3.98.82 \(\int \frac {-1090000-336000 x+313600 x^2+(2360000+336000 x-627200 x^2) \log (x)+(-1605000-84000 x+470400 x^2) \log ^2(x)+(425000-156800 x^2) \log ^3(x)+(-38125+19600 x^2) \log ^4(x)}{372490000-601388000 x+363786000 x^2-97717760 x^3+9834496 x^4+(-420740000+811336000 x-570189600 x^2+174361600 x^3-19668992 x^4) \log (x)+(177675000-399414000 x+326539800 x^2-114965760 x^3+14751744 x^4) \log ^2(x)+(-33245000+85558000 x-80790600 x^2+33053440 x^3-4917248 x^4) \log ^3(x)+(2325625-6755750 x+7297425 x^2-3473120 x^3+614656 x^4) \log ^4(x)} \, dx\)
Optimal. Leaf size=31 \[ 3-\frac {x}{-3+x+16 \left (\frac {2}{5} (-5+x)+x+\frac {3}{-2+\log (x)}\right )^2} \]
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Rubi [F] time = 131.28, 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 {-1090000-336000 x+313600 x^2+\left (2360000+336000 x-627200 x^2\right ) \log (x)+\left (-1605000-84000 x+470400 x^2\right ) \log ^2(x)+\left (425000-156800 x^2\right ) \log ^3(x)+\left (-38125+19600 x^2\right ) \log ^4(x)}{372490000-601388000 x+363786000 x^2-97717760 x^3+9834496 x^4+\left (-420740000+811336000 x-570189600 x^2+174361600 x^3-19668992 x^4\right ) \log (x)+\left (177675000-399414000 x+326539800 x^2-114965760 x^3+14751744 x^4\right ) \log ^2(x)+\left (-33245000+85558000 x-80790600 x^2+33053440 x^3-4917248 x^4\right ) \log ^3(x)+\left (2325625-6755750 x+7297425 x^2-3473120 x^3+614656 x^4\right ) \log ^4(x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(-1090000 - 336000*x + 313600*x^2 + (2360000 + 336000*x - 627200*x^2)*Log[x] + (-1605000 - 84000*x + 47040
0*x^2)*Log[x]^2 + (425000 - 156800*x^2)*Log[x]^3 + (-38125 + 19600*x^2)*Log[x]^4)/(372490000 - 601388000*x + 3
63786000*x^2 - 97717760*x^3 + 9834496*x^4 + (-420740000 + 811336000*x - 570189600*x^2 + 174361600*x^3 - 196689
92*x^4)*Log[x] + (177675000 - 399414000*x + 326539800*x^2 - 114965760*x^3 + 14751744*x^4)*Log[x]^2 + (-3324500
0 + 85558000*x - 80790600*x^2 + 33053440*x^3 - 4917248*x^4)*Log[x]^3 + (2325625 - 6755750*x + 7297425*x^2 - 34
73120*x^3 + 614656*x^4)*Log[x]^4),x]
[Out]
(-25*x)/(1525 - 2215*x + 784*x^2) - 360000*Defer[Int][(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log
[x] - 3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)^(-2), x] + 130636800000*Sqrt[3/165
1]*Defer[Int][1/((2215 + 5*Sqrt[4953] - 1568*x)*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] -
3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)^2), x] + (308400000*(4953 + 443*Sqrt[495
3])*Defer[Int][1/((-2215 - 5*Sqrt[4953] + 1568*x)*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x]
- 3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)^2), x])/1651 + 130636800000*Sqrt[3/165
1]*Defer[Int][1/((-2215 + 5*Sqrt[4953] + 1568*x)*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] -
3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)^2), x] + (308400000*(4953 - 443*Sqrt[49
53])*Defer[Int][1/((-2215 + 5*Sqrt[4953] + 1568*x)*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x]
- 3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)^2), x])/1651 + (58592282343750000*Def
er[Int][1/((1525 - 2215*x + 784*x^2)^3*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 3136*x^2*
Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)^2), x])/343 - (39047274281250000*Defer[Int][x/((1
525 - 2215*x + 784*x^2)^3*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 3136*x^2*Log[x] + 1525
*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)^2), x])/343 + (361058681250000*Defer[Int][1/((1525 - 2215*x +
784*x^2)^2*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 3136*x^2*Log[x] + 1525*Log[x]^2 - 221
5*x*Log[x]^2 + 784*x^2*Log[x]^2)^2), x])/343 - (4226310000000*Defer[Int][x/((1525 - 2215*x + 784*x^2)^2*(19300
- 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 78
4*x^2*Log[x]^2)^2), x])/7 + 180000*Defer[Int][Log[x]/(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[
x] - 3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)^2, x] + 623265000000*Sqrt[3/1651]*D
efer[Int][Log[x]/((2215 + 5*Sqrt[4953] - 1568*x)*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] -
3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)^2), x] - 48625800000*Sqrt[39/127]*Defer
[Int][Log[x]/((2215 + 5*Sqrt[4953] - 1568*x)*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 313
6*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)^2), x] - (103800000*(4953 + 443*Sqrt[4953])
*Defer[Int][Log[x]/((-2215 - 5*Sqrt[4953] + 1568*x)*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x
] - 3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)^2), x])/1651 + 623265000000*Sqrt[3/1
651]*Defer[Int][Log[x]/((-2215 + 5*Sqrt[4953] + 1568*x)*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*L
og[x] - 3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)^2), x] - 48625800000*Sqrt[39/127
]*Defer[Int][Log[x]/((-2215 + 5*Sqrt[4953] + 1568*x)*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[
x] - 3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)^2), x] - (103800000*(4953 - 443*Sqr
t[4953])*Defer[Int][Log[x]/((-2215 + 5*Sqrt[4953] + 1568*x)*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220
*x*Log[x] - 3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)^2), x])/1651 - (239394023437
5000*Defer[Int][Log[x]/((1525 - 2215*x + 784*x^2)^3*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x
] - 3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)^2), x])/343 + (425269828125000*Defer
[Int][(x*Log[x])/((1525 - 2215*x + 784*x^2)^3*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 31
36*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)^2), x])/343 - (28693828125000*Defer[Int][L
og[x]/((1525 - 2215*x + 784*x^2)^2*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 3136*x^2*Log[
x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)^2), x])/343 - (228555000000*Defer[Int][(x*Log[x])/((1
525 - 2215*x + 784*x^2)^2*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 3136*x^2*Log[x] + 1525
*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)^2), x])/7 - 45920000*Sqrt[3/1651]*Defer[Int][1/((2215 + 5*Sqrt
[4953] - 1568*x)*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 3136*x^2*Log[x] + 1525*Log[x]^2
- 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)), x] + (84000*(4953 + 443*Sqrt[4953])*Defer[Int][1/((-2215 - 5*Sqrt[495
3] + 1568*x)*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 3136*x^2*Log[x] + 1525*Log[x]^2 - 2
215*x*Log[x]^2 + 784*x^2*Log[x]^2)), x])/1651 - 45920000*Sqrt[3/1651]*Defer[Int][1/((-2215 + 5*Sqrt[4953] + 15
68*x)*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*L
og[x]^2 + 784*x^2*Log[x]^2)), x] + (84000*(4953 - 443*Sqrt[4953])*Defer[Int][1/((-2215 + 5*Sqrt[4953] + 1568*x
)*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x
]^2 + 784*x^2*Log[x]^2)), x])/1651 - (2135095312500*Defer[Int][1/((1525 - 2215*x + 784*x^2)^3*(19300 - 15580*x
+ 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[
x]^2)), x])/49 + (1515743437500*Defer[Int][x/((1525 - 2215*x + 784*x^2)^3*(19300 - 15580*x + 3136*x^2 - 10900*
Log[x] + 12220*x*Log[x] - 3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)), x])/49 + (22
00687500*Defer[Int][1/((1525 - 2215*x + 784*x^2)^2*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x]
- 3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)), x])/49 + (8175000*Defer[Int][x/((15
25 - 2215*x + 784*x^2)^2*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 3136*x^2*Log[x] + 1525*
Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)), x])/7 + 11984000*Sqrt[3/1651]*Defer[Int][Log[x]/((2215 + 5*Sq
rt[4953] - 1568*x)*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 3136*x^2*Log[x] + 1525*Log[x]
^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)), x] - (56000*(4953 + 443*Sqrt[4953])*Defer[Int][Log[x]/((-2215 - 5*S
qrt[4953] + 1568*x)*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 3136*x^2*Log[x] + 1525*Log[x
]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)), x])/1651 + 11984000*Sqrt[3/1651]*Defer[Int][Log[x]/((-2215 + 5*Sqr
t[4953] + 1568*x)*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 3136*x^2*Log[x] + 1525*Log[x]^
2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)), x] - (56000*(4953 - 443*Sqrt[4953])*Defer[Int][Log[x]/((-2215 + 5*Sq
rt[4953] + 1568*x)*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 3136*x^2*Log[x] + 1525*Log[x]
^2 - 2215*x*Log[x]^2 + 784*x^2*Log[x]^2)), x])/1651 - (57187500*Defer[Int][Log[x]/((1525 - 2215*x + 784*x^2)^2
*(19300 - 15580*x + 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]
^2 + 784*x^2*Log[x]^2)), x])/7 - (51337500*Defer[Int][(x*Log[x])/((1525 - 2215*x + 784*x^2)^2*(19300 - 15580*x
+ 3136*x^2 - 10900*Log[x] + 12220*x*Log[x] - 3136*x^2*Log[x] + 1525*Log[x]^2 - 2215*x*Log[x]^2 + 784*x^2*Log[
x]^2)), x])/7
Rubi steps
Aborted
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Mathematica [A] time = 0.10, size = 53, normalized size = 1.71 \begin {gather*} -\frac {25 x (-2+\log (x))^2}{4 \left (4825-3895 x+784 x^2\right )-4 \left (2725-3055 x+784 x^2\right ) \log (x)+\left (1525-2215 x+784 x^2\right ) \log ^2(x)} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-1090000 - 336000*x + 313600*x^2 + (2360000 + 336000*x - 627200*x^2)*Log[x] + (-1605000 - 84000*x +
470400*x^2)*Log[x]^2 + (425000 - 156800*x^2)*Log[x]^3 + (-38125 + 19600*x^2)*Log[x]^4)/(372490000 - 601388000
*x + 363786000*x^2 - 97717760*x^3 + 9834496*x^4 + (-420740000 + 811336000*x - 570189600*x^2 + 174361600*x^3 -
19668992*x^4)*Log[x] + (177675000 - 399414000*x + 326539800*x^2 - 114965760*x^3 + 14751744*x^4)*Log[x]^2 + (-3
3245000 + 85558000*x - 80790600*x^2 + 33053440*x^3 - 4917248*x^4)*Log[x]^3 + (2325625 - 6755750*x + 7297425*x^
2 - 3473120*x^3 + 614656*x^4)*Log[x]^4),x]
[Out]
(-25*x*(-2 + Log[x])^2)/(4*(4825 - 3895*x + 784*x^2) - 4*(2725 - 3055*x + 784*x^2)*Log[x] + (1525 - 2215*x + 7
84*x^2)*Log[x]^2)
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fricas [A] time = 0.58, size = 58, normalized size = 1.87 \begin {gather*} -\frac {25 \, {\left (x \log \relax (x)^{2} - 4 \, x \log \relax (x) + 4 \, x\right )}}{{\left (784 \, x^{2} - 2215 \, x + 1525\right )} \log \relax (x)^{2} + 3136 \, x^{2} - 4 \, {\left (784 \, x^{2} - 3055 \, x + 2725\right )} \log \relax (x) - 15580 \, x + 19300} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((19600*x^2-38125)*log(x)^4+(-156800*x^2+425000)*log(x)^3+(470400*x^2-84000*x-1605000)*log(x)^2+(-62
7200*x^2+336000*x+2360000)*log(x)+313600*x^2-336000*x-1090000)/((614656*x^4-3473120*x^3+7297425*x^2-6755750*x+
2325625)*log(x)^4+(-4917248*x^4+33053440*x^3-80790600*x^2+85558000*x-33245000)*log(x)^3+(14751744*x^4-11496576
0*x^3+326539800*x^2-399414000*x+177675000)*log(x)^2+(-19668992*x^4+174361600*x^3-570189600*x^2+811336000*x-420
740000)*log(x)+9834496*x^4-97717760*x^3+363786000*x^2-601388000*x+372490000),x, algorithm="fricas")
[Out]
-25*(x*log(x)^2 - 4*x*log(x) + 4*x)/((784*x^2 - 2215*x + 1525)*log(x)^2 + 3136*x^2 - 4*(784*x^2 - 3055*x + 272
5)*log(x) - 15580*x + 19300)
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giac [B] time = 0.81, size = 131, normalized size = 4.23 \begin {gather*} \frac {6000 \, {\left (14 \, x^{2} \log \relax (x) - 28 \, x^{2} - 20 \, x \log \relax (x) + 55 \, x\right )}}{614656 \, x^{4} \log \relax (x)^{2} - 2458624 \, x^{4} \log \relax (x) - 3473120 \, x^{3} \log \relax (x)^{2} + 2458624 \, x^{4} + 16526720 \, x^{3} \log \relax (x) + 7297425 \, x^{2} \log \relax (x)^{2} - 19160960 \, x^{3} - 40395300 \, x^{2} \log \relax (x) - 6755750 \, x \log \relax (x)^{2} + 54423300 \, x^{2} + 42779000 \, x \log \relax (x) + 2325625 \, \log \relax (x)^{2} - 66509000 \, x - 16622500 \, \log \relax (x) + 29432500} - \frac {25 \, x}{784 \, x^{2} - 2215 \, x + 1525} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((19600*x^2-38125)*log(x)^4+(-156800*x^2+425000)*log(x)^3+(470400*x^2-84000*x-1605000)*log(x)^2+(-62
7200*x^2+336000*x+2360000)*log(x)+313600*x^2-336000*x-1090000)/((614656*x^4-3473120*x^3+7297425*x^2-6755750*x+
2325625)*log(x)^4+(-4917248*x^4+33053440*x^3-80790600*x^2+85558000*x-33245000)*log(x)^3+(14751744*x^4-11496576
0*x^3+326539800*x^2-399414000*x+177675000)*log(x)^2+(-19668992*x^4+174361600*x^3-570189600*x^2+811336000*x-420
740000)*log(x)+9834496*x^4-97717760*x^3+363786000*x^2-601388000*x+372490000),x, algorithm="giac")
[Out]
6000*(14*x^2*log(x) - 28*x^2 - 20*x*log(x) + 55*x)/(614656*x^4*log(x)^2 - 2458624*x^4*log(x) - 3473120*x^3*log
(x)^2 + 2458624*x^4 + 16526720*x^3*log(x) + 7297425*x^2*log(x)^2 - 19160960*x^3 - 40395300*x^2*log(x) - 675575
0*x*log(x)^2 + 54423300*x^2 + 42779000*x*log(x) + 2325625*log(x)^2 - 66509000*x - 16622500*log(x) + 29432500)
- 25*x/(784*x^2 - 2215*x + 1525)
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maple [A] time = 0.13, size = 68, normalized size = 2.19
|
|
|
| method |
result |
size |
|
|
|
| norman |
\(\frac {-100 x -25 x \ln \relax (x )^{2}+100 x \ln \relax (x )}{784 x^{2} \ln \relax (x )^{2}-2215 x \ln \relax (x )^{2}-3136 x^{2} \ln \relax (x )+1525 \ln \relax (x )^{2}+12220 x \ln \relax (x )+3136 x^{2}-10900 \ln \relax (x )-15580 x +19300}\) |
\(68\) |
| risch |
\(-\frac {25 x}{784 x^{2}-2215 x +1525}+\frac {6000 x \left (14 x \ln \relax (x )-28 x -20 \ln \relax (x )+55\right )}{\left (784 x^{2}-2215 x +1525\right ) \left (784 x^{2} \ln \relax (x )^{2}-2215 x \ln \relax (x )^{2}-3136 x^{2} \ln \relax (x )+1525 \ln \relax (x )^{2}+12220 x \ln \relax (x )+3136 x^{2}-10900 \ln \relax (x )-15580 x +19300\right )}\) |
\(96\) |
|
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| |
| |
| |
| |
|
|
|
|
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((19600*x^2-38125)*ln(x)^4+(-156800*x^2+425000)*ln(x)^3+(470400*x^2-84000*x-1605000)*ln(x)^2+(-627200*x^2+
336000*x+2360000)*ln(x)+313600*x^2-336000*x-1090000)/((614656*x^4-3473120*x^3+7297425*x^2-6755750*x+2325625)*l
n(x)^4+(-4917248*x^4+33053440*x^3-80790600*x^2+85558000*x-33245000)*ln(x)^3+(14751744*x^4-114965760*x^3+326539
800*x^2-399414000*x+177675000)*ln(x)^2+(-19668992*x^4+174361600*x^3-570189600*x^2+811336000*x-420740000)*ln(x)
+9834496*x^4-97717760*x^3+363786000*x^2-601388000*x+372490000),x,method=_RETURNVERBOSE)
[Out]
(-100*x-25*x*ln(x)^2+100*x*ln(x))/(784*x^2*ln(x)^2-2215*x*ln(x)^2-3136*x^2*ln(x)+1525*ln(x)^2+12220*x*ln(x)+31
36*x^2-10900*ln(x)-15580*x+19300)
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maxima [A] time = 0.42, size = 58, normalized size = 1.87 \begin {gather*} -\frac {25 \, {\left (x \log \relax (x)^{2} - 4 \, x \log \relax (x) + 4 \, x\right )}}{{\left (784 \, x^{2} - 2215 \, x + 1525\right )} \log \relax (x)^{2} + 3136 \, x^{2} - 4 \, {\left (784 \, x^{2} - 3055 \, x + 2725\right )} \log \relax (x) - 15580 \, x + 19300} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((19600*x^2-38125)*log(x)^4+(-156800*x^2+425000)*log(x)^3+(470400*x^2-84000*x-1605000)*log(x)^2+(-62
7200*x^2+336000*x+2360000)*log(x)+313600*x^2-336000*x-1090000)/((614656*x^4-3473120*x^3+7297425*x^2-6755750*x+
2325625)*log(x)^4+(-4917248*x^4+33053440*x^3-80790600*x^2+85558000*x-33245000)*log(x)^3+(14751744*x^4-11496576
0*x^3+326539800*x^2-399414000*x+177675000)*log(x)^2+(-19668992*x^4+174361600*x^3-570189600*x^2+811336000*x-420
740000)*log(x)+9834496*x^4-97717760*x^3+363786000*x^2-601388000*x+372490000),x, algorithm="maxima")
[Out]
-25*(x*log(x)^2 - 4*x*log(x) + 4*x)/((784*x^2 - 2215*x + 1525)*log(x)^2 + 3136*x^2 - 4*(784*x^2 - 3055*x + 272
5)*log(x) - 15580*x + 19300)
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {336000\,x+{\ln \relax (x)}^2\,\left (-470400\,x^2+84000\,x+1605000\right )-{\ln \relax (x)}^4\,\left (19600\,x^2-38125\right )+{\ln \relax (x)}^3\,\left (156800\,x^2-425000\right )-\ln \relax (x)\,\left (-627200\,x^2+336000\,x+2360000\right )-313600\,x^2+1090000}{{\ln \relax (x)}^4\,\left (614656\,x^4-3473120\,x^3+7297425\,x^2-6755750\,x+2325625\right )-601388000\,x-{\ln \relax (x)}^3\,\left (4917248\,x^4-33053440\,x^3+80790600\,x^2-85558000\,x+33245000\right )-\ln \relax (x)\,\left (19668992\,x^4-174361600\,x^3+570189600\,x^2-811336000\,x+420740000\right )+{\ln \relax (x)}^2\,\left (14751744\,x^4-114965760\,x^3+326539800\,x^2-399414000\,x+177675000\right )+363786000\,x^2-97717760\,x^3+9834496\,x^4+372490000} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(336000*x + log(x)^2*(84000*x - 470400*x^2 + 1605000) - log(x)^4*(19600*x^2 - 38125) + log(x)^3*(156800*x
^2 - 425000) - log(x)*(336000*x - 627200*x^2 + 2360000) - 313600*x^2 + 1090000)/(log(x)^4*(7297425*x^2 - 67557
50*x - 3473120*x^3 + 614656*x^4 + 2325625) - 601388000*x - log(x)^3*(80790600*x^2 - 85558000*x - 33053440*x^3
+ 4917248*x^4 + 33245000) - log(x)*(570189600*x^2 - 811336000*x - 174361600*x^3 + 19668992*x^4 + 420740000) +
log(x)^2*(326539800*x^2 - 399414000*x - 114965760*x^3 + 14751744*x^4 + 177675000) + 363786000*x^2 - 97717760*x
^3 + 9834496*x^4 + 372490000),x)
[Out]
int(-(336000*x + log(x)^2*(84000*x - 470400*x^2 + 1605000) - log(x)^4*(19600*x^2 - 38125) + log(x)^3*(156800*x
^2 - 425000) - log(x)*(336000*x - 627200*x^2 + 2360000) - 313600*x^2 + 1090000)/(log(x)^4*(7297425*x^2 - 67557
50*x - 3473120*x^3 + 614656*x^4 + 2325625) - 601388000*x - log(x)^3*(80790600*x^2 - 85558000*x - 33053440*x^3
+ 4917248*x^4 + 33245000) - log(x)*(570189600*x^2 - 811336000*x - 174361600*x^3 + 19668992*x^4 + 420740000) +
log(x)^2*(326539800*x^2 - 399414000*x - 114965760*x^3 + 14751744*x^4 + 177675000) + 363786000*x^2 - 97717760*x
^3 + 9834496*x^4 + 372490000), x)
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sympy [B] time = 0.80, size = 102, normalized size = 3.29 \begin {gather*} - \frac {25 x}{784 x^{2} - 2215 x + 1525} + \frac {- 168000 x^{2} + 330000 x + \left (84000 x^{2} - 120000 x\right ) \log {\relax (x )}}{2458624 x^{4} - 19160960 x^{3} + 54423300 x^{2} - 66509000 x + \left (- 2458624 x^{4} + 16526720 x^{3} - 40395300 x^{2} + 42779000 x - 16622500\right ) \log {\relax (x )} + \left (614656 x^{4} - 3473120 x^{3} + 7297425 x^{2} - 6755750 x + 2325625\right ) \log {\relax (x )}^{2} + 29432500} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((19600*x**2-38125)*ln(x)**4+(-156800*x**2+425000)*ln(x)**3+(470400*x**2-84000*x-1605000)*ln(x)**2+(
-627200*x**2+336000*x+2360000)*ln(x)+313600*x**2-336000*x-1090000)/((614656*x**4-3473120*x**3+7297425*x**2-675
5750*x+2325625)*ln(x)**4+(-4917248*x**4+33053440*x**3-80790600*x**2+85558000*x-33245000)*ln(x)**3+(14751744*x*
*4-114965760*x**3+326539800*x**2-399414000*x+177675000)*ln(x)**2+(-19668992*x**4+174361600*x**3-570189600*x**2
+811336000*x-420740000)*ln(x)+9834496*x**4-97717760*x**3+363786000*x**2-601388000*x+372490000),x)
[Out]
-25*x/(784*x**2 - 2215*x + 1525) + (-168000*x**2 + 330000*x + (84000*x**2 - 120000*x)*log(x))/(2458624*x**4 -
19160960*x**3 + 54423300*x**2 - 66509000*x + (-2458624*x**4 + 16526720*x**3 - 40395300*x**2 + 42779000*x - 166
22500)*log(x) + (614656*x**4 - 3473120*x**3 + 7297425*x**2 - 6755750*x + 2325625)*log(x)**2 + 29432500)
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