3.37.29 \(\int \frac {-524880 x^2-430920 x^3-102960 x^4-10078 x^5-437 x^6-7 x^7+(1574640 x^2+677806 x^3+118800 x^4+9944 x^5+395 x^6+6 x^7) \log (x)+(-9715 x^2-2737 x^3-266 x^4-8 x^5) \log ^2(x)+(15 x^2+2 x^3) \log ^3(x)}{x^2+(-10 x-2 x^2) \log (x)+(25+10 x+x^2) \log ^2(x)} \, dx\)

Optimal. Leaf size=28 \[ \frac {x^3 \left (-(18+x)^2+\log (x)\right )^2}{-x+(5+x) \log (x)} \]

________________________________________________________________________________________

Rubi [F]  time = 3.34, 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 {-524880 x^2-430920 x^3-102960 x^4-10078 x^5-437 x^6-7 x^7+\left (1574640 x^2+677806 x^3+118800 x^4+9944 x^5+395 x^6+6 x^7\right ) \log (x)+\left (-9715 x^2-2737 x^3-266 x^4-8 x^5\right ) \log ^2(x)+\left (15 x^2+2 x^3\right ) \log ^3(x)}{x^2+\left (-10 x-2 x^2\right ) \log (x)+\left (25+10 x+x^2\right ) \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-524880*x^2 - 430920*x^3 - 102960*x^4 - 10078*x^5 - 437*x^6 - 7*x^7 + (1574640*x^2 + 677806*x^3 + 118800*
x^4 + 9944*x^5 + 395*x^6 + 6*x^7)*Log[x] + (-9715*x^2 - 2737*x^3 - 266*x^4 - 8*x^5)*Log[x]^2 + (15*x^2 + 2*x^3
)*Log[x]^3)/(x^2 + (-10*x - 2*x^2)*Log[x] + (25 + 10*x + x^2)*Log[x]^2),x]

[Out]

1680*x - 337*x^2 - 62*x^3 - 2*x^4 + 625/(5 + x)^2 + 41750/(5 + x) - 5*x*Log[x] + x^2*Log[x] + (25*x*Log[x])/(5
+ x) + 3476750*Defer[Int][(-x + 5*Log[x] + x*Log[x])^(-2), x] - 703725*Defer[Int][x/(-x + 5*Log[x] + x*Log[x]
)^2, x] - 382455*Defer[Int][x^2/(-x + 5*Log[x] + x*Log[x])^2, x] - 144814*Defer[Int][x^3/(-x + 5*Log[x] + x*Lo
g[x])^2, x] - 24941*Defer[Int][x^4/(-x + 5*Log[x] + x*Log[x])^2, x] - 1967*Defer[Int][x^5/(-x + 5*Log[x] + x*L
og[x])^2, x] - 72*Defer[Int][x^6/(-x + 5*Log[x] + x*Log[x])^2, x] - Defer[Int][x^7/(-x + 5*Log[x] + x*Log[x])^
2, x] - 15625*Defer[Int][1/((5 + x)^3*(-x + 5*Log[x] + x*Log[x])^2), x] - 1040625*Defer[Int][1/((5 + x)^2*(-x
+ 5*Log[x] + x*Log[x])^2), x] - 17175000*Defer[Int][1/((5 + x)*(-x + 5*Log[x] + x*Log[x])^2), x] - 703700*Defe
r[Int][(-x + 5*Log[x] + x*Log[x])^(-1), x] + 144100*Defer[Int][x/(-x + 5*Log[x] + x*Log[x]), x] + 285433*Defer
[Int][x^2/(-x + 5*Log[x] + x*Log[x]), x] + 77833*Defer[Int][x^3/(-x + 5*Log[x] + x*Log[x]), x] + 8103*Defer[In
t][x^4/(-x + 5*Log[x] + x*Log[x]), x] + 365*Defer[Int][x^5/(-x + 5*Log[x] + x*Log[x]), x] + 6*Defer[Int][x^6/(
-x + 5*Log[x] + x*Log[x]), x] + 9375*Defer[Int][1/((5 + x)^3*(-x + 5*Log[x] + x*Log[x])), x] + 416250*Defer[In
t][1/((5 + x)^2*(-x + 5*Log[x] + x*Log[x])), x] + 3434875*Defer[Int][1/((5 + x)*(-x + 5*Log[x] + x*Log[x])), x
]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x^2 \left (-(18+x)^2 \left (1620+1150 x+185 x^2+7 x^3\right )+\left (1574640+677806 x+118800 x^2+9944 x^3+395 x^4+6 x^5\right ) \log (x)-\left (9715+2737 x+266 x^2+8 x^3\right ) \log ^2(x)+(15+2 x) \log ^3(x)\right )}{(x-(5+x) \log (x))^2} \, dx\\ &=\int \left (-\frac {x^2 \left (48575+23370 x+4063 x^2+306 x^3+8 x^4\right )}{(5+x)^3}+\frac {x^2 (15+2 x) \log (x)}{(5+x)^2}-\frac {x^2 \left (25+5 x+x^2\right ) \left (1620+503 x+41 x^2+x^3\right )^2}{(5+x)^3 (-x+5 \log (x)+x \log (x))^2}+\frac {x^2 \left (39366000+32594400 x+11275945 x^2+2106278 x^3+227503 x^4+14028 x^5+455 x^6+6 x^7\right )}{(5+x)^3 (-x+5 \log (x)+x \log (x))}\right ) \, dx\\ &=-\int \frac {x^2 \left (48575+23370 x+4063 x^2+306 x^3+8 x^4\right )}{(5+x)^3} \, dx+\int \frac {x^2 (15+2 x) \log (x)}{(5+x)^2} \, dx-\int \frac {x^2 \left (25+5 x+x^2\right ) \left (1620+503 x+41 x^2+x^3\right )^2}{(5+x)^3 (-x+5 \log (x)+x \log (x))^2} \, dx+\int \frac {x^2 \left (39366000+32594400 x+11275945 x^2+2106278 x^3+227503 x^4+14028 x^5+455 x^6+6 x^7\right )}{(5+x)^3 (-x+5 \log (x)+x \log (x))} \, dx\\ &=-\int \left (-1675+673 x+186 x^2+8 x^3+\frac {1250}{(5+x)^3}+\frac {41750}{(5+x)^2}-\frac {25}{5+x}\right ) \, dx+\int \left (-5 \log (x)+2 x \log (x)+\frac {125 \log (x)}{(5+x)^2}\right ) \, dx-\int \left (-\frac {3476750}{(-x+5 \log (x)+x \log (x))^2}+\frac {703725 x}{(-x+5 \log (x)+x \log (x))^2}+\frac {382455 x^2}{(-x+5 \log (x)+x \log (x))^2}+\frac {144814 x^3}{(-x+5 \log (x)+x \log (x))^2}+\frac {24941 x^4}{(-x+5 \log (x)+x \log (x))^2}+\frac {1967 x^5}{(-x+5 \log (x)+x \log (x))^2}+\frac {72 x^6}{(-x+5 \log (x)+x \log (x))^2}+\frac {x^7}{(-x+5 \log (x)+x \log (x))^2}+\frac {15625}{(5+x)^3 (-x+5 \log (x)+x \log (x))^2}+\frac {1040625}{(5+x)^2 (-x+5 \log (x)+x \log (x))^2}+\frac {17175000}{(5+x) (-x+5 \log (x)+x \log (x))^2}\right ) \, dx+\int \left (-\frac {703700}{-x+5 \log (x)+x \log (x)}+\frac {144100 x}{-x+5 \log (x)+x \log (x)}+\frac {285433 x^2}{-x+5 \log (x)+x \log (x)}+\frac {77833 x^3}{-x+5 \log (x)+x \log (x)}+\frac {8103 x^4}{-x+5 \log (x)+x \log (x)}+\frac {365 x^5}{-x+5 \log (x)+x \log (x)}+\frac {6 x^6}{-x+5 \log (x)+x \log (x)}+\frac {9375}{(5+x)^3 (-x+5 \log (x)+x \log (x))}+\frac {416250}{(5+x)^2 (-x+5 \log (x)+x \log (x))}+\frac {3434875}{(5+x) (-x+5 \log (x)+x \log (x))}\right ) \, dx\\ &=1675 x-\frac {673 x^2}{2}-62 x^3-2 x^4+\frac {625}{(5+x)^2}+\frac {41750}{5+x}+25 \log (5+x)+2 \int x \log (x) \, dx-5 \int \log (x) \, dx+6 \int \frac {x^6}{-x+5 \log (x)+x \log (x)} \, dx-72 \int \frac {x^6}{(-x+5 \log (x)+x \log (x))^2} \, dx+125 \int \frac {\log (x)}{(5+x)^2} \, dx+365 \int \frac {x^5}{-x+5 \log (x)+x \log (x)} \, dx-1967 \int \frac {x^5}{(-x+5 \log (x)+x \log (x))^2} \, dx+8103 \int \frac {x^4}{-x+5 \log (x)+x \log (x)} \, dx+9375 \int \frac {1}{(5+x)^3 (-x+5 \log (x)+x \log (x))} \, dx-15625 \int \frac {1}{(5+x)^3 (-x+5 \log (x)+x \log (x))^2} \, dx-24941 \int \frac {x^4}{(-x+5 \log (x)+x \log (x))^2} \, dx+77833 \int \frac {x^3}{-x+5 \log (x)+x \log (x)} \, dx+144100 \int \frac {x}{-x+5 \log (x)+x \log (x)} \, dx-144814 \int \frac {x^3}{(-x+5 \log (x)+x \log (x))^2} \, dx+285433 \int \frac {x^2}{-x+5 \log (x)+x \log (x)} \, dx-382455 \int \frac {x^2}{(-x+5 \log (x)+x \log (x))^2} \, dx+416250 \int \frac {1}{(5+x)^2 (-x+5 \log (x)+x \log (x))} \, dx-703700 \int \frac {1}{-x+5 \log (x)+x \log (x)} \, dx-703725 \int \frac {x}{(-x+5 \log (x)+x \log (x))^2} \, dx-1040625 \int \frac {1}{(5+x)^2 (-x+5 \log (x)+x \log (x))^2} \, dx+3434875 \int \frac {1}{(5+x) (-x+5 \log (x)+x \log (x))} \, dx+3476750 \int \frac {1}{(-x+5 \log (x)+x \log (x))^2} \, dx-17175000 \int \frac {1}{(5+x) (-x+5 \log (x)+x \log (x))^2} \, dx-\int \frac {x^7}{(-x+5 \log (x)+x \log (x))^2} \, dx\\ &=1680 x-337 x^2-62 x^3-2 x^4+\frac {625}{(5+x)^2}+\frac {41750}{5+x}-5 x \log (x)+x^2 \log (x)+\frac {25 x \log (x)}{5+x}+25 \log (5+x)+6 \int \frac {x^6}{-x+5 \log (x)+x \log (x)} \, dx-25 \int \frac {1}{5+x} \, dx-72 \int \frac {x^6}{(-x+5 \log (x)+x \log (x))^2} \, dx+365 \int \frac {x^5}{-x+5 \log (x)+x \log (x)} \, dx-1967 \int \frac {x^5}{(-x+5 \log (x)+x \log (x))^2} \, dx+8103 \int \frac {x^4}{-x+5 \log (x)+x \log (x)} \, dx+9375 \int \frac {1}{(5+x)^3 (-x+5 \log (x)+x \log (x))} \, dx-15625 \int \frac {1}{(5+x)^3 (-x+5 \log (x)+x \log (x))^2} \, dx-24941 \int \frac {x^4}{(-x+5 \log (x)+x \log (x))^2} \, dx+77833 \int \frac {x^3}{-x+5 \log (x)+x \log (x)} \, dx+144100 \int \frac {x}{-x+5 \log (x)+x \log (x)} \, dx-144814 \int \frac {x^3}{(-x+5 \log (x)+x \log (x))^2} \, dx+285433 \int \frac {x^2}{-x+5 \log (x)+x \log (x)} \, dx-382455 \int \frac {x^2}{(-x+5 \log (x)+x \log (x))^2} \, dx+416250 \int \frac {1}{(5+x)^2 (-x+5 \log (x)+x \log (x))} \, dx-703700 \int \frac {1}{-x+5 \log (x)+x \log (x)} \, dx-703725 \int \frac {x}{(-x+5 \log (x)+x \log (x))^2} \, dx-1040625 \int \frac {1}{(5+x)^2 (-x+5 \log (x)+x \log (x))^2} \, dx+3434875 \int \frac {1}{(5+x) (-x+5 \log (x)+x \log (x))} \, dx+3476750 \int \frac {1}{(-x+5 \log (x)+x \log (x))^2} \, dx-17175000 \int \frac {1}{(5+x) (-x+5 \log (x)+x \log (x))^2} \, dx-\int \frac {x^7}{(-x+5 \log (x)+x \log (x))^2} \, dx\\ &=1680 x-337 x^2-62 x^3-2 x^4+\frac {625}{(5+x)^2}+\frac {41750}{5+x}-5 x \log (x)+x^2 \log (x)+\frac {25 x \log (x)}{5+x}+6 \int \frac {x^6}{-x+5 \log (x)+x \log (x)} \, dx-72 \int \frac {x^6}{(-x+5 \log (x)+x \log (x))^2} \, dx+365 \int \frac {x^5}{-x+5 \log (x)+x \log (x)} \, dx-1967 \int \frac {x^5}{(-x+5 \log (x)+x \log (x))^2} \, dx+8103 \int \frac {x^4}{-x+5 \log (x)+x \log (x)} \, dx+9375 \int \frac {1}{(5+x)^3 (-x+5 \log (x)+x \log (x))} \, dx-15625 \int \frac {1}{(5+x)^3 (-x+5 \log (x)+x \log (x))^2} \, dx-24941 \int \frac {x^4}{(-x+5 \log (x)+x \log (x))^2} \, dx+77833 \int \frac {x^3}{-x+5 \log (x)+x \log (x)} \, dx+144100 \int \frac {x}{-x+5 \log (x)+x \log (x)} \, dx-144814 \int \frac {x^3}{(-x+5 \log (x)+x \log (x))^2} \, dx+285433 \int \frac {x^2}{-x+5 \log (x)+x \log (x)} \, dx-382455 \int \frac {x^2}{(-x+5 \log (x)+x \log (x))^2} \, dx+416250 \int \frac {1}{(5+x)^2 (-x+5 \log (x)+x \log (x))} \, dx-703700 \int \frac {1}{-x+5 \log (x)+x \log (x)} \, dx-703725 \int \frac {x}{(-x+5 \log (x)+x \log (x))^2} \, dx-1040625 \int \frac {1}{(5+x)^2 (-x+5 \log (x)+x \log (x))^2} \, dx+3434875 \int \frac {1}{(5+x) (-x+5 \log (x)+x \log (x))} \, dx+3476750 \int \frac {1}{(-x+5 \log (x)+x \log (x))^2} \, dx-17175000 \int \frac {1}{(5+x) (-x+5 \log (x)+x \log (x))^2} \, dx-\int \frac {x^7}{(-x+5 \log (x)+x \log (x))^2} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [B]  time = 0.06, size = 72, normalized size = 2.57 \begin {gather*} \frac {x \left (-8375+104976 x^2+23328 x^3+1944 x^4+72 x^5+x^6\right )+\left (41875+8375 x-648 x^3-72 x^4-2 x^5\right ) \log (x)+x^3 \log ^2(x)}{-x+(5+x) \log (x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-524880*x^2 - 430920*x^3 - 102960*x^4 - 10078*x^5 - 437*x^6 - 7*x^7 + (1574640*x^2 + 677806*x^3 + 1
18800*x^4 + 9944*x^5 + 395*x^6 + 6*x^7)*Log[x] + (-9715*x^2 - 2737*x^3 - 266*x^4 - 8*x^5)*Log[x]^2 + (15*x^2 +
2*x^3)*Log[x]^3)/(x^2 + (-10*x - 2*x^2)*Log[x] + (25 + 10*x + x^2)*Log[x]^2),x]

[Out]

(x*(-8375 + 104976*x^2 + 23328*x^3 + 1944*x^4 + 72*x^5 + x^6) + (41875 + 8375*x - 648*x^3 - 72*x^4 - 2*x^5)*Lo
g[x] + x^3*Log[x]^2)/(-x + (5 + x)*Log[x])

________________________________________________________________________________________

fricas [B]  time = 0.65, size = 72, normalized size = 2.57 \begin {gather*} \frac {x^{7} + 72 \, x^{6} + 1944 \, x^{5} + x^{3} \log \relax (x)^{2} + 23328 \, x^{4} + 104976 \, x^{3} - {\left (2 \, x^{5} + 72 \, x^{4} + 648 \, x^{3} - 8375 \, x - 41875\right )} \log \relax (x) - 8375 \, x}{{\left (x + 5\right )} \log \relax (x) - x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^3+15*x^2)*log(x)^3+(-8*x^5-266*x^4-2737*x^3-9715*x^2)*log(x)^2+(6*x^7+395*x^6+9944*x^5+118800*
x^4+677806*x^3+1574640*x^2)*log(x)-7*x^7-437*x^6-10078*x^5-102960*x^4-430920*x^3-524880*x^2)/((x^2+10*x+25)*lo
g(x)^2+(-2*x^2-10*x)*log(x)+x^2),x, algorithm="fricas")

[Out]

(x^7 + 72*x^6 + 1944*x^5 + x^3*log(x)^2 + 23328*x^4 + 104976*x^3 - (2*x^5 + 72*x^4 + 648*x^3 - 8375*x - 41875)
*log(x) - 8375*x)/((x + 5)*log(x) - x)

________________________________________________________________________________________

giac [B]  time = 0.16, size = 130, normalized size = 4.64 \begin {gather*} -2 \, x^{4} - 62 \, x^{3} - 337 \, x^{2} + {\left (x^{2} - 5 \, x - \frac {125}{x + 5}\right )} \log \relax (x) + 1680 \, x + \frac {x^{9} + 82 \, x^{8} + 2687 \, x^{7} + 44486 \, x^{6} + 385849 \, x^{5} + 1629720 \, x^{4} + 2624400 \, x^{3}}{x^{3} \log \relax (x) - x^{3} + 15 \, x^{2} \log \relax (x) - 10 \, x^{2} + 75 \, x \log \relax (x) - 25 \, x + 125 \, \log \relax (x)} + \frac {125 \, {\left (334 \, x + 1675\right )}}{x^{2} + 10 \, x + 25} + 25 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^3+15*x^2)*log(x)^3+(-8*x^5-266*x^4-2737*x^3-9715*x^2)*log(x)^2+(6*x^7+395*x^6+9944*x^5+118800*
x^4+677806*x^3+1574640*x^2)*log(x)-7*x^7-437*x^6-10078*x^5-102960*x^4-430920*x^3-524880*x^2)/((x^2+10*x+25)*lo
g(x)^2+(-2*x^2-10*x)*log(x)+x^2),x, algorithm="giac")

[Out]

-2*x^4 - 62*x^3 - 337*x^2 + (x^2 - 5*x - 125/(x + 5))*log(x) + 1680*x + (x^9 + 82*x^8 + 2687*x^7 + 44486*x^6 +
385849*x^5 + 1629720*x^4 + 2624400*x^3)/(x^3*log(x) - x^3 + 15*x^2*log(x) - 10*x^2 + 75*x*log(x) - 25*x + 125
*log(x)) + 125*(334*x + 1675)/(x^2 + 10*x + 25) + 25*log(x)

________________________________________________________________________________________

maple [B]  time = 0.04, size = 131, normalized size = 4.68

method	result	size
risch	\(\frac {\left (x^{3}-25 x -125\right ) \ln \relax (x )}{5+x}+\frac {-2 x^{6}-82 x^{5}-1007 x^{4}+25 x^{2} \ln \relax (x )-3240 x^{3}+250 x \ln \relax (x )+8375 x^{2}+625 \ln \relax (x )+83750 x +209375}{x^{2}+10 x +25}+\frac {\left (x^{6}+82 x^{5}+2687 x^{4}+44486 x^{3}+385849 x^{2}+1629720 x +2624400\right ) x^{3}}{\left (x^{2}+10 x +25\right ) \left (x \ln \relax (x )+5 \ln \relax (x )-x \right )}\)	\(131\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*x^3+15*x^2)*ln(x)^3+(-8*x^5-266*x^4-2737*x^3-9715*x^2)*ln(x)^2+(6*x^7+395*x^6+9944*x^5+118800*x^4+6778
06*x^3+1574640*x^2)*ln(x)-7*x^7-437*x^6-10078*x^5-102960*x^4-430920*x^3-524880*x^2)/((x^2+10*x+25)*ln(x)^2+(-2
*x^2-10*x)*ln(x)+x^2),x,method=_RETURNVERBOSE)

[Out]

(x^3-25*x-125)/(5+x)*ln(x)+(-2*x^6-82*x^5-1007*x^4+25*x^2*ln(x)-3240*x^3+250*x*ln(x)+8375*x^2+625*ln(x)+83750*
x+209375)/(x^2+10*x+25)+(x^6+82*x^5+2687*x^4+44486*x^3+385849*x^2+1629720*x+2624400)*x^3/(x^2+10*x+25)/(x*ln(x
)+5*ln(x)-x)

________________________________________________________________________________________

maxima [B]  time = 0.48, size = 72, normalized size = 2.57 \begin {gather*} \frac {x^{7} + 72 \, x^{6} + 1944 \, x^{5} + x^{3} \log \relax (x)^{2} + 23328 \, x^{4} + 104976 \, x^{3} - {\left (2 \, x^{5} + 72 \, x^{4} + 648 \, x^{3} - 8375 \, x - 41875\right )} \log \relax (x) - 8375 \, x}{{\left (x + 5\right )} \log \relax (x) - x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^3+15*x^2)*log(x)^3+(-8*x^5-266*x^4-2737*x^3-9715*x^2)*log(x)^2+(6*x^7+395*x^6+9944*x^5+118800*
x^4+677806*x^3+1574640*x^2)*log(x)-7*x^7-437*x^6-10078*x^5-102960*x^4-430920*x^3-524880*x^2)/((x^2+10*x+25)*lo
g(x)^2+(-2*x^2-10*x)*log(x)+x^2),x, algorithm="maxima")

[Out]

(x^7 + 72*x^6 + 1944*x^5 + x^3*log(x)^2 + 23328*x^4 + 104976*x^3 - (2*x^5 + 72*x^4 + 648*x^3 - 8375*x - 41875)
*log(x) - 8375*x)/((x + 5)*log(x) - x)

________________________________________________________________________________________

mupad [B]  time = 2.43, size = 122, normalized size = 4.36 \begin {gather*} 1680\,x+\frac {41750\,x+209375}{x^2+10\,x+25}-337\,x^2-62\,x^3-2\,x^4+\frac {x^3\,\ln \relax (x)}{x+5}-\frac {x^{12}+87\,x^{11}+3122\,x^{10}+59971\,x^9+675454\,x^8+4671115\,x^7+20419225\,x^6+53865000\,x^5+65610000\,x^4}{{\left (x+5\right )}^2\,\left (x-\ln \relax (x)\,\left (x+5\right )\right )\,\left (x^3+5\,x^2+25\,x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(524880*x^2 - log(x)^3*(15*x^2 + 2*x^3) + 430920*x^3 + 102960*x^4 + 10078*x^5 + 437*x^6 + 7*x^7 + log(x)^
2*(9715*x^2 + 2737*x^3 + 266*x^4 + 8*x^5) - log(x)*(1574640*x^2 + 677806*x^3 + 118800*x^4 + 9944*x^5 + 395*x^6
+ 6*x^7))/(log(x)^2*(10*x + x^2 + 25) - log(x)*(10*x + 2*x^2) + x^2),x)

[Out]

1680*x + (41750*x + 209375)/(10*x + x^2 + 25) - 337*x^2 - 62*x^3 - 2*x^4 + (x^3*log(x))/(x + 5) - (65610000*x^
4 + 53865000*x^5 + 20419225*x^6 + 4671115*x^7 + 675454*x^8 + 59971*x^9 + 3122*x^10 + 87*x^11 + x^12)/((x + 5)^
2*(x - log(x)*(x + 5))*(25*x + 5*x^2 + x^3))

________________________________________________________________________________________

sympy [B]  time = 0.38, size = 116, normalized size = 4.14 \begin {gather*} - 2 x^{4} - 62 x^{3} - 337 x^{2} + 1680 x - \frac {- 41750 x - 209375}{x^{2} + 10 x + 25} + 25 \log {\relax (x )} + \frac {x^{9} + 82 x^{8} + 2687 x^{7} + 44486 x^{6} + 385849 x^{5} + 1629720 x^{4} + 2624400 x^{3}}{- x^{3} - 10 x^{2} - 25 x + \left (x^{3} + 15 x^{2} + 75 x + 125\right ) \log {\relax (x )}} + \frac {\left (x^{3} - 25 x - 125\right ) \log {\relax (x )}}{x + 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x**3+15*x**2)*ln(x)**3+(-8*x**5-266*x**4-2737*x**3-9715*x**2)*ln(x)**2+(6*x**7+395*x**6+9944*x**
5+118800*x**4+677806*x**3+1574640*x**2)*ln(x)-7*x**7-437*x**6-10078*x**5-102960*x**4-430920*x**3-524880*x**2)/
((x**2+10*x+25)*ln(x)**2+(-2*x**2-10*x)*ln(x)+x**2),x)

[Out]

-2*x**4 - 62*x**3 - 337*x**2 + 1680*x - (-41750*x - 209375)/(x**2 + 10*x + 25) + 25*log(x) + (x**9 + 82*x**8 +
2687*x**7 + 44486*x**6 + 385849*x**5 + 1629720*x**4 + 2624400*x**3)/(-x**3 - 10*x**2 - 25*x + (x**3 + 15*x**2
+ 75*x + 125)*log(x)) + (x**3 - 25*x - 125)*log(x)/(x + 5)

________________________________________________________________________________________