3.87.90 \(\int \frac {-2812500 x^3-2250000 x^4 \log (2)-675000 x^5 \log ^2(2)-90000 x^6 \log ^3(2)-4500 x^7 \log ^4(2)+(1012500 x^2+2812500 x^3+(607500 x^3+2812500 x^4) \log (2)+(121500 x^4+1012500 x^5) \log ^2(2)+(8100 x^5+157500 x^6) \log ^3(2)+9000 x^7 \log ^4(2)) \log (x)+(-121500 x-1012500 x^2+(-48600 x^2-810000 x^3) \log (2)+(-4860 x^3-202500 x^4) \log ^2(2)-16200 x^5 \log ^3(2)) \log ^2(x)+(4860+121500 x+(972 x+72900 x^2) \log (2)+9720 x^3 \log ^2(2)) \log ^3(x)+(-4860-1944 x \log (2)) \log ^4(x)}{5834375 x^5+5834375 x^6 \log (2)+2333750 x^7 \log ^2(2)+466750 x^8 \log ^3(2)+46675 x^9 \log ^4(2)+1867 x^{10} \log ^5(2)+(-2812500 x^4-2250000 x^5 \log (2)-675000 x^6 \log ^2(2)-90000 x^7 \log ^3(2)-4500 x^8 \log ^4(2)) \log (x)+(506250 x^3+303750 x^4 \log (2)+60750 x^5 \log ^2(2)+4050 x^6 \log ^3(2)) \log ^2(x)+(-40500 x^2-16200 x^3 \log (2)-1620 x^4 \log ^2(2)) \log ^3(x)+(1215 x+243 x^2 \log (2)) \log ^4(x)} \, dx\)

Optimal. Leaf size=24 \[ \log \left (-\frac {8}{3}+\left (-5+\frac {3 \log (x)}{x (5+x \log (2))}\right )^4\right ) \]

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Rubi [F]  time = 58.59, 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 {-2812500 x^3-2250000 x^4 \log (2)-675000 x^5 \log ^2(2)-90000 x^6 \log ^3(2)-4500 x^7 \log ^4(2)+\left (1012500 x^2+2812500 x^3+\left (607500 x^3+2812500 x^4\right ) \log (2)+\left (121500 x^4+1012500 x^5\right ) \log ^2(2)+\left (8100 x^5+157500 x^6\right ) \log ^3(2)+9000 x^7 \log ^4(2)\right ) \log (x)+\left (-121500 x-1012500 x^2+\left (-48600 x^2-810000 x^3\right ) \log (2)+\left (-4860 x^3-202500 x^4\right ) \log ^2(2)-16200 x^5 \log ^3(2)\right ) \log ^2(x)+\left (4860+121500 x+\left (972 x+72900 x^2\right ) \log (2)+9720 x^3 \log ^2(2)\right ) \log ^3(x)+(-4860-1944 x \log (2)) \log ^4(x)}{5834375 x^5+5834375 x^6 \log (2)+2333750 x^7 \log ^2(2)+466750 x^8 \log ^3(2)+46675 x^9 \log ^4(2)+1867 x^{10} \log ^5(2)+\left (-2812500 x^4-2250000 x^5 \log (2)-675000 x^6 \log ^2(2)-90000 x^7 \log ^3(2)-4500 x^8 \log ^4(2)\right ) \log (x)+\left (506250 x^3+303750 x^4 \log (2)+60750 x^5 \log ^2(2)+4050 x^6 \log ^3(2)\right ) \log ^2(x)+\left (-40500 x^2-16200 x^3 \log (2)-1620 x^4 \log ^2(2)\right ) \log ^3(x)+\left (1215 x+243 x^2 \log (2)\right ) \log ^4(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-2812500*x^3 - 2250000*x^4*Log[2] - 675000*x^5*Log[2]^2 - 90000*x^6*Log[2]^3 - 4500*x^7*Log[2]^4 + (10125
00*x^2 + 2812500*x^3 + (607500*x^3 + 2812500*x^4)*Log[2] + (121500*x^4 + 1012500*x^5)*Log[2]^2 + (8100*x^5 + 1
57500*x^6)*Log[2]^3 + 9000*x^7*Log[2]^4)*Log[x] + (-121500*x - 1012500*x^2 + (-48600*x^2 - 810000*x^3)*Log[2]
+ (-4860*x^3 - 202500*x^4)*Log[2]^2 - 16200*x^5*Log[2]^3)*Log[x]^2 + (4860 + 121500*x + (972*x + 72900*x^2)*Lo
g[2] + 9720*x^3*Log[2]^2)*Log[x]^3 + (-4860 - 1944*x*Log[2])*Log[x]^4)/(5834375*x^5 + 5834375*x^6*Log[2] + 233
3750*x^7*Log[2]^2 + 466750*x^8*Log[2]^3 + 46675*x^9*Log[2]^4 + 1867*x^10*Log[2]^5 + (-2812500*x^4 - 2250000*x^
5*Log[2] - 675000*x^6*Log[2]^2 - 90000*x^7*Log[2]^3 - 4500*x^8*Log[2]^4)*Log[x] + (506250*x^3 + 303750*x^4*Log
[2] + 60750*x^5*Log[2]^2 + 4050*x^6*Log[2]^3)*Log[x]^2 + (-40500*x^2 - 16200*x^3*Log[2] - 1620*x^4*Log[2]^2)*L
og[x]^3 + (1215*x + 243*x^2*Log[2])*Log[x]^4),x]

[Out]

-4*Log[x] - 4*Log[5 + x*Log[2]] - 562500*Defer[Int][x^2/(1867*x^4*(5 + x*Log[2])^4 - 4500*x^3*(5 + x*Log[2])^3
*Log[x] + 4050*x^2*(5 + x*Log[2])^2*Log[x]^2 - 1620*x*(5 + x*Log[2])*Log[x]^3 + 243*Log[x]^4), x] + 2500*(1867
- 135*Log[2])*Defer[Int][x^3/(1867*x^4*(5 + x*Log[2])^4 - 4500*x^3*(5 + x*Log[2])^3*Log[x] + 4050*x^2*(5 + x*
Log[2])^2*Log[x]^2 - 1620*x*(5 + x*Log[2])*Log[x]^3 + 243*Log[x]^4), x] + (7500*(1867 - 27*Log[2])*Log[2]^2*De
fer[Int][x^4/(1867*x^4*(5 + x*Log[2])^4 - 4500*x^3*(5 + x*Log[2])^3*Log[x] + 4050*x^2*(5 + x*Log[2])^2*Log[x]^
2 - 1620*x*(5 + x*Log[2])*Log[x]^3 + 243*Log[x]^4), x])/Log[8] + 300*Log[2]*(1867*Log[2] - 15*Log[2]^2 + 1867*
Log[4])*Defer[Int][x^5/(1867*x^4*(5 + x*Log[2])^4 - 4500*x^3*(5 + x*Log[2])^3*Log[x] + 4050*x^2*(5 + x*Log[2])
^2*Log[x]^2 - 1620*x*(5 + x*Log[2])*Log[x]^3 + 243*Log[x]^4), x] + 37340*Log[2]^2*Log[128]*Defer[Int][x^6/(186
7*x^4*(5 + x*Log[2])^4 - 4500*x^3*(5 + x*Log[2])^3*Log[x] + 4050*x^2*(5 + x*Log[2])^2*Log[x]^2 - 1620*x*(5 + x
*Log[2])*Log[x]^3 + 243*Log[x]^4), x] + 7468*Log[2]^3*Log[4]*Defer[Int][x^7/(1867*x^4*(5 + x*Log[2])^4 - 4500*
x^3*(5 + x*Log[2])^3*Log[x] + 4050*x^2*(5 + x*Log[2])^2*Log[x]^2 - 1620*x*(5 + x*Log[2])*Log[x]^3 + 243*Log[x]
^4), x] + 202500*Defer[Int][(x*Log[x])/(1867*x^4*(5 + x*Log[2])^4 - 4500*x^3*(5 + x*Log[2])^3*Log[x] + 4050*x^
2*(5 + x*Log[2])^2*Log[x]^2 - 1620*x*(5 + x*Log[2])*Log[x]^3 + 243*Log[x]^4), x] - 13500*(125 - Log[64])*Defer
[Int][(x^2*Log[x])/(1867*x^4*(5 + x*Log[2])^4 - 4500*x^3*(5 + x*Log[2])^3*Log[x] + 4050*x^2*(5 + x*Log[2])^2*L
og[x]^2 - 1620*x*(5 + x*Log[2])*Log[x]^3 + 243*Log[x]^4), x] - 2700*Log[2]*(500 - Log[8])*Defer[Int][(x^3*Log[
x])/(1867*x^4*(5 + x*Log[2])^4 - 4500*x^3*(5 + x*Log[2])^3*Log[x] + 4050*x^2*(5 + x*Log[2])^2*Log[x]^2 - 1620*
x*(5 + x*Log[2])*Log[x]^3 + 243*Log[x]^4), x] - 67500*Log[2]*Log[32]*Defer[Int][(x^4*Log[x])/(1867*x^4*(5 + x*
Log[2])^4 - 4500*x^3*(5 + x*Log[2])^3*Log[x] + 4050*x^2*(5 + x*Log[2])^2*Log[x]^2 - 1620*x*(5 + x*Log[2])*Log[
x]^3 + 243*Log[x]^4), x] - 13500*Log[2]^2*Log[4]*Defer[Int][(x^5*Log[x])/(1867*x^4*(5 + x*Log[2])^4 - 4500*x^3
*(5 + x*Log[2])^3*Log[x] + 4050*x^2*(5 + x*Log[2])^2*Log[x]^2 - 1620*x*(5 + x*Log[2])*Log[x]^3 + 243*Log[x]^4)
, x] - 24300*Defer[Int][Log[x]^2/(1867*x^4*(5 + x*Log[2])^4 - 4500*x^3*(5 + x*Log[2])^3*Log[x] + 4050*x^2*(5 +
x*Log[2])^2*Log[x]^2 - 1620*x*(5 + x*Log[2])*Log[x]^3 + 243*Log[x]^4), x] + 1620*(125 - Log[8])*Defer[Int][(x
*Log[x]^2)/(1867*x^4*(5 + x*Log[2])^4 - 4500*x^3*(5 + x*Log[2])^3*Log[x] + 4050*x^2*(5 + x*Log[2])^2*Log[x]^2
- 1620*x*(5 + x*Log[2])*Log[x]^3 + 243*Log[x]^4), x] + 40500*Log[8]*Defer[Int][(x^2*Log[x]^2)/(1867*x^4*(5 + x
*Log[2])^4 - 4500*x^3*(5 + x*Log[2])^3*Log[x] + 4050*x^2*(5 + x*Log[2])^2*Log[x]^2 - 1620*x*(5 + x*Log[2])*Log
[x]^3 + 243*Log[x]^4), x] + 8100*Log[2]*Log[4]*Defer[Int][(x^3*Log[x]^2)/(1867*x^4*(5 + x*Log[2])^4 - 4500*x^3
*(5 + x*Log[2])^3*Log[x] + 4050*x^2*(5 + x*Log[2])^2*Log[x]^2 - 1620*x*(5 + x*Log[2])*Log[x]^3 + 243*Log[x]^4)
, x] - 8100*Defer[Int][Log[x]^3/(1867*x^4*(5 + x*Log[2])^4 - 4500*x^3*(5 + x*Log[2])^3*Log[x] + 4050*x^2*(5 +
x*Log[2])^2*Log[x]^2 - 1620*x*(5 + x*Log[2])*Log[x]^3 + 243*Log[x]^4), x] + 972*Defer[Int][Log[x]^3/(x*(1867*x
^4*(5 + x*Log[2])^4 - 4500*x^3*(5 + x*Log[2])^3*Log[x] + 4050*x^2*(5 + x*Log[2])^2*Log[x]^2 - 1620*x*(5 + x*Lo
g[2])*Log[x]^3 + 243*Log[x]^4)), x] - 1620*Log[4]*Defer[Int][(x*Log[x]^3)/(1867*x^4*(5 + x*Log[2])^4 - 4500*x^
3*(5 + x*Log[2])^3*Log[x] + 4050*x^2*(5 + x*Log[2])^2*Log[x]^2 - 1620*x*(5 + x*Log[2])*Log[x]^3 + 243*Log[x]^4
), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {36 (5 x (5+x \log (2))-3 \log (x))^3 (-5-x \log (2)+(5+x \log (4)) \log (x))}{x (5+x \log (2)) \left (1867 x^4 (5+x \log (2))^4-4500 x^3 (5+x \log (2))^3 \log (x)+4050 x^2 (5+x \log (2))^2 \log ^2(x)-1620 x (5+x \log (2)) \log ^3(x)+243 \log ^4(x)\right )} \, dx\\ &=36 \int \frac {(5 x (5+x \log (2))-3 \log (x))^3 (-5-x \log (2)+(5+x \log (4)) \log (x))}{x (5+x \log (2)) \left (1867 x^4 (5+x \log (2))^4-4500 x^3 (5+x \log (2))^3 \log (x)+4050 x^2 (5+x \log (2))^2 \log ^2(x)-1620 x (5+x \log (2)) \log ^3(x)+243 \log ^4(x)\right )} \, dx\\ &=36 \int \left (\frac {-5-x \log (4)}{9 x (5+x \log (2))}+\frac {-140625 x^3+1166875 x^4 \left (1-\frac {135 \log (2)}{1867}\right )+1867 x^8 \log ^3(2) \log (4)+140025 x^6 \log ^2(2) \left (1-\frac {15 \log (2)}{1867}+\frac {\log (4)}{\log (2)}\right )+700125 x^5 \log (2) \left (1-\frac {45 \log (2)}{1867}+\frac {\log (4)}{\log (8)}\right )+9335 x^7 \log ^3(2) \left (1+\frac {\log (64)}{\log (2)}\right )+50625 x^2 \log (x)-421875 x^3 \left (1-\frac {6 \log (2)}{125}\right ) \log (x)-168750 x^4 \left (2-\frac {3 \log (2)}{250}\right ) \log (2) \log (x)-3375 x^6 \log ^2(2) \log (4) \log (x)-16875 x^5 \log ^2(2) \left (1+\frac {\log (16)}{\log (2)}\right ) \log (x)-6075 x \log ^2(x)+50625 x^2 \left (1-\frac {3 \log (2)}{125}\right ) \log ^2(x)+2025 x^4 \log (2) \log (4) \log ^2(x)+10125 x^3 \log (2) \left (1+\frac {\log (4)}{\log (2)}\right ) \log ^2(x)+243 \log ^3(x)-2025 x \log ^3(x)-405 x^2 \log (4) \log ^3(x)}{9 x \left (1166875 x^4+933500 x^5 \log (2)+280050 x^6 \log ^2(2)+37340 x^7 \log ^3(2)+1867 x^8 \log ^4(2)-562500 x^3 \log (x)-337500 x^4 \log (2) \log (x)-67500 x^5 \log ^2(2) \log (x)-4500 x^6 \log ^3(2) \log (x)+101250 x^2 \log ^2(x)+40500 x^3 \log (2) \log ^2(x)+4050 x^4 \log ^2(2) \log ^2(x)-8100 x \log ^3(x)-1620 x^2 \log (2) \log ^3(x)+243 \log ^4(x)\right )}\right ) \, dx\\ &=4 \int \frac {-5-x \log (4)}{x (5+x \log (2))} \, dx+4 \int \frac {-140625 x^3+1166875 x^4 \left (1-\frac {135 \log (2)}{1867}\right )+1867 x^8 \log ^3(2) \log (4)+140025 x^6 \log ^2(2) \left (1-\frac {15 \log (2)}{1867}+\frac {\log (4)}{\log (2)}\right )+700125 x^5 \log (2) \left (1-\frac {45 \log (2)}{1867}+\frac {\log (4)}{\log (8)}\right )+9335 x^7 \log ^3(2) \left (1+\frac {\log (64)}{\log (2)}\right )+50625 x^2 \log (x)-421875 x^3 \left (1-\frac {6 \log (2)}{125}\right ) \log (x)-168750 x^4 \left (2-\frac {3 \log (2)}{250}\right ) \log (2) \log (x)-3375 x^6 \log ^2(2) \log (4) \log (x)-16875 x^5 \log ^2(2) \left (1+\frac {\log (16)}{\log (2)}\right ) \log (x)-6075 x \log ^2(x)+50625 x^2 \left (1-\frac {3 \log (2)}{125}\right ) \log ^2(x)+2025 x^4 \log (2) \log (4) \log ^2(x)+10125 x^3 \log (2) \left (1+\frac {\log (4)}{\log (2)}\right ) \log ^2(x)+243 \log ^3(x)-2025 x \log ^3(x)-405 x^2 \log (4) \log ^3(x)}{x \left (1166875 x^4+933500 x^5 \log (2)+280050 x^6 \log ^2(2)+37340 x^7 \log ^3(2)+1867 x^8 \log ^4(2)-562500 x^3 \log (x)-337500 x^4 \log (2) \log (x)-67500 x^5 \log ^2(2) \log (x)-4500 x^6 \log ^3(2) \log (x)+101250 x^2 \log ^2(x)+40500 x^3 \log (2) \log ^2(x)+4050 x^4 \log ^2(2) \log ^2(x)-8100 x \log ^3(x)-1620 x^2 \log (2) \log ^3(x)+243 \log ^4(x)\right )} \, dx\\ &=4 \int \left (-\frac {1}{x}-\frac {\log (2)}{5+x \log (2)}\right ) \, dx+4 \int \frac {x^3 \left (-140625 \log (8)-625 x (-1867+135 \log (2)) \log (8)-75 x^3 \log (2) \left (-1867 \log (2)+15 \log ^2(2)-1867 \log (4)\right ) \log (8)+1867 x^5 \log ^3(2) \log (4) \log (8)-375 x^2 \log (2) (-1867 \log (4)+(-1867+45 \log (2)) \log (8))+9335 x^4 \log ^2(2) \log (8) \log (128)\right )-675 x^2 \log (8) \left (-75+x (625-30 \log (2))+5 x^4 \log ^2(2) \log (4)-x^2 \log (2) (-500+\log (8))+25 x^3 \log (2) \log (32)\right ) \log (x)+405 x (5+x \log (2)) \left (-3+25 x+5 x^2 \log (4)\right ) \log (8) \log ^2(x)-81 \left (-3+25 x+5 x^2 \log (4)\right ) \log (8) \log ^3(x)}{x \log (8) \left (1867 x^4 (5+x \log (2))^4-4500 x^3 (5+x \log (2))^3 \log (x)+4050 x^2 (5+x \log (2))^2 \log ^2(x)-1620 x (5+x \log (2)) \log ^3(x)+243 \log ^4(x)\right )} \, dx\\ &=-4 \log (x)-4 \log (5+x \log (2))+\frac {4 \int \frac {x^3 \left (-140625 \log (8)-625 x (-1867+135 \log (2)) \log (8)-75 x^3 \log (2) \left (-1867 \log (2)+15 \log ^2(2)-1867 \log (4)\right ) \log (8)+1867 x^5 \log ^3(2) \log (4) \log (8)-375 x^2 \log (2) (-1867 \log (4)+(-1867+45 \log (2)) \log (8))+9335 x^4 \log ^2(2) \log (8) \log (128)\right )-675 x^2 \log (8) \left (-75+x (625-30 \log (2))+5 x^4 \log ^2(2) \log (4)-x^2 \log (2) (-500+\log (8))+25 x^3 \log (2) \log (32)\right ) \log (x)+405 x (5+x \log (2)) \left (-3+25 x+5 x^2 \log (4)\right ) \log (8) \log ^2(x)-81 \left (-3+25 x+5 x^2 \log (4)\right ) \log (8) \log ^3(x)}{x \left (1867 x^4 (5+x \log (2))^4-4500 x^3 (5+x \log (2))^3 \log (x)+4050 x^2 (5+x \log (2))^2 \log ^2(x)-1620 x (5+x \log (2)) \log ^3(x)+243 \log ^4(x)\right )} \, dx}{\log (8)}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [F]  time = 0.60, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-2812500 x^3-2250000 x^4 \log (2)-675000 x^5 \log ^2(2)-90000 x^6 \log ^3(2)-4500 x^7 \log ^4(2)+\left (1012500 x^2+2812500 x^3+\left (607500 x^3+2812500 x^4\right ) \log (2)+\left (121500 x^4+1012500 x^5\right ) \log ^2(2)+\left (8100 x^5+157500 x^6\right ) \log ^3(2)+9000 x^7 \log ^4(2)\right ) \log (x)+\left (-121500 x-1012500 x^2+\left (-48600 x^2-810000 x^3\right ) \log (2)+\left (-4860 x^3-202500 x^4\right ) \log ^2(2)-16200 x^5 \log ^3(2)\right ) \log ^2(x)+\left (4860+121500 x+\left (972 x+72900 x^2\right ) \log (2)+9720 x^3 \log ^2(2)\right ) \log ^3(x)+(-4860-1944 x \log (2)) \log ^4(x)}{5834375 x^5+5834375 x^6 \log (2)+2333750 x^7 \log ^2(2)+466750 x^8 \log ^3(2)+46675 x^9 \log ^4(2)+1867 x^{10} \log ^5(2)+\left (-2812500 x^4-2250000 x^5 \log (2)-675000 x^6 \log ^2(2)-90000 x^7 \log ^3(2)-4500 x^8 \log ^4(2)\right ) \log (x)+\left (506250 x^3+303750 x^4 \log (2)+60750 x^5 \log ^2(2)+4050 x^6 \log ^3(2)\right ) \log ^2(x)+\left (-40500 x^2-16200 x^3 \log (2)-1620 x^4 \log ^2(2)\right ) \log ^3(x)+\left (1215 x+243 x^2 \log (2)\right ) \log ^4(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(-2812500*x^3 - 2250000*x^4*Log[2] - 675000*x^5*Log[2]^2 - 90000*x^6*Log[2]^3 - 4500*x^7*Log[2]^4 +
(1012500*x^2 + 2812500*x^3 + (607500*x^3 + 2812500*x^4)*Log[2] + (121500*x^4 + 1012500*x^5)*Log[2]^2 + (8100*x
^5 + 157500*x^6)*Log[2]^3 + 9000*x^7*Log[2]^4)*Log[x] + (-121500*x - 1012500*x^2 + (-48600*x^2 - 810000*x^3)*L
og[2] + (-4860*x^3 - 202500*x^4)*Log[2]^2 - 16200*x^5*Log[2]^3)*Log[x]^2 + (4860 + 121500*x + (972*x + 72900*x
^2)*Log[2] + 9720*x^3*Log[2]^2)*Log[x]^3 + (-4860 - 1944*x*Log[2])*Log[x]^4)/(5834375*x^5 + 5834375*x^6*Log[2]
+ 2333750*x^7*Log[2]^2 + 466750*x^8*Log[2]^3 + 46675*x^9*Log[2]^4 + 1867*x^10*Log[2]^5 + (-2812500*x^4 - 2250
000*x^5*Log[2] - 675000*x^6*Log[2]^2 - 90000*x^7*Log[2]^3 - 4500*x^8*Log[2]^4)*Log[x] + (506250*x^3 + 303750*x
^4*Log[2] + 60750*x^5*Log[2]^2 + 4050*x^6*Log[2]^3)*Log[x]^2 + (-40500*x^2 - 16200*x^3*Log[2] - 1620*x^4*Log[2
]^2)*Log[x]^3 + (1215*x + 243*x^2*Log[2])*Log[x]^4),x]

[Out]

Integrate[(-2812500*x^3 - 2250000*x^4*Log[2] - 675000*x^5*Log[2]^2 - 90000*x^6*Log[2]^3 - 4500*x^7*Log[2]^4 +
(1012500*x^2 + 2812500*x^3 + (607500*x^3 + 2812500*x^4)*Log[2] + (121500*x^4 + 1012500*x^5)*Log[2]^2 + (8100*x
^5 + 157500*x^6)*Log[2]^3 + 9000*x^7*Log[2]^4)*Log[x] + (-121500*x - 1012500*x^2 + (-48600*x^2 - 810000*x^3)*L
og[2] + (-4860*x^3 - 202500*x^4)*Log[2]^2 - 16200*x^5*Log[2]^3)*Log[x]^2 + (4860 + 121500*x + (972*x + 72900*x
^2)*Log[2] + 9720*x^3*Log[2]^2)*Log[x]^3 + (-4860 - 1944*x*Log[2])*Log[x]^4)/(5834375*x^5 + 5834375*x^6*Log[2]
+ 2333750*x^7*Log[2]^2 + 466750*x^8*Log[2]^3 + 46675*x^9*Log[2]^4 + 1867*x^10*Log[2]^5 + (-2812500*x^4 - 2250
000*x^5*Log[2] - 675000*x^6*Log[2]^2 - 90000*x^7*Log[2]^3 - 4500*x^8*Log[2]^4)*Log[x] + (506250*x^3 + 303750*x
^4*Log[2] + 60750*x^5*Log[2]^2 + 4050*x^6*Log[2]^3)*Log[x]^2 + (-40500*x^2 - 16200*x^3*Log[2] - 1620*x^4*Log[2
]^2)*Log[x]^3 + (1215*x + 243*x^2*Log[2])*Log[x]^4), x]

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fricas [B]  time = 1.06, size = 138, normalized size = 5.75 \begin {gather*} \log \left (1867 \, x^{8} \log \relax (2)^{4} + 37340 \, x^{7} \log \relax (2)^{3} + 280050 \, x^{6} \log \relax (2)^{2} + 933500 \, x^{5} \log \relax (2) + 1166875 \, x^{4} - 1620 \, {\left (x^{2} \log \relax (2) + 5 \, x\right )} \log \relax (x)^{3} + 243 \, \log \relax (x)^{4} + 4050 \, {\left (x^{4} \log \relax (2)^{2} + 10 \, x^{3} \log \relax (2) + 25 \, x^{2}\right )} \log \relax (x)^{2} - 4500 \, {\left (x^{6} \log \relax (2)^{3} + 15 \, x^{5} \log \relax (2)^{2} + 75 \, x^{4} \log \relax (2) + 125 \, x^{3}\right )} \log \relax (x)\right ) - 4 \, \log \left (x^{2} \log \relax (2) + 5 \, x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-1944*x*log(2)-4860)*log(x)^4+(9720*x^3*log(2)^2+(72900*x^2+972*x)*log(2)+121500*x+4860)*log(x)^3+
(-16200*x^5*log(2)^3+(-202500*x^4-4860*x^3)*log(2)^2+(-810000*x^3-48600*x^2)*log(2)-1012500*x^2-121500*x)*log(
x)^2+(9000*x^7*log(2)^4+(157500*x^6+8100*x^5)*log(2)^3+(1012500*x^5+121500*x^4)*log(2)^2+(2812500*x^4+607500*x
^3)*log(2)+2812500*x^3+1012500*x^2)*log(x)-4500*x^7*log(2)^4-90000*x^6*log(2)^3-675000*x^5*log(2)^2-2250000*x^
4*log(2)-2812500*x^3)/((243*x^2*log(2)+1215*x)*log(x)^4+(-1620*x^4*log(2)^2-16200*x^3*log(2)-40500*x^2)*log(x)
^3+(4050*x^6*log(2)^3+60750*x^5*log(2)^2+303750*x^4*log(2)+506250*x^3)*log(x)^2+(-4500*x^8*log(2)^4-90000*x^7*
log(2)^3-675000*x^6*log(2)^2-2250000*x^5*log(2)-2812500*x^4)*log(x)+1867*x^10*log(2)^5+46675*x^9*log(2)^4+4667
50*x^8*log(2)^3+2333750*x^7*log(2)^2+5834375*x^6*log(2)+5834375*x^5),x, algorithm="fricas")

[Out]

log(1867*x^8*log(2)^4 + 37340*x^7*log(2)^3 + 280050*x^6*log(2)^2 + 933500*x^5*log(2) + 1166875*x^4 - 1620*(x^2
*log(2) + 5*x)*log(x)^3 + 243*log(x)^4 + 4050*(x^4*log(2)^2 + 10*x^3*log(2) + 25*x^2)*log(x)^2 - 4500*(x^6*log
(2)^3 + 15*x^5*log(2)^2 + 75*x^4*log(2) + 125*x^3)*log(x)) - 4*log(x^2*log(2) + 5*x)

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giac [B]  time = 6.14, size = 150, normalized size = 6.25 \begin {gather*} \log \left (1867 \, x^{8} \log \relax (2)^{4} + 37340 \, x^{7} \log \relax (2)^{3} - 4500 \, x^{6} \log \relax (2)^{3} \log \relax (x) + 280050 \, x^{6} \log \relax (2)^{2} - 67500 \, x^{5} \log \relax (2)^{2} \log \relax (x) + 4050 \, x^{4} \log \relax (2)^{2} \log \relax (x)^{2} + 933500 \, x^{5} \log \relax (2) - 337500 \, x^{4} \log \relax (2) \log \relax (x) + 40500 \, x^{3} \log \relax (2) \log \relax (x)^{2} - 1620 \, x^{2} \log \relax (2) \log \relax (x)^{3} + 1166875 \, x^{4} - 562500 \, x^{3} \log \relax (x) + 101250 \, x^{2} \log \relax (x)^{2} - 8100 \, x \log \relax (x)^{3} + 243 \, \log \relax (x)^{4}\right ) - 4 \, \log \left (x \log \relax (2) + 5\right ) - 4 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-1944*x*log(2)-4860)*log(x)^4+(9720*x^3*log(2)^2+(72900*x^2+972*x)*log(2)+121500*x+4860)*log(x)^3+
(-16200*x^5*log(2)^3+(-202500*x^4-4860*x^3)*log(2)^2+(-810000*x^3-48600*x^2)*log(2)-1012500*x^2-121500*x)*log(
x)^2+(9000*x^7*log(2)^4+(157500*x^6+8100*x^5)*log(2)^3+(1012500*x^5+121500*x^4)*log(2)^2+(2812500*x^4+607500*x
^3)*log(2)+2812500*x^3+1012500*x^2)*log(x)-4500*x^7*log(2)^4-90000*x^6*log(2)^3-675000*x^5*log(2)^2-2250000*x^
4*log(2)-2812500*x^3)/((243*x^2*log(2)+1215*x)*log(x)^4+(-1620*x^4*log(2)^2-16200*x^3*log(2)-40500*x^2)*log(x)
^3+(4050*x^6*log(2)^3+60750*x^5*log(2)^2+303750*x^4*log(2)+506250*x^3)*log(x)^2+(-4500*x^8*log(2)^4-90000*x^7*
log(2)^3-675000*x^6*log(2)^2-2250000*x^5*log(2)-2812500*x^4)*log(x)+1867*x^10*log(2)^5+46675*x^9*log(2)^4+4667
50*x^8*log(2)^3+2333750*x^7*log(2)^2+5834375*x^6*log(2)+5834375*x^5),x, algorithm="giac")

[Out]

log(1867*x^8*log(2)^4 + 37340*x^7*log(2)^3 - 4500*x^6*log(2)^3*log(x) + 280050*x^6*log(2)^2 - 67500*x^5*log(2)
^2*log(x) + 4050*x^4*log(2)^2*log(x)^2 + 933500*x^5*log(2) - 337500*x^4*log(2)*log(x) + 40500*x^3*log(2)*log(x
)^2 - 1620*x^2*log(2)*log(x)^3 + 1166875*x^4 - 562500*x^3*log(x) + 101250*x^2*log(x)^2 - 8100*x*log(x)^3 + 243
*log(x)^4) - 4*log(x*log(2) + 5) - 4*log(x)

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maple [B]  time = 0.07, size = 137, normalized size = 5.71

method	result	size
risch	\(-4 \ln \left (x^{2} \ln \relax (2)+5 x \right )+\ln \left (\ln \relax (x )^{4}+\left (-\frac {20 x^{2} \ln \relax (2)}{3}-\frac {100 x}{3}\right ) \ln \relax (x )^{3}+\left (\frac {50 x^{4} \ln \relax (2)^{2}}{3}+\frac {500 x^{3} \ln \relax (2)}{3}+\frac {1250 x^{2}}{3}\right ) \ln \relax (x )^{2}+\left (-\frac {500 x^{6} \ln \relax (2)^{3}}{27}-\frac {2500 x^{5} \ln \relax (2)^{2}}{9}-\frac {12500 x^{4} \ln \relax (2)}{9}-\frac {62500 x^{3}}{27}\right ) \ln \relax (x )+\frac {1867 x^{8} \ln \relax (2)^{4}}{243}+\frac {37340 x^{7} \ln \relax (2)^{3}}{243}+\frac {93350 x^{6} \ln \relax (2)^{2}}{81}+\frac {933500 x^{5} \ln \relax (2)}{243}+\frac {1166875 x^{4}}{243}\right )\)	\(137\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-1944*x*ln(2)-4860)*ln(x)^4+(9720*x^3*ln(2)^2+(72900*x^2+972*x)*ln(2)+121500*x+4860)*ln(x)^3+(-16200*x^5
*ln(2)^3+(-202500*x^4-4860*x^3)*ln(2)^2+(-810000*x^3-48600*x^2)*ln(2)-1012500*x^2-121500*x)*ln(x)^2+(9000*x^7*
ln(2)^4+(157500*x^6+8100*x^5)*ln(2)^3+(1012500*x^5+121500*x^4)*ln(2)^2+(2812500*x^4+607500*x^3)*ln(2)+2812500*
x^3+1012500*x^2)*ln(x)-4500*x^7*ln(2)^4-90000*x^6*ln(2)^3-675000*x^5*ln(2)^2-2250000*x^4*ln(2)-2812500*x^3)/((
243*x^2*ln(2)+1215*x)*ln(x)^4+(-1620*x^4*ln(2)^2-16200*x^3*ln(2)-40500*x^2)*ln(x)^3+(4050*x^6*ln(2)^3+60750*x^
5*ln(2)^2+303750*x^4*ln(2)+506250*x^3)*ln(x)^2+(-4500*x^8*ln(2)^4-90000*x^7*ln(2)^3-675000*x^6*ln(2)^2-2250000
*x^5*ln(2)-2812500*x^4)*ln(x)+1867*x^10*ln(2)^5+46675*x^9*ln(2)^4+466750*x^8*ln(2)^3+2333750*x^7*ln(2)^2+58343
75*x^6*ln(2)+5834375*x^5),x,method=_RETURNVERBOSE)

[Out]

-4*ln(x^2*ln(2)+5*x)+ln(ln(x)^4+(-20/3*x^2*ln(2)-100/3*x)*ln(x)^3+(50/3*x^4*ln(2)^2+500/3*x^3*ln(2)+1250/3*x^2
)*ln(x)^2+(-500/27*x^6*ln(2)^3-2500/9*x^5*ln(2)^2-12500/9*x^4*ln(2)-62500/27*x^3)*ln(x)+1867/243*x^8*ln(2)^4+3
7340/243*x^7*ln(2)^3+93350/81*x^6*ln(2)^2+933500/243*x^5*ln(2)+1166875/243*x^4)

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maxima [B]  time = 0.52, size = 136, normalized size = 5.67 \begin {gather*} \log \left (\frac {1867}{243} \, x^{8} \log \relax (2)^{4} + \frac {37340}{243} \, x^{7} \log \relax (2)^{3} + \frac {93350}{81} \, x^{6} \log \relax (2)^{2} + \frac {933500}{243} \, x^{5} \log \relax (2) + \frac {1166875}{243} \, x^{4} - \frac {20}{3} \, {\left (x^{2} \log \relax (2) + 5 \, x\right )} \log \relax (x)^{3} + \log \relax (x)^{4} + \frac {50}{3} \, {\left (x^{4} \log \relax (2)^{2} + 10 \, x^{3} \log \relax (2) + 25 \, x^{2}\right )} \log \relax (x)^{2} - \frac {500}{27} \, {\left (x^{6} \log \relax (2)^{3} + 15 \, x^{5} \log \relax (2)^{2} + 75 \, x^{4} \log \relax (2) + 125 \, x^{3}\right )} \log \relax (x)\right ) - 4 \, \log \left (x \log \relax (2) + 5\right ) - 4 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-1944*x*log(2)-4860)*log(x)^4+(9720*x^3*log(2)^2+(72900*x^2+972*x)*log(2)+121500*x+4860)*log(x)^3+
(-16200*x^5*log(2)^3+(-202500*x^4-4860*x^3)*log(2)^2+(-810000*x^3-48600*x^2)*log(2)-1012500*x^2-121500*x)*log(
x)^2+(9000*x^7*log(2)^4+(157500*x^6+8100*x^5)*log(2)^3+(1012500*x^5+121500*x^4)*log(2)^2+(2812500*x^4+607500*x
^3)*log(2)+2812500*x^3+1012500*x^2)*log(x)-4500*x^7*log(2)^4-90000*x^6*log(2)^3-675000*x^5*log(2)^2-2250000*x^
4*log(2)-2812500*x^3)/((243*x^2*log(2)+1215*x)*log(x)^4+(-1620*x^4*log(2)^2-16200*x^3*log(2)-40500*x^2)*log(x)
^3+(4050*x^6*log(2)^3+60750*x^5*log(2)^2+303750*x^4*log(2)+506250*x^3)*log(x)^2+(-4500*x^8*log(2)^4-90000*x^7*
log(2)^3-675000*x^6*log(2)^2-2250000*x^5*log(2)-2812500*x^4)*log(x)+1867*x^10*log(2)^5+46675*x^9*log(2)^4+4667
50*x^8*log(2)^3+2333750*x^7*log(2)^2+5834375*x^6*log(2)+5834375*x^5),x, algorithm="maxima")

[Out]

log(1867/243*x^8*log(2)^4 + 37340/243*x^7*log(2)^3 + 93350/81*x^6*log(2)^2 + 933500/243*x^5*log(2) + 1166875/2
43*x^4 - 20/3*(x^2*log(2) + 5*x)*log(x)^3 + log(x)^4 + 50/3*(x^4*log(2)^2 + 10*x^3*log(2) + 25*x^2)*log(x)^2 -
500/27*(x^6*log(2)^3 + 15*x^5*log(2)^2 + 75*x^4*log(2) + 125*x^3)*log(x)) - 4*log(x*log(2) + 5) - 4*log(x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {675000\,x^5\,{\ln \relax (2)}^2+90000\,x^6\,{\ln \relax (2)}^3+4500\,x^7\,{\ln \relax (2)}^4-{\ln \relax (x)}^3\,\left (121500\,x+9720\,x^3\,{\ln \relax (2)}^2+\ln \relax (2)\,\left (72900\,x^2+972\,x\right )+4860\right )+{\ln \relax (x)}^4\,\left (1944\,x\,\ln \relax (2)+4860\right )-\ln \relax (x)\,\left (9000\,x^7\,{\ln \relax (2)}^4+\ln \relax (2)\,\left (2812500\,x^4+607500\,x^3\right )+1012500\,x^2+2812500\,x^3+{\ln \relax (2)}^3\,\left (157500\,x^6+8100\,x^5\right )+{\ln \relax (2)}^2\,\left (1012500\,x^5+121500\,x^4\right )\right )+2250000\,x^4\,\ln \relax (2)+{\ln \relax (x)}^2\,\left (121500\,x+16200\,x^5\,{\ln \relax (2)}^3+\ln \relax (2)\,\left (810000\,x^3+48600\,x^2\right )+1012500\,x^2+{\ln \relax (2)}^2\,\left (202500\,x^4+4860\,x^3\right )\right )+2812500\,x^3}{2333750\,x^7\,{\ln \relax (2)}^2+466750\,x^8\,{\ln \relax (2)}^3+46675\,x^9\,{\ln \relax (2)}^4+1867\,x^{10}\,{\ln \relax (2)}^5+{\ln \relax (x)}^4\,\left (243\,\ln \relax (2)\,x^2+1215\,x\right )-\ln \relax (x)\,\left (4500\,{\ln \relax (2)}^4\,x^8+90000\,{\ln \relax (2)}^3\,x^7+675000\,{\ln \relax (2)}^2\,x^6+2250000\,\ln \relax (2)\,x^5+2812500\,x^4\right )+5834375\,x^6\,\ln \relax (2)+5834375\,x^5-{\ln \relax (x)}^3\,\left (1620\,{\ln \relax (2)}^2\,x^4+16200\,\ln \relax (2)\,x^3+40500\,x^2\right )+{\ln \relax (x)}^2\,\left (4050\,{\ln \relax (2)}^3\,x^6+60750\,{\ln \relax (2)}^2\,x^5+303750\,\ln \relax (2)\,x^4+506250\,x^3\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(675000*x^5*log(2)^2 + 90000*x^6*log(2)^3 + 4500*x^7*log(2)^4 - log(x)^3*(121500*x + 9720*x^3*log(2)^2 +
log(2)*(972*x + 72900*x^2) + 4860) + log(x)^4*(1944*x*log(2) + 4860) - log(x)*(9000*x^7*log(2)^4 + log(2)*(607
500*x^3 + 2812500*x^4) + 1012500*x^2 + 2812500*x^3 + log(2)^3*(8100*x^5 + 157500*x^6) + log(2)^2*(121500*x^4 +
1012500*x^5)) + 2250000*x^4*log(2) + log(x)^2*(121500*x + 16200*x^5*log(2)^3 + log(2)*(48600*x^2 + 810000*x^3
) + 1012500*x^2 + log(2)^2*(4860*x^3 + 202500*x^4)) + 2812500*x^3)/(2333750*x^7*log(2)^2 + 466750*x^8*log(2)^3
+ 46675*x^9*log(2)^4 + 1867*x^10*log(2)^5 + log(x)^4*(1215*x + 243*x^2*log(2)) - log(x)*(675000*x^6*log(2)^2
+ 90000*x^7*log(2)^3 + 4500*x^8*log(2)^4 + 2250000*x^5*log(2) + 2812500*x^4) + 5834375*x^6*log(2) + 5834375*x^
5 - log(x)^3*(1620*x^4*log(2)^2 + 16200*x^3*log(2) + 40500*x^2) + log(x)^2*(60750*x^5*log(2)^2 + 4050*x^6*log(
2)^3 + 303750*x^4*log(2) + 506250*x^3)),x)

[Out]

int(-(675000*x^5*log(2)^2 + 90000*x^6*log(2)^3 + 4500*x^7*log(2)^4 - log(x)^3*(121500*x + 9720*x^3*log(2)^2 +
log(2)*(972*x + 72900*x^2) + 4860) + log(x)^4*(1944*x*log(2) + 4860) - log(x)*(9000*x^7*log(2)^4 + log(2)*(607
500*x^3 + 2812500*x^4) + 1012500*x^2 + 2812500*x^3 + log(2)^3*(8100*x^5 + 157500*x^6) + log(2)^2*(121500*x^4 +
1012500*x^5)) + 2250000*x^4*log(2) + log(x)^2*(121500*x + 16200*x^5*log(2)^3 + log(2)*(48600*x^2 + 810000*x^3
) + 1012500*x^2 + log(2)^2*(4860*x^3 + 202500*x^4)) + 2812500*x^3)/(2333750*x^7*log(2)^2 + 466750*x^8*log(2)^3
+ 46675*x^9*log(2)^4 + 1867*x^10*log(2)^5 + log(x)^4*(1215*x + 243*x^2*log(2)) - log(x)*(675000*x^6*log(2)^2
+ 90000*x^7*log(2)^3 + 4500*x^8*log(2)^4 + 2250000*x^5*log(2) + 2812500*x^4) + 5834375*x^6*log(2) + 5834375*x^
5 - log(x)^3*(1620*x^4*log(2)^2 + 16200*x^3*log(2) + 40500*x^2) + log(x)^2*(60750*x^5*log(2)^2 + 4050*x^6*log(
2)^3 + 303750*x^4*log(2) + 506250*x^3)), x)

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sympy [B]  time = 1.98, size = 173, normalized size = 7.21 \begin {gather*} - 4 \log {\left (x^{2} \log {\relax (2 )} + 5 x \right )} + \log {\left (\frac {1867 x^{8} \log {\relax (2 )}^{4}}{243} + \frac {37340 x^{7} \log {\relax (2 )}^{3}}{243} + \frac {93350 x^{6} \log {\relax (2 )}^{2}}{81} + \frac {933500 x^{5} \log {\relax (2 )}}{243} + \frac {1166875 x^{4}}{243} + \left (- \frac {20 x^{2} \log {\relax (2 )}}{3} - \frac {100 x}{3}\right ) \log {\relax (x )}^{3} + \left (\frac {50 x^{4} \log {\relax (2 )}^{2}}{3} + \frac {500 x^{3} \log {\relax (2 )}}{3} + \frac {1250 x^{2}}{3}\right ) \log {\relax (x )}^{2} + \left (- \frac {500 x^{6} \log {\relax (2 )}^{3}}{27} - \frac {2500 x^{5} \log {\relax (2 )}^{2}}{9} - \frac {12500 x^{4} \log {\relax (2 )}}{9} - \frac {62500 x^{3}}{27}\right ) \log {\relax (x )} + \log {\relax (x )}^{4} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-1944*x*ln(2)-4860)*ln(x)**4+(9720*x**3*ln(2)**2+(72900*x**2+972*x)*ln(2)+121500*x+4860)*ln(x)**3+
(-16200*x**5*ln(2)**3+(-202500*x**4-4860*x**3)*ln(2)**2+(-810000*x**3-48600*x**2)*ln(2)-1012500*x**2-121500*x)
*ln(x)**2+(9000*x**7*ln(2)**4+(157500*x**6+8100*x**5)*ln(2)**3+(1012500*x**5+121500*x**4)*ln(2)**2+(2812500*x*
*4+607500*x**3)*ln(2)+2812500*x**3+1012500*x**2)*ln(x)-4500*x**7*ln(2)**4-90000*x**6*ln(2)**3-675000*x**5*ln(2
)**2-2250000*x**4*ln(2)-2812500*x**3)/((243*x**2*ln(2)+1215*x)*ln(x)**4+(-1620*x**4*ln(2)**2-16200*x**3*ln(2)-
40500*x**2)*ln(x)**3+(4050*x**6*ln(2)**3+60750*x**5*ln(2)**2+303750*x**4*ln(2)+506250*x**3)*ln(x)**2+(-4500*x*
*8*ln(2)**4-90000*x**7*ln(2)**3-675000*x**6*ln(2)**2-2250000*x**5*ln(2)-2812500*x**4)*ln(x)+1867*x**10*ln(2)**
5+46675*x**9*ln(2)**4+466750*x**8*ln(2)**3+2333750*x**7*ln(2)**2+5834375*x**6*ln(2)+5834375*x**5),x)

[Out]

-4*log(x**2*log(2) + 5*x) + log(1867*x**8*log(2)**4/243 + 37340*x**7*log(2)**3/243 + 93350*x**6*log(2)**2/81 +
933500*x**5*log(2)/243 + 1166875*x**4/243 + (-20*x**2*log(2)/3 - 100*x/3)*log(x)**3 + (50*x**4*log(2)**2/3 +
500*x**3*log(2)/3 + 1250*x**2/3)*log(x)**2 + (-500*x**6*log(2)**3/27 - 2500*x**5*log(2)**2/9 - 12500*x**4*log(
2)/9 - 62500*x**3/27)*log(x) + log(x)**4)

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