3.80.49 \(\int \frac {-645248-249920 x+38032 x^2+848 x^3+4 x^4+(1290496-147680 x-4512 x^2-24 x^3) \log (x^2)+(4544 x+32 x^2) \log ^2(x^2)}{6505390336 x+13194031104 x^2+10126522112 x^3+3531451392 x^4+501133920 x^5+12434688 x^6+125552 x^7+576 x^8+x^9+(-161312 x-163584 x^2-42608 x^3-576 x^4-2 x^5) \log (5)+x \log ^2(5)+(-52043122688 x-79530687488 x^2-41246833152 x^3-7628194560 x^4-194974080 x^5-1990464 x^6-9184 x^7-16 x^8+(645248 x+331712 x^2+4576 x^3+16 x^4) \log (5)) \log (x^2)+(156129368064 x+160527378432 x^2+43476810240 x^3+1146178560 x^4+11832960 x^5+54912 x^6+96 x^7+(-645248 x-9088 x^2-32 x^3) \log (5)) \log ^2(x^2)+(-208172490752 x-109950259200 x^2-2993950720 x^3-31262720 x^4-145920 x^5-256 x^6) \log ^3(x^2)+(104086245376 x+2932006912 x^2+30971904 x^3+145408 x^4+256 x^5) \log ^4(x^2)} \, dx\)

Optimal. Leaf size=27 \[ \frac {1}{\log (5)-(-142-x)^2 \left (-2-x+4 \log \left (x^2\right )\right )^2} \]

________________________________________________________________________________________

Rubi [F]  time = 67.92, 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 {-645248-249920 x+38032 x^2+848 x^3+4 x^4+\left (1290496-147680 x-4512 x^2-24 x^3\right ) \log \left (x^2\right )+\left (4544 x+32 x^2\right ) \log ^2\left (x^2\right )}{6505390336 x+13194031104 x^2+10126522112 x^3+3531451392 x^4+501133920 x^5+12434688 x^6+125552 x^7+576 x^8+x^9+\left (-161312 x-163584 x^2-42608 x^3-576 x^4-2 x^5\right ) \log (5)+x \log ^2(5)+\left (-52043122688 x-79530687488 x^2-41246833152 x^3-7628194560 x^4-194974080 x^5-1990464 x^6-9184 x^7-16 x^8+\left (645248 x+331712 x^2+4576 x^3+16 x^4\right ) \log (5)\right ) \log \left (x^2\right )+\left (156129368064 x+160527378432 x^2+43476810240 x^3+1146178560 x^4+11832960 x^5+54912 x^6+96 x^7+\left (-645248 x-9088 x^2-32 x^3\right ) \log (5)\right ) \log ^2\left (x^2\right )+\left (-208172490752 x-109950259200 x^2-2993950720 x^3-31262720 x^4-145920 x^5-256 x^6\right ) \log ^3\left (x^2\right )+\left (104086245376 x+2932006912 x^2+30971904 x^3+145408 x^4+256 x^5\right ) \log ^4\left (x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-645248 - 249920*x + 38032*x^2 + 848*x^3 + 4*x^4 + (1290496 - 147680*x - 4512*x^2 - 24*x^3)*Log[x^2] + (4
544*x + 32*x^2)*Log[x^2]^2)/(6505390336*x + 13194031104*x^2 + 10126522112*x^3 + 3531451392*x^4 + 501133920*x^5
+ 12434688*x^6 + 125552*x^7 + 576*x^8 + x^9 + (-161312*x - 163584*x^2 - 42608*x^3 - 576*x^4 - 2*x^5)*Log[5] +
x*Log[5]^2 + (-52043122688*x - 79530687488*x^2 - 41246833152*x^3 - 7628194560*x^4 - 194974080*x^5 - 1990464*x
^6 - 9184*x^7 - 16*x^8 + (645248*x + 331712*x^2 + 4576*x^3 + 16*x^4)*Log[5])*Log[x^2] + (156129368064*x + 1605
27378432*x^2 + 43476810240*x^3 + 1146178560*x^4 + 11832960*x^5 + 54912*x^6 + 96*x^7 + (-645248*x - 9088*x^2 -
32*x^3)*Log[5])*Log[x^2]^2 + (-208172490752*x - 109950259200*x^2 - 2993950720*x^3 - 31262720*x^4 - 145920*x^5
- 256*x^6)*Log[x^2]^3 + (104086245376*x + 2932006912*x^2 + 30971904*x^3 + 145408*x^4 + 256*x^5)*Log[x^2]^4),x]

[Out]

-251056*Defer[Int][(81792*x + 21304*x^2 + 288*x^3 + x^4 + 80656*(1 - Log[5]/80656) - 8*(2 + x)*(142 + x)^2*Log
[x^2] + 16*(142 + x)^2*Log[x^2]^2)^(-2), x] + 3113321600*Defer[Int][1/((-142 - x)*(81792*x + 21304*x^2 + 288*x
^3 + x^4 + 80656*(1 - Log[5]/80656) - 8*(2 + x)*(142 + x)^2*Log[x^2] + 16*(142 + x)^2*Log[x^2]^2)^2), x] + 2*(
18147600 - Log[5])*Defer[Int][1/((-142 - x)*(81792*x + 21304*x^2 + 288*x^3 + x^4 + 80656*(1 - Log[5]/80656) -
8*(2 + x)*(142 + x)^2*Log[x^2] + 16*(142 + x)^2*Log[x^2]^2)^2), x] - 645248*Defer[Int][1/(x*(81792*x + 21304*x
^2 + 288*x^3 + x^4 + 80656*(1 - Log[5]/80656) - 8*(2 + x)*(142 + x)^2*Log[x^2] + 16*(142 + x)^2*Log[x^2]^2)^2)
, x] + 36888*Defer[Int][x/(81792*x + 21304*x^2 + 288*x^3 + x^4 + 80656*(1 - Log[5]/80656) - 8*(2 + x)*(142 + x
)^2*Log[x^2] + 16*(142 + x)^2*Log[x^2]^2)^2, x] + 556*Defer[Int][x^2/(81792*x + 21304*x^2 + 288*x^3 + x^4 + 80
656*(1 - Log[5]/80656) - 8*(2 + x)*(142 + x)^2*Log[x^2] + 16*(142 + x)^2*Log[x^2]^2)^2, x] + 2*Defer[Int][x^3/
(81792*x + 21304*x^2 + 288*x^3 + x^4 + 80656*(1 - Log[5]/80656) - 8*(2 + x)*(142 + x)^2*Log[x^2] + 16*(142 + x
)^2*Log[x^2]^2)^2, x] + 3149616800*Defer[Int][1/((142 + x)*(81792*x + 21304*x^2 + 288*x^3 + x^4 + 80656*(1 - L
og[5]/80656) - 8*(2 + x)*(142 + x)^2*Log[x^2] + 16*(142 + x)^2*Log[x^2]^2)^2), x] - 143136*Defer[Int][Log[x^2]
/(81792*x + 21304*x^2 + 288*x^3 + x^4 + 80656*(1 - Log[5]/80656) - 8*(2 + x)*(142 + x)^2*Log[x^2] + 16*(142 +
x)^2*Log[x^2]^2)^2, x] + 87753728*Defer[Int][Log[x^2]/((-142 - x)*(81792*x + 21304*x^2 + 288*x^3 + x^4 + 80656
*(1 - Log[5]/80656) - 8*(2 + x)*(142 + x)^2*Log[x^2] + 16*(142 + x)^2*Log[x^2]^2)^2), x] + 1290496*Defer[Int][
Log[x^2]/(x*(81792*x + 21304*x^2 + 288*x^3 + x^4 + 80656*(1 - Log[5]/80656) - 8*(2 + x)*(142 + x)^2*Log[x^2] +
16*(142 + x)^2*Log[x^2]^2)^2), x] - 2208*Defer[Int][(x*Log[x^2])/(81792*x + 21304*x^2 + 288*x^3 + x^4 + 80656
*(1 - Log[5]/80656) - 8*(2 + x)*(142 + x)^2*Log[x^2] + 16*(142 + x)^2*Log[x^2]^2)^2, x] - 8*Defer[Int][(x^2*Lo
g[x^2])/(81792*x + 21304*x^2 + 288*x^3 + x^4 + 80656*(1 - Log[5]/80656) - 8*(2 + x)*(142 + x)^2*Log[x^2] + 16*
(142 + x)^2*Log[x^2]^2)^2, x] + 87753728*Defer[Int][Log[x^2]/((142 + x)*(81792*x + 21304*x^2 + 288*x^3 + x^4 +
80656*(1 - Log[5]/80656) - 8*(2 + x)*(142 + x)^2*Log[x^2] + 16*(142 + x)^2*Log[x^2]^2)^2), x] + 2*Defer[Int][
1/((142 + x)*(81792*x + 21304*x^2 + 288*x^3 + x^4 + 80656*(1 - Log[5]/80656) - 8*(2 + x)*(142 + x)^2*Log[x^2]
+ 16*(142 + x)^2*Log[x^2]^2)), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-645248-249920 x+38032 x^2+848 x^3+4 x^4+\left (1290496-147680 x-4512 x^2-24 x^3\right ) \log \left (x^2\right )+\left (4544 x+32 x^2\right ) \log ^2\left (x^2\right )}{13194031104 x^2+10126522112 x^3+3531451392 x^4+501133920 x^5+12434688 x^6+125552 x^7+576 x^8+x^9+\left (-161312 x-163584 x^2-42608 x^3-576 x^4-2 x^5\right ) \log (5)+x \left (6505390336+\log ^2(5)\right )+\left (-52043122688 x-79530687488 x^2-41246833152 x^3-7628194560 x^4-194974080 x^5-1990464 x^6-9184 x^7-16 x^8+\left (645248 x+331712 x^2+4576 x^3+16 x^4\right ) \log (5)\right ) \log \left (x^2\right )+\left (156129368064 x+160527378432 x^2+43476810240 x^3+1146178560 x^4+11832960 x^5+54912 x^6+96 x^7+\left (-645248 x-9088 x^2-32 x^3\right ) \log (5)\right ) \log ^2\left (x^2\right )+\left (-208172490752 x-109950259200 x^2-2993950720 x^3-31262720 x^4-145920 x^5-256 x^6\right ) \log ^3\left (x^2\right )+\left (104086245376 x+2932006912 x^2+30971904 x^3+145408 x^4+256 x^5\right ) \log ^4\left (x^2\right )} \, dx\\ &=\int \frac {4 (142+x) \left (-1136-432 x+70 x^2+x^3+\left (2272-276 x-6 x^2\right ) \log \left (x^2\right )+8 x \log ^2\left (x^2\right )\right )}{x \left (81792 x+21304 x^2+288 x^3+x^4+80656 \left (1-\frac {\log (5)}{80656}\right )-8 (2+x) (142+x)^2 \log \left (x^2\right )+16 (142+x)^2 \log ^2\left (x^2\right )\right )^2} \, dx\\ &=4 \int \frac {(142+x) \left (-1136-432 x+70 x^2+x^3+\left (2272-276 x-6 x^2\right ) \log \left (x^2\right )+8 x \log ^2\left (x^2\right )\right )}{x \left (81792 x+21304 x^2+288 x^3+x^4+80656 \left (1-\frac {\log (5)}{80656}\right )-8 (2+x) (142+x)^2 \log \left (x^2\right )+16 (142+x)^2 \log ^2\left (x^2\right )\right )^2} \, dx\\ &=4 \int \left (\frac {-45812608+2493520 x^2+57920 x^3+420 x^4+x^5-18147600 x \left (1-\frac {\log (5)}{18147600}\right )[phone] \log \left (x^2\right )-9517408 x \log \left (x^2\right )-228336 x^2 \log \left (x^2\right )-1672 x^3 \log \left (x^2\right )-4 x^4 \log \left (x^2\right )}{2 x (142+x) \left (81792 x+21304 x^2+288 x^3+x^4+80656 \left (1-\frac {\log (5)}{80656}\right )-322624 \log \left (x^2\right )-165856 x \log \left (x^2\right )-2288 x^2 \log \left (x^2\right )-8 x^3 \log \left (x^2\right )+322624 \log ^2\left (x^2\right )+4544 x \log ^2\left (x^2\right )+16 x^2 \log ^2\left (x^2\right )\right )^2}+\frac {1}{2 (142+x) \left (81792 x+21304 x^2+288 x^3+x^4+80656 \left (1-\frac {\log (5)}{80656}\right )-322624 \log \left (x^2\right )-165856 x \log \left (x^2\right )-2288 x^2 \log \left (x^2\right )-8 x^3 \log \left (x^2\right )+322624 \log ^2\left (x^2\right )+4544 x \log ^2\left (x^2\right )+16 x^2 \log ^2\left (x^2\right )\right )}\right ) \, dx\\ &=2 \int \frac {-45812608+2493520 x^2+57920 x^3+420 x^4+x^5-18147600 x \left (1-\frac {\log (5)}{18147600}\right )[phone] \log \left (x^2\right )-9517408 x \log \left (x^2\right )-228336 x^2 \log \left (x^2\right )-1672 x^3 \log \left (x^2\right )-4 x^4 \log \left (x^2\right )}{x (142+x) \left (81792 x+21304 x^2+288 x^3+x^4+80656 \left (1-\frac {\log (5)}{80656}\right )-322624 \log \left (x^2\right )-165856 x \log \left (x^2\right )-2288 x^2 \log \left (x^2\right )-8 x^3 \log \left (x^2\right )+322624 \log ^2\left (x^2\right )+4544 x \log ^2\left (x^2\right )+16 x^2 \log ^2\left (x^2\right )\right )^2} \, dx+2 \int \frac {1}{(142+x) \left (81792 x+21304 x^2+288 x^3+x^4+80656 \left (1-\frac {\log (5)}{80656}\right )-322624 \log \left (x^2\right )-165856 x \log \left (x^2\right )-2288 x^2 \log \left (x^2\right )-8 x^3 \log \left (x^2\right )+322624 \log ^2\left (x^2\right )+4544 x \log ^2\left (x^2\right )+16 x^2 \log ^2\left (x^2\right )\right )} \, dx\\ &=2 \int \frac {-45812608+2493520 x^2+57920 x^3+420 x^4+x^5+x (-18147600+\log (5))-4 (-8+x) (142+x)^3 \log \left (x^2\right )}{x (142+x) \left (81792 x+21304 x^2+288 x^3+x^4+80656 \left (1-\frac {\log (5)}{80656}\right )-8 (2+x) (142+x)^2 \log \left (x^2\right )+16 (142+x)^2 \log ^2\left (x^2\right )\right )^2} \, dx+2 \int \frac {1}{(142+x) \left (81792 x+21304 x^2+288 x^3+x^4+80656 \left (1-\frac {\log (5)}{80656}\right )-8 (2+x) (142+x)^2 \log \left (x^2\right )+16 (142+x)^2 \log ^2\left (x^2\right )\right )} \, dx\\ &=2 \int \frac {1}{(142+x) \left (81792 x+21304 x^2+288 x^3+x^4+80656 \left (1-\frac {\log (5)}{80656}\right )-8 (2+x) (142+x)^2 \log \left (x^2\right )+16 (142+x)^2 \log ^2\left (x^2\right )\right )} \, dx+2 \int \left (\frac {-45812608+2493520 x^2+57920 x^3+420 x^4+x^5-18147600 x \left (1-\frac {\log (5)}{18147600}\right )[phone] \log \left (x^2\right )-9517408 x \log \left (x^2\right )-228336 x^2 \log \left (x^2\right )-1672 x^3 \log \left (x^2\right )-4 x^4 \log \left (x^2\right )}{142 x \left (81792 x+21304 x^2+288 x^3+x^4+80656 \left (1-\frac {\log (5)}{80656}\right )-322624 \log \left (x^2\right )-165856 x \log \left (x^2\right )-2288 x^2 \log \left (x^2\right )-8 x^3 \log \left (x^2\right )+322624 \log ^2\left (x^2\right )+4544 x \log ^2\left (x^2\right )+16 x^2 \log ^2\left (x^2\right )\right )^2}+\frac {45812608-2493520 x^2-57920 x^3-420 x^4-x^5+18147600 x \left (1-\frac {\log (5)}{18147600}\right )-91625216 \log \left (x^2\right )+9517408 x \log \left (x^2\right )+228336 x^2 \log \left (x^2\right )+1672 x^3 \log \left (x^2\right )+4 x^4 \log \left (x^2\right )}{142 (142+x) \left (81792 x+21304 x^2+288 x^3+x^4+80656 \left (1-\frac {\log (5)}{80656}\right )-322624 \log \left (x^2\right )-165856 x \log \left (x^2\right )-2288 x^2 \log \left (x^2\right )-8 x^3 \log \left (x^2\right )+322624 \log ^2\left (x^2\right )+4544 x \log ^2\left (x^2\right )+16 x^2 \log ^2\left (x^2\right )\right )^2}\right ) \, dx\\ &=\frac {1}{71} \int \frac {-45812608+2493520 x^2+57920 x^3+420 x^4+x^5-18147600 x \left (1-\frac {\log (5)}{18147600}\right )[phone] \log \left (x^2\right )-9517408 x \log \left (x^2\right )-228336 x^2 \log \left (x^2\right )-1672 x^3 \log \left (x^2\right )-4 x^4 \log \left (x^2\right )}{x \left (81792 x+21304 x^2+288 x^3+x^4+80656 \left (1-\frac {\log (5)}{80656}\right )-322624 \log \left (x^2\right )-165856 x \log \left (x^2\right )-2288 x^2 \log \left (x^2\right )-8 x^3 \log \left (x^2\right )+322624 \log ^2\left (x^2\right )+4544 x \log ^2\left (x^2\right )+16 x^2 \log ^2\left (x^2\right )\right )^2} \, dx+\frac {1}{71} \int \frac {45812608-2493520 x^2-57920 x^3-420 x^4-x^5+18147600 x \left (1-\frac {\log (5)}{18147600}\right )-91625216 \log \left (x^2\right )+9517408 x \log \left (x^2\right )+228336 x^2 \log \left (x^2\right )+1672 x^3 \log \left (x^2\right )+4 x^4 \log \left (x^2\right )}{(142+x) \left (81792 x+21304 x^2+288 x^3+x^4+80656 \left (1-\frac {\log (5)}{80656}\right )-322624 \log \left (x^2\right )-165856 x \log \left (x^2\right )-2288 x^2 \log \left (x^2\right )-8 x^3 \log \left (x^2\right )+322624 \log ^2\left (x^2\right )+4544 x \log ^2\left (x^2\right )+16 x^2 \log ^2\left (x^2\right )\right )^2} \, dx+2 \int \frac {1}{(142+x) \left (81792 x+21304 x^2+288 x^3+x^4+80656 \left (1-\frac {\log (5)}{80656}\right )-8 (2+x) (142+x)^2 \log \left (x^2\right )+16 (142+x)^2 \log ^2\left (x^2\right )\right )} \, dx\\ &=\frac {1}{71} \int \frac {-45812608+2493520 x^2+57920 x^3+420 x^4+x^5+x (-18147600+\log (5))-4 (-8+x) (142+x)^3 \log \left (x^2\right )}{x \left (81792 x+21304 x^2+288 x^3+x^4+80656 \left (1-\frac {\log (5)}{80656}\right )-8 (2+x) (142+x)^2 \log \left (x^2\right )+16 (142+x)^2 \log ^2\left (x^2\right )\right )^2} \, dx+\frac {1}{71} \int \frac {45812608-2493520 x^2-57920 x^3-420 x^4-x^5-x (-18147600+\log (5))+4 (-8+x) (142+x)^3 \log \left (x^2\right )}{(142+x) \left (81792 x+21304 x^2+288 x^3+x^4+80656 \left (1-\frac {\log (5)}{80656}\right )-8 (2+x) (142+x)^2 \log \left (x^2\right )+16 (142+x)^2 \log ^2\left (x^2\right )\right )^2} \, dx+2 \int \frac {1}{(142+x) \left (81792 x+21304 x^2+288 x^3+x^4+80656 \left (1-\frac {\log (5)}{80656}\right )-8 (2+x) (142+x)^2 \log \left (x^2\right )+16 (142+x)^2 \log ^2\left (x^2\right )\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.09, size = 53, normalized size = 1.96 \begin {gather*} -\frac {1}{80656+81792 x+21304 x^2+288 x^3+x^4-\log (5)-8 (2+x) (142+x)^2 \log \left (x^2\right )+16 (142+x)^2 \log ^2\left (x^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-645248 - 249920*x + 38032*x^2 + 848*x^3 + 4*x^4 + (1290496 - 147680*x - 4512*x^2 - 24*x^3)*Log[x^2
] + (4544*x + 32*x^2)*Log[x^2]^2)/(6505390336*x + 13194031104*x^2 + 10126522112*x^3 + 3531451392*x^4 + 5011339
20*x^5 + 12434688*x^6 + 125552*x^7 + 576*x^8 + x^9 + (-161312*x - 163584*x^2 - 42608*x^3 - 576*x^4 - 2*x^5)*Lo
g[5] + x*Log[5]^2 + (-52043122688*x - 79530687488*x^2 - 41246833152*x^3 - 7628194560*x^4 - 194974080*x^5 - 199
0464*x^6 - 9184*x^7 - 16*x^8 + (645248*x + 331712*x^2 + 4576*x^3 + 16*x^4)*Log[5])*Log[x^2] + (156129368064*x
+ 160527378432*x^2 + 43476810240*x^3 + 1146178560*x^4 + 11832960*x^5 + 54912*x^6 + 96*x^7 + (-645248*x - 9088*
x^2 - 32*x^3)*Log[5])*Log[x^2]^2 + (-208172490752*x - 109950259200*x^2 - 2993950720*x^3 - 31262720*x^4 - 14592
0*x^5 - 256*x^6)*Log[x^2]^3 + (104086245376*x + 2932006912*x^2 + 30971904*x^3 + 145408*x^4 + 256*x^5)*Log[x^2]
^4),x]

[Out]

-(80656 + 81792*x + 21304*x^2 + 288*x^3 + x^4 - Log[5] - 8*(2 + x)*(142 + x)^2*Log[x^2] + 16*(142 + x)^2*Log[x
^2]^2)^(-1)

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fricas [B]  time = 1.08, size = 61, normalized size = 2.26 \begin {gather*} -\frac {1}{x^{4} + 288 \, x^{3} + 16 \, {\left (x^{2} + 284 \, x + 20164\right )} \log \left (x^{2}\right )^{2} + 21304 \, x^{2} - 8 \, {\left (x^{3} + 286 \, x^{2} + 20732 \, x + 40328\right )} \log \left (x^{2}\right ) + 81792 \, x - \log \relax (5) + 80656} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*x^2+4544*x)*log(x^2)^2+(-24*x^3-4512*x^2-147680*x+1290496)*log(x^2)+4*x^4+848*x^3+38032*x^2-249
920*x-645248)/((256*x^5+145408*x^4+30971904*x^3+2932006912*x^2+104086245376*x)*log(x^2)^4+(-256*x^6-145920*x^5
-31262720*x^4-2993950720*x^3-109950259200*x^2-208172490752*x)*log(x^2)^3+((-32*x^3-9088*x^2-645248*x)*log(5)+9
6*x^7+54912*x^6+11832960*x^5+1146178560*x^4+43476810240*x^3+160527378432*x^2+156129368064*x)*log(x^2)^2+((16*x
^4+4576*x^3+331712*x^2+645248*x)*log(5)-16*x^8-9184*x^7-1990464*x^6-194974080*x^5-7628194560*x^4-41246833152*x
^3-79530687488*x^2-52043122688*x)*log(x^2)+x*log(5)^2+(-2*x^5-576*x^4-42608*x^3-163584*x^2-161312*x)*log(5)+x^
9+576*x^8+125552*x^7+12434688*x^6+501133920*x^5+3531451392*x^4+10126522112*x^3+13194031104*x^2+6505390336*x),x
, algorithm="fricas")

[Out]

-1/(x^4 + 288*x^3 + 16*(x^2 + 284*x + 20164)*log(x^2)^2 + 21304*x^2 - 8*(x^3 + 286*x^2 + 20732*x + 40328)*log(
x^2) + 81792*x - log(5) + 80656)

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giac [B]  time = 1.34, size = 85, normalized size = 3.15 \begin {gather*} -\frac {1}{x^{4} - 8 \, x^{3} \log \left (x^{2}\right ) + 16 \, x^{2} \log \left (x^{2}\right )^{2} + 288 \, x^{3} - 2288 \, x^{2} \log \left (x^{2}\right ) + 4544 \, x \log \left (x^{2}\right )^{2} + 21304 \, x^{2} - 165856 \, x \log \left (x^{2}\right ) + 322624 \, \log \left (x^{2}\right )^{2} + 81792 \, x - \log \relax (5) - 322624 \, \log \left (x^{2}\right ) + 80656} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*x^2+4544*x)*log(x^2)^2+(-24*x^3-4512*x^2-147680*x+1290496)*log(x^2)+4*x^4+848*x^3+38032*x^2-249
920*x-645248)/((256*x^5+145408*x^4+30971904*x^3+2932006912*x^2+104086245376*x)*log(x^2)^4+(-256*x^6-145920*x^5
-31262720*x^4-2993950720*x^3-109950259200*x^2-208172490752*x)*log(x^2)^3+((-32*x^3-9088*x^2-645248*x)*log(5)+9
6*x^7+54912*x^6+11832960*x^5+1146178560*x^4+43476810240*x^3+160527378432*x^2+156129368064*x)*log(x^2)^2+((16*x
^4+4576*x^3+331712*x^2+645248*x)*log(5)-16*x^8-9184*x^7-1990464*x^6-194974080*x^5-7628194560*x^4-41246833152*x
^3-79530687488*x^2-52043122688*x)*log(x^2)+x*log(5)^2+(-2*x^5-576*x^4-42608*x^3-163584*x^2-161312*x)*log(5)+x^
9+576*x^8+125552*x^7+12434688*x^6+501133920*x^5+3531451392*x^4+10126522112*x^3+13194031104*x^2+6505390336*x),x
, algorithm="giac")

[Out]

-1/(x^4 - 8*x^3*log(x^2) + 16*x^2*log(x^2)^2 + 288*x^3 - 2288*x^2*log(x^2) + 4544*x*log(x^2)^2 + 21304*x^2 - 1
65856*x*log(x^2) + 322624*log(x^2)^2 + 81792*x - log(5) - 322624*log(x^2) + 80656)

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maple [B]  time = 0.04, size = 84, normalized size = 3.11

method	result	size
risch	\(\frac {1}{-x^{4}+8 x^{3} \ln \left (x^{2}\right )-16 x^{2} \ln \left (x^{2}\right )^{2}-288 x^{3}+2288 x^{2} \ln \left (x^{2}\right )-4544 x \ln \left (x^{2}\right )^{2}-21304 x^{2}+165856 x \ln \left (x^{2}\right )-322624 \ln \left (x^{2}\right )^{2}+\ln \relax (5)-81792 x +322624 \ln \left (x^{2}\right )-80656}\)	\(84\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((32*x^2+4544*x)*ln(x^2)^2+(-24*x^3-4512*x^2-147680*x+1290496)*ln(x^2)+4*x^4+848*x^3+38032*x^2-249920*x-64
5248)/((256*x^5+145408*x^4+30971904*x^3+2932006912*x^2+104086245376*x)*ln(x^2)^4+(-256*x^6-145920*x^5-31262720
*x^4-2993950720*x^3-109950259200*x^2-208172490752*x)*ln(x^2)^3+((-32*x^3-9088*x^2-645248*x)*ln(5)+96*x^7+54912
*x^6+11832960*x^5+1146178560*x^4+43476810240*x^3+160527378432*x^2+156129368064*x)*ln(x^2)^2+((16*x^4+4576*x^3+
331712*x^2+645248*x)*ln(5)-16*x^8-9184*x^7-1990464*x^6-194974080*x^5-7628194560*x^4-41246833152*x^3-7953068748
8*x^2-52043122688*x)*ln(x^2)+x*ln(5)^2+(-2*x^5-576*x^4-42608*x^3-163584*x^2-161312*x)*ln(5)+x^9+576*x^8+125552
*x^7+12434688*x^6+501133920*x^5+3531451392*x^4+10126522112*x^3+13194031104*x^2+6505390336*x),x,method=_RETURNV
ERBOSE)

[Out]

1/(-x^4+8*x^3*ln(x^2)-16*x^2*ln(x^2)^2-288*x^3+2288*x^2*ln(x^2)-4544*x*ln(x^2)^2-21304*x^2+165856*x*ln(x^2)-32
2624*ln(x^2)^2+ln(5)-81792*x+322624*ln(x^2)-80656)

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maxima [B]  time = 0.53, size = 57, normalized size = 2.11 \begin {gather*} -\frac {1}{x^{4} + 288 \, x^{3} + 64 \, {\left (x^{2} + 284 \, x + 20164\right )} \log \relax (x)^{2} + 21304 \, x^{2} - 16 \, {\left (x^{3} + 286 \, x^{2} + 20732 \, x + 40328\right )} \log \relax (x) + 81792 \, x - \log \relax (5) + 80656} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*x^2+4544*x)*log(x^2)^2+(-24*x^3-4512*x^2-147680*x+1290496)*log(x^2)+4*x^4+848*x^3+38032*x^2-249
920*x-645248)/((256*x^5+145408*x^4+30971904*x^3+2932006912*x^2+104086245376*x)*log(x^2)^4+(-256*x^6-145920*x^5
-31262720*x^4-2993950720*x^3-109950259200*x^2-208172490752*x)*log(x^2)^3+((-32*x^3-9088*x^2-645248*x)*log(5)+9
6*x^7+54912*x^6+11832960*x^5+1146178560*x^4+43476810240*x^3+160527378432*x^2+156129368064*x)*log(x^2)^2+((16*x
^4+4576*x^3+331712*x^2+645248*x)*log(5)-16*x^8-9184*x^7-1990464*x^6-194974080*x^5-7628194560*x^4-41246833152*x
^3-79530687488*x^2-52043122688*x)*log(x^2)+x*log(5)^2+(-2*x^5-576*x^4-42608*x^3-163584*x^2-161312*x)*log(5)+x^
9+576*x^8+125552*x^7+12434688*x^6+501133920*x^5+3531451392*x^4+10126522112*x^3+13194031104*x^2+6505390336*x),x
, algorithm="maxima")

[Out]

-1/(x^4 + 288*x^3 + 64*(x^2 + 284*x + 20164)*log(x)^2 + 21304*x^2 - 16*(x^3 + 286*x^2 + 20732*x + 40328)*log(x
) + 81792*x - log(5) + 80656)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\ln \left (x^2\right )}^2\,\left (32\,x^2+4544\,x\right )-\ln \left (x^2\right )\,\left (24\,x^3+4512\,x^2+147680\,x-1290496\right )-249920\,x+38032\,x^2+848\,x^3+4\,x^4-645248}{6505390336\,x+{\ln \left (x^2\right )}^4\,\left (256\,x^5+145408\,x^4+30971904\,x^3+2932006912\,x^2+104086245376\,x\right )-\ln \left (x^2\right )\,\left (52043122688\,x-\ln \relax (5)\,\left (16\,x^4+4576\,x^3+331712\,x^2+645248\,x\right )[phone]\,x^2+41246833152\,x^3+7628194560\,x^4+194974080\,x^5+1990464\,x^6+9184\,x^7+16\,x^8\right )-{\ln \left (x^2\right )}^3\,\left (256\,x^6+145920\,x^5+31262720\,x^4+2993950720\,x^3+109950259200\,x^2+208172490752\,x\right )+{\ln \left (x^2\right )}^2\,\left (156129368064\,x-\ln \relax (5)\,\left (32\,x^3+9088\,x^2+645248\,x\right )[phone]\,x^2+43476810240\,x^3+1146178560\,x^4+11832960\,x^5+54912\,x^6+96\,x^7\right )+x\,{\ln \relax (5)}^2+13194031104\,x^2+10126522112\,x^3+3531451392\,x^4+501133920\,x^5+12434688\,x^6+125552\,x^7+576\,x^8+x^9-\ln \relax (5)\,\left (2\,x^5+576\,x^4+42608\,x^3+163584\,x^2+161312\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x^2)^2*(4544*x + 32*x^2) - log(x^2)*(147680*x + 4512*x^2 + 24*x^3 - 1290496) - 249920*x + 38032*x^2 +
848*x^3 + 4*x^4 - 645248)/(6505390336*x + log(x^2)^4*(104086245376*x + 2932006912*x^2 + 30971904*x^3 + 145408
*x^4 + 256*x^5) - log(x^2)*(52043122688*x - log(5)*(645248*x + 331712*x^2 + 4576*x^3 + 16*x^4) + 79530687488*x
^2 + 41246833152*x^3 + 7628194560*x^4 + 194974080*x^5 + 1990464*x^6 + 9184*x^7 + 16*x^8) - log(x^2)^3*(2081724
90752*x + 109950259200*x^2 + 2993950720*x^3 + 31262720*x^4 + 145920*x^5 + 256*x^6) + log(x^2)^2*(156129368064*
x - log(5)*(645248*x + 9088*x^2 + 32*x^3) + 160527378432*x^2 + 43476810240*x^3 + 1146178560*x^4 + 11832960*x^5
+ 54912*x^6 + 96*x^7) + x*log(5)^2 + 13194031104*x^2 + 10126522112*x^3 + 3531451392*x^4 + 501133920*x^5 + 124
34688*x^6 + 125552*x^7 + 576*x^8 + x^9 - log(5)*(161312*x + 163584*x^2 + 42608*x^3 + 576*x^4 + 2*x^5)),x)

[Out]

int((log(x^2)^2*(4544*x + 32*x^2) - log(x^2)*(147680*x + 4512*x^2 + 24*x^3 - 1290496) - 249920*x + 38032*x^2 +
848*x^3 + 4*x^4 - 645248)/(6505390336*x + log(x^2)^4*(104086245376*x + 2932006912*x^2 + 30971904*x^3 + 145408
*x^4 + 256*x^5) - log(x^2)*(52043122688*x - log(5)*(645248*x + 331712*x^2 + 4576*x^3 + 16*x^4) + 79530687488*x
^2 + 41246833152*x^3 + 7628194560*x^4 + 194974080*x^5 + 1990464*x^6 + 9184*x^7 + 16*x^8) - log(x^2)^3*(2081724
90752*x + 109950259200*x^2 + 2993950720*x^3 + 31262720*x^4 + 145920*x^5 + 256*x^6) + log(x^2)^2*(156129368064*
x - log(5)*(645248*x + 9088*x^2 + 32*x^3) + 160527378432*x^2 + 43476810240*x^3 + 1146178560*x^4 + 11832960*x^5
+ 54912*x^6 + 96*x^7) + x*log(5)^2 + 13194031104*x^2 + 10126522112*x^3 + 3531451392*x^4 + 501133920*x^5 + 124
34688*x^6 + 125552*x^7 + 576*x^8 + x^9 - log(5)*(161312*x + 163584*x^2 + 42608*x^3 + 576*x^4 + 2*x^5)), x)

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sympy [B]  time = 0.87, size = 63, normalized size = 2.33 \begin {gather*} - \frac {1}{x^{4} + 288 x^{3} + 21304 x^{2} + 81792 x + \left (16 x^{2} + 4544 x + 322624\right ) \log {\left (x^{2} \right )}^{2} + \left (- 8 x^{3} - 2288 x^{2} - 165856 x - 322624\right ) \log {\left (x^{2} \right )} - \log {\relax (5 )} + 80656} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*x**2+4544*x)*ln(x**2)**2+(-24*x**3-4512*x**2-147680*x+1290496)*ln(x**2)+4*x**4+848*x**3+38032*x
**2-249920*x-645248)/((256*x**5+145408*x**4+30971904*x**3+2932006912*x**2+104086245376*x)*ln(x**2)**4+(-256*x*
*6-145920*x**5-31262720*x**4-2993950720*x**3-109950259200*x**2-208172490752*x)*ln(x**2)**3+((-32*x**3-9088*x**
2-645248*x)*ln(5)+96*x**7+54912*x**6+11832960*x**5+1146178560*x**4+43476810240*x**3+160527378432*x**2+15612936
8064*x)*ln(x**2)**2+((16*x**4+4576*x**3+331712*x**2+645248*x)*ln(5)-16*x**8-9184*x**7-1990464*x**6-194974080*x
**5-7628194560*x**4-41246833152*x**3-79530687488*x**2-52043122688*x)*ln(x**2)+x*ln(5)**2+(-2*x**5-576*x**4-426
08*x**3-163584*x**2-161312*x)*ln(5)+x**9+576*x**8+125552*x**7+12434688*x**6+501133920*x**5+3531451392*x**4+101
26522112*x**3+13194031104*x**2+6505390336*x),x)

[Out]

-1/(x**4 + 288*x**3 + 21304*x**2 + 81792*x + (16*x**2 + 4544*x + 322624)*log(x**2)**2 + (-8*x**3 - 2288*x**2 -
165856*x - 322624)*log(x**2) - log(5) + 80656)

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