^2}\right )} \, dx+\frac {1}{9} \left (4 \log ^2(8)\right ) \int \frac {1}{(-5+x) \left (x^3-\log (x)\right )^2 \log ^3\left (\frac {x}{(-5+x)^2}\right )} \, dx-\frac {1}{3} \left (2 \log ^2(8)\right ) \int \frac {x^2}{\left (x^3-\log (x)\right )^3 \log ^2\left (\frac {x}{(-5+x)^2}\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A] time = 0.99, size = 28, normalized size = 1.00 \begin {gather*} \frac {\log ^2(8)}{9 \left (x^3-\log (x)\right )^2 \log ^2\left (\frac {x}{(-5+x)^2}\right )} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[((-10*x^3 - 2*x^4)*Log[8]^2 + (10 + 2*x)*Log[8]^2*Log[x] + (10 - 2*x - 30*x^3 + 6*x^4)*Log[8]^2*Log[

x/(25 - 10*x + x^2)])/((45*x^10 - 9*x^11)*Log[x/(25 - 10*x + x^2)]^3 + (-135*x^7 + 27*x^8)*Log[x]*Log[x/(25 -

10*x + x^2)]^3 + (135*x^4 - 27*x^5)*Log[x]^2*Log[x/(25 - 10*x + x^2)]^3 + (-45*x + 9*x^2)*Log[x]^3*Log[x/(25 -

10*x + x^2)]^3),x]

[Out]

Log[8]^2/(9*(x^3 - Log[x])^2*Log[x/(-5 + x)^2]^2)

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fricas [B] time = 0.58, size = 69, normalized size = 2.46 \begin {gather*} \frac {\log \relax (2)^{2}}{x^{6} \log \left (\frac {x}{x^{2} - 10 \, x + 25}\right )^{2} - 2 \, x^{3} \log \relax (x) \log \left (\frac {x}{x^{2} - 10 \, x + 25}\right )^{2} + \log \relax (x)^{2} \log \left (\frac {x}{x^{2} - 10 \, x + 25}\right )^{2}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((9*(2*x+10)*log(2)^2*log(x)+9*(6*x^4-30*x^3-2*x+10)*log(2)^2*log(x/(x^2-10*x+25))+9*(-2*x^4-10*x^3)*

log(2)^2)/((9*x^2-45*x)*log(x/(x^2-10*x+25))^3*log(x)^3+(-27*x^5+135*x^4)*log(x/(x^2-10*x+25))^3*log(x)^2+(27*

x^8-135*x^7)*log(x/(x^2-10*x+25))^3*log(x)+(-9*x^11+45*x^10)*log(x/(x^2-10*x+25))^3),x, algorithm="fricas")

[Out]

log(2)^2/(x^6*log(x/(x^2 - 10*x + 25))^2 - 2*x^3*log(x)*log(x/(x^2 - 10*x + 25))^2 + log(x)^2*log(x/(x^2 - 10*

x + 25))^2)

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giac [B] time = 3.89, size = 264, normalized size = 9.43 \begin {gather*} \frac {x \log \relax (2)^{2} + 5 \, \log \relax (2)^{2}}{x^{7} \log \left (x^{2} - 10 \, x + 25\right )^{2} - 2 \, x^{7} \log \left (x^{2} - 10 \, x + 25\right ) \log \relax (x) + x^{7} \log \relax (x)^{2} + 5 \, x^{6} \log \left (x^{2} - 10 \, x + 25\right )^{2} - 10 \, x^{6} \log \left (x^{2} - 10 \, x + 25\right ) \log \relax (x) + 5 \, x^{6} \log \relax (x)^{2} - 2 \, x^{4} \log \left (x^{2} - 10 \, x + 25\right )^{2} \log \relax (x) + 4 \, x^{4} \log \left (x^{2} - 10 \, x + 25\right ) \log \relax (x)^{2} - 2 \, x^{4} \log \relax (x)^{3} - 10 \, x^{3} \log \left (x^{2} - 10 \, x + 25\right )^{2} \log \relax (x) + 20 \, x^{3} \log \left (x^{2} - 10 \, x + 25\right ) \log \relax (x)^{2} - 10 \, x^{3} \log \relax (x)^{3} + x \log \left (x^{2} - 10 \, x + 25\right )^{2} \log \relax (x)^{2} - 2 \, x \log \left (x^{2} - 10 \, x + 25\right ) \log \relax (x)^{3} + x \log \relax (x)^{4} + 5 \, \log \left (x^{2} - 10 \, x + 25\right )^{2} \log \relax (x)^{2} - 10 \, \log \left (x^{2} - 10 \, x + 25\right ) \log \relax (x)^{3} + 5 \, \log \relax (x)^{4}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((9*(2*x+10)*log(2)^2*log(x)+9*(6*x^4-30*x^3-2*x+10)*log(2)^2*log(x/(x^2-10*x+25))+9*(-2*x^4-10*x^3)*

log(2)^2)/((9*x^2-45*x)*log(x/(x^2-10*x+25))^3*log(x)^3+(-27*x^5+135*x^4)*log(x/(x^2-10*x+25))^3*log(x)^2+(27*

x^8-135*x^7)*log(x/(x^2-10*x+25))^3*log(x)+(-9*x^11+45*x^10)*log(x/(x^2-10*x+25))^3),x, algorithm="giac")

[Out]

(x*log(2)^2 + 5*log(2)^2)/(x^7*log(x^2 - 10*x + 25)^2 - 2*x^7*log(x^2 - 10*x + 25)*log(x) + x^7*log(x)^2 + 5*x

^6*log(x^2 - 10*x + 25)^2 - 10*x^6*log(x^2 - 10*x + 25)*log(x) + 5*x^6*log(x)^2 - 2*x^4*log(x^2 - 10*x + 25)^2

*log(x) + 4*x^4*log(x^2 - 10*x + 25)*log(x)^2 - 2*x^4*log(x)^3 - 10*x^3*log(x^2 - 10*x + 25)^2*log(x) + 20*x^3

*log(x^2 - 10*x + 25)*log(x)^2 - 10*x^3*log(x)^3 + x*log(x^2 - 10*x + 25)^2*log(x)^2 - 2*x*log(x^2 - 10*x + 25

)*log(x)^3 + x*log(x)^4 + 5*log(x^2 - 10*x + 25)^2*log(x)^2 - 10*log(x^2 - 10*x + 25)*log(x)^3 + 5*log(x)^4)

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maple [C] time = 0.90, size = 172, normalized size = 6.14


method	result	size

risch	\(-\frac {4 \ln \relax (2)^{2}}{\left (\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i}{\left (x -5\right )^{2}}\right ) \mathrm {csgn}\left (\frac {i x}{\left (x -5\right )^{2}}\right )-\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i x}{\left (x -5\right )^{2}}\right )^{2}-\pi \,\mathrm {csgn}\left (\frac {i}{\left (x -5\right )^{2}}\right ) \mathrm {csgn}\left (\frac {i x}{\left (x -5\right )^{2}}\right )^{2}-\pi \mathrm {csgn}\left (i \left (x -5\right )\right )^{2} \mathrm {csgn}\left (i \left (x -5\right )^{2}\right )+2 \pi \,\mathrm {csgn}\left (i \left (x -5\right )\right ) \mathrm {csgn}\left (i \left (x -5\right )^{2}\right )^{2}-\pi \mathrm {csgn}\left (i \left (x -5\right )^{2}\right )^{3}+\pi \mathrm {csgn}\left (\frac {i x}{\left (x -5\right )^{2}}\right )^{3}+2 i \ln \relax (x )-4 i \ln \left (x -5\right )\right )^{2} \left (x^{3}-\ln \relax (x )\right )^{2}}\)	\(172\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((9*(2*x+10)*ln(2)^2*ln(x)+9*(6*x^4-30*x^3-2*x+10)*ln(2)^2*ln(x/(x^2-10*x+25))+9*(-2*x^4-10*x^3)*ln(2)^2)/(

(9*x^2-45*x)*ln(x/(x^2-10*x+25))^3*ln(x)^3+(-27*x^5+135*x^4)*ln(x/(x^2-10*x+25))^3*ln(x)^2+(27*x^8-135*x^7)*ln

(x/(x^2-10*x+25))^3*ln(x)+(-9*x^11+45*x^10)*ln(x/(x^2-10*x+25))^3),x,method=_RETURNVERBOSE)

[Out]

-4*ln(2)^2/(Pi*csgn(I*x)*csgn(I/(x-5)^2)*csgn(I*x/(x-5)^2)-Pi*csgn(I*x)*csgn(I*x/(x-5)^2)^2-Pi*csgn(I/(x-5)^2)

*csgn(I*x/(x-5)^2)^2-Pi*csgn(I*(x-5))^2*csgn(I*(x-5)^2)+2*Pi*csgn(I*(x-5))*csgn(I*(x-5)^2)^2-Pi*csgn(I*(x-5)^2

)^3+Pi*csgn(I*x/(x-5)^2)^3+2*I*ln(x)-4*I*ln(x-5))^2/(x^3-ln(x))^2

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maxima [B] time = 0.53, size = 78, normalized size = 2.79 \begin {gather*} \frac {\log \relax (2)^{2}}{x^{6} \log \relax (x)^{2} - 2 \, x^{3} \log \relax (x)^{3} + \log \relax (x)^{4} + 4 \, {\left (x^{6} - 2 \, x^{3} \log \relax (x) + \log \relax (x)^{2}\right )} \log \left (x - 5\right )^{2} - 4 \, {\left (x^{6} \log \relax (x) - 2 \, x^{3} \log \relax (x)^{2} + \log \relax (x)^{3}\right )} \log \left (x - 5\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((9*(2*x+10)*log(2)^2*log(x)+9*(6*x^4-30*x^3-2*x+10)*log(2)^2*log(x/(x^2-10*x+25))+9*(-2*x^4-10*x^3)*

log(2)^2)/((9*x^2-45*x)*log(x/(x^2-10*x+25))^3*log(x)^3+(-27*x^5+135*x^4)*log(x/(x^2-10*x+25))^3*log(x)^2+(27*

x^8-135*x^7)*log(x/(x^2-10*x+25))^3*log(x)+(-9*x^11+45*x^10)*log(x/(x^2-10*x+25))^3),x, algorithm="maxima")

[Out]

log(2)^2/(x^6*log(x)^2 - 2*x^3*log(x)^3 + log(x)^4 + 4*(x^6 - 2*x^3*log(x) + log(x)^2)*log(x - 5)^2 - 4*(x^6*l

og(x) - 2*x^3*log(x)^2 + log(x)^3)*log(x - 5))

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mupad [B] time = 6.59, size = 2546, normalized size = 90.93 result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(-(9*log(2)^2*(10*x^3 + 2*x^4) - 9*log(2)^2*log(x)*(2*x + 10) + 9*log(2)^2*log(x/(x^2 - 10*x + 25))*(2*x +

30*x^3 - 6*x^4 - 10))/(log(x/(x^2 - 10*x + 25))^3*(45*x^10 - 9*x^11) - log(x/(x^2 - 10*x + 25))^3*log(x)^3*(45

*x - 9*x^2) - log(x/(x^2 - 10*x + 25))^3*log(x)*(135*x^7 - 27*x^8) + log(x/(x^2 - 10*x + 25))^3*log(x)^2*(135*

x^4 - 27*x^5)),x)

[Out]

((log(2)^2*(600*x^2 + 67500*x^3 + 2238*x^4 - 5400*x^5 - 151965*x^6 - 13142*x^7 + 11950*x^8 + 68050*x^9 + 12507

*x^10 - 4800*x^11 - 570*x^12 + 108*x^13 - 7500))/(4*(3*x^3 - 1)*(x + 5)^4) + (x*log(2)^2*log(x)^2*(16885*x^2 -

200*x - 7500*x^3 - 750*x^4 + 240*x^5 + 27*x^6 + 250))/(4*(3*x^3 - 1)*(x + 5)^4) + (x*log(2)^2*log(x)*(13000*x

^3 - 50535*x^2 + 4450*x^4 + 117565*x^5 - 5331*x^6 - 10650*x^7 + 330*x^8 + 189*x^9 - 2250))/(4*(3*x^3 - 1)*(x +

5)^4))/(log(x)^4 - 4*x^9*log(x) - 4*x^3*log(x)^3 + 6*x^6*log(x)^2 + x^12) - ((x*log(x)*(589575*x^2*log(2)^2 -

194305*x^3*log(2)^2 - 52750*x^4*log(2)^2 - 3026950*x^5*log(2)^2 + 628435*x^6*log(2)^2 + 390939*x^7*log(2)^2 +

5294175*x^8*log(2)^2 - 681405*x^9*log(2)^2 - 799722*x^10*log(2)^2 - 2250*x^11*log(2)^2 + 21825*x^12*log(2)^2

+ 1701*x^13*log(2)^2 - 5250*x*log(2)^2 + 8750*log(2)^2))/(12*(3*x^3 - 1)^3*(x + 5)^5) - (x*(421125*x^2*log(2)^

2 - 132025*x^3*log(2)^2 - 84000*x^4*log(2)^2 - 3205050*x^5*log(2)^2 + 60045*x^6*log(2)^2 + 456385*x^7*log(2)^2

+ 8130250*x^8*log(2)^2 + 1026770*x^9*log(2)^2 - 909276*x^10*log(2)^2 - 6201150*x^11*log(2)^2 - 1722900*x^12*l

og(2)^2 + 463842*x^13*log(2)^2 + 134550*x^14*log(2)^2 - 7650*x^15*log(2)^2 - 1944*x^16*log(2)^2 + 3750*x*log(2

)^2 + 18750*log(2)^2))/(12*(3*x^3 - 1)^3*(x + 5)^5) + (x*log(2)^2*log(x)^2*(2750*x - 253675*x^2 + 159385*x^3 +

17250*x^4 - 3450*x^5 - 316545*x^6 + 44919*x^7 + 15300*x^8 + 900*x^9 - 1250))/(12*(3*x^3 - 1)^3*(x + 5)^5))/(3

*x^6*log(x) + log(x)^3 - 3*x^3*log(x)^2 - x^9) + (log(2)^2/(log(x) - x^3)^2 + (log(2)^2*log(x/(x^2 - 10*x + 25

))*(3*x^3 - 1)*(x - 5))/((log(x) - x^3)^3*(x + 5)))/log(x/(x^2 - 10*x + 25))^2 - (((3*x^3*log(2)^2 - log(2)^2)

*(x - 5))/((log(x) - x^3)^3*(x + 5)) - (log(2)^2*log(x/(x^2 - 10*x + 25))*(x - 5)*(225*x^3*log(x) - 30*x^4*log

(x) - 9*x^5*log(x) + 10*x*log(x) - 3*x^2 - 450*x^3 - 10*x^4 + 18*x^5 + 450*x^6 + 30*x^7 - 18*x^8 + 75))/((log(

x) - x^3)^4*(x + 5)^3))/log(x/(x^2 - 10*x + 25)) + ((x*(3363000*x^2*log(2)^2 - 719550*x^3*log(2)^2 - 437420*x^

4*log(2)^2 - 34099875*x^5*log(2)^2 + 1630700*x^6*log(2)^2 + 5417445*x^7*log(2)^2 + 148310841*x^8*log(2)^2 + 71

98175*x^9*log(2)^2 - 24340205*x^10*log(2)^2 - 287913312*x^11*log(2)^2 - 43289775*x^12*log(2)^2 + 44214885*x^13

*log(2)^2 + 282699477*x^14*log(2)^2 + 67221225*x^15*log(2)^2 - 40115250*x^16*log(2)^2 - 12127725*x^17*log(2)^2

+ 399600*x^18*log(2)^2 + 279180*x^19*log(2)^2 + 17496*x^20*log(2)^2 - 20000*x*log(2)^2 + 50000*log(2)^2))/(24

*(3*x^3 - 1)^5*(x + 5)^6) + (x*log(x)*(2891250*x^3*log(2)^2 - 6328125*x^2*log(2)^2 + 918175*x^4*log(2)^2 + 303

42000*x^5*log(2)^2 - 17419525*x^6*log(2)^2 - 6242570*x^7*log(2)^2 - 102016530*x^8*log(2)^2 + 57130650*x^9*log(

2)^2 + 27777015*x^10*log(2)^2 - 1375056*x^11*log(2)^2 - 90917775*x^12*log(2)^2 - 16103070*x^13*log(2)^2 + 7080

939*x^14*log(2)^2 + 1323000*x^15*log(2)^2 + 62100*x^16*log(2)^2 + 62500*x*log(2)^2 - 31250*log(2)^2))/(24*(3*x

^3 - 1)^5*(x + 5)^6) - (x*log(2)^2*log(x)^2*(32500*x - 3813375*x^2 + 3545050*x^3 + 511865*x^4 - 22835250*x^5 -

7499925*x^6 + 6980220*x^7 + 1133757*x^8 - 9472950*x^9 - 5969160*x^10 + 808542*x^11 + 216000*x^12 + 10800*x^13

- 6250))/(24*(3*x^3 - 1)^5*(x + 5)^6))/(log(x)^2 - 2*x^3*log(x) + x^6) + (38068750*x^3*log(2)^2 - 312500*x^2*

log(2)^2 - 28167500*x^4*log(2)^2 - 10690000*x^5*log(2)^2 + 56246895*x^6*log(2)^2 + 207146125*x^7*log(2)^2 + 39

68625*x^8*log(2)^2 + 323472485*x^9*log(2)^2 - 998483889*x^10*log(2)^2 - 231713325*x^11*log(2)^2 + 5194809615*x

^12*log(2)^2 + 2925302229*x^13*log(2)^2 - 1017316800*x^14*log(2)^2 - 643754520*x^15*log(2)^2 + 1505585124*x^16

*log(2)^2 + 1379466450*x^17*log(2)^2 + 177409710*x^18*log(2)^2 - 62304390*x^19*log(2)^2 - 10206000*x^20*log(2)

^2 - 421200*x^21*log(2)^2 + 62500*x*log(2)^2)/(38850000*x^3 - 1575000*x^2 - 2625000*x + 55020000*x^4 + 3306240

0*x^5 - 343350840*x^6 - 493920024*x^7 - 297410400*x^8 + 1672667640*x^9 + 2460780504*x^10 + 1485993600*x^11 - 4

819658760*x^12 - 7342654536*x^13 - 4453218000*x^14 + 8080543800*x^15 + 13097722680*x^16 + 8001504000*x^17 - 68

91431400*x^18 - 12859628040*x^19 - 7972927200*x^20 + 1425836520*x^21 + 5205182472*x^22 + 3380227200*x^23 + 114

3888480*x^24 + 229512528*x^25 + 27556200*x^26 + 1837080*x^27 + 52488*x^28 - 1875000) - ((x*log(x)*(57103125*x^

2*log(2)^2 - 42235625*x^3*log(2)^2 - 16213125*x^4*log(2)^2 + 113035655*x^5*log(2)^2 + 270204875*x^6*log(2)^2 +

118425*x^7*log(2)^2 + 1170270910*x^8*log(2)^2 - 1555982646*x^9*log(2)^2 - 612213075*x^10*log(2)^2 + 928881928

5*x^11*log(2)^2 + 5586865083*x^12*log(2)^2 - 1551840525*x^13*log(2)^2 - 1162098495*x^14*log(2)^2 + 2583760059*

x^15*log(2)^2 + 2403444150*x^16*log(2)^2 + 337416570*x^17*log(2)^2 - 107611902*x^18*log(2)^2 - 17982000*x^19*l

og(2)^2 - 745200*x^20*log(2)^2 - 468750*x*log(2)^2 + 93750*log(2)^2))/(24*(3*x^3 - 1)^7*(x + 5)^7) - (x*(18946

875*x^2*log(2)^2 - 5383125*x^3*log(2)^2 - 3758025*x^4*log(2)^2 - 170996280*x^5*log(2)^2 + 38810750*x^6*log(2)^

2 + 44939700*x^7*log(2)^2 + 1086133705*x^8*log(2)^2 - 180065507*x^9*log(2)^2 - 330684600*x^10*log(2)^2 - 22673

66305*x^11*log(2)^2 + 330864063*x^12*log(2)^2 + 809660700*x^13*log(2)^2 + 7826471085*x^14*log(2)^2 + 231228351

*x^15*log(2)^2 - 2597382450*x^16*log(2)^2 - 662093190*x^17*log(2)^2 + 3931613694*x^18*log(2)^2 + 2239988175*x^

19*log(2)^2 + 69923925*x^20*log(2)^2 - 132863085*x^21*log(2)^2 - 18540900*x^22*log(2)^2 - 737100*x^23*log(2)^2

- 168750*x*log(2)^2 + 93750*log(2)^2))/(24*(3*x^3 - 1)^7*(x + 5)^7) + (x*log(2)^2*log(x)^2*(356250*x - 573306

25*x^2 + 81028625*x^3 + 11669025*x^4 - 1370124365*x^5 + 116513625*x^6 + 529286175*x^7 - 2993209725*x^8 - 23978

23479*x^9 + 51730650*x^10 + 392933430*x^11 - 650764746*x^12 - 668488950*x^13 - 142604010*x^14 + 28310634*x^15

+ 5346000*x^16 + 226800*x^17 - 31250))/(24*(3*x^3 - 1)^7*(x + 5)^7))/(log(x) - x^3) + (log(x)*((59375*x^2*log(

2)^2)/8748 - (57330625*x^3*log(2)^2)/52488 + (81028625*x^4*log(2)^2)/52488 + (3889675*x^5*log(2)^2)/17496 - (1

370124365*x^6*log(2)^2)/52488 + (38837875*x^7*log(2)^2)/17496 + (58809575*x^8*log(2)^2)/5832 - (997736575*x^9*

log(2)^2)/17496 - (29602759*x^10*log(2)^2)/648 + (319325*x^11*log(2)^2)/324 + (808505*x^12*log(2)^2)/108 - (12

051199*x^13*log(2)^2)/972 - (4126475*x^14*log(2)^2)/324 - (2640815*x^15*log(2)^2)/972 + (174757*x^16*log(2)^2)

/324 + (2750*x^17*log(2)^2)/27 + (350*x^18*log(2)^2)/81 - (15625*x*log(2)^2)/26244))/((1618750*x^3)/2187 - (21

875*x^2)/729 - (109375*x)/2187 + (2292500*x^4)/2187 + (459200*x^5)/729 - (14306285*x^6)/2187 - (20580001*x^7)/

2187 - (1376900*x^8)/243 + (23231495*x^9)/729 + (34177507*x^10)/729 + (254800*x^11)/9 - (7437745*x^12)/81 - (1

1331257*x^13)/81 - (2290750*x^14)/27 + (12469975*x^15)/81 + (20212535*x^16)/81 + (1372000*x^17)/9 - (3544975*x

^18)/27 - (6615035*x^19)/27 - 151900*x^20 + 27165*x^21 + 99169*x^22 + 64400*x^23 + (65380*x^24)/3 + (13118*x^2

5)/3 + 525*x^26 + 35*x^27 + x^28 - 78125/2187)

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sympy [A] time = 0.54, size = 34, normalized size = 1.21 \begin {gather*} \frac {\log {\relax (2 )}^{2}}{\left (x^{6} - 2 x^{3} \log {\relax (x )} + \log {\relax (x )}^{2}\right ) \log {\left (\frac {x}{x^{2} - 10 x + 25} \right )}^{2}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((9*(2*x+10)*ln(2)**2*ln(x)+9*(6*x**4-30*x**3-2*x+10)*ln(2)**2*ln(x/(x**2-10*x+25))+9*(-2*x**4-10*x**

3)*ln(2)**2)/((9*x**2-45*x)*ln(x/(x**2-10*x+25))**3*ln(x)**3+(-27*x**5+135*x**4)*ln(x/(x**2-10*x+25))**3*ln(x)

**2+(27*x**8-135*x**7)*ln(x/(x**2-10*x+25))**3*ln(x)+(-9*x**11+45*x**10)*ln(x/(x**2-10*x+25))**3),x)

[Out]

log(2)**2/((x**6 - 2*x**3*log(x) + log(x)**2)*log(x/(x**2 - 10*x + 25))**2)

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