\(\int \frac {375000-6937500 x+52250000 x^2-201000000 x^3+396000000 x^4-320000000 x^5}{-x^5-x^6+(-25 x^4+75 x^5+100 x^6) \log (1+x)+(-250 x^3+1750 x^4-2000 x^5-4000 x^6) \log ^2(1+x)+(-1250 x^2+13750 x^3-45000 x^4+20000 x^5+80000 x^6) \log ^3(1+x)+(-3125 x+46875 x^2-250000 x^3+500000 x^4-800000 x^6) \log ^4(1+x)+(-3125+59375 x-437500 x^2+1500000 x^3-2000000 x^4-800000 x^5+3200000 x^6) \log ^5(1+x)} \, dx\) [6455]

Optimal result

Integrand size = 189, antiderivative size = 27 \[ \int \frac {375000-6937500 x+52250000 x^2-201000000 x^3+396000000 x^4-320000000 x^5}{-x^5-x^6+\left (-25 x^4+75 x^5+100 x^6\right ) \log (1+x)+\left (-250 x^3+1750 x^4-2000 x^5-4000 x^6\right ) \log ^2(1+x)+\left (-1250 x^2+13750 x^3-45000 x^4+20000 x^5+80000 x^6\right ) \log ^3(1+x)+\left (-3125 x+46875 x^2-250000 x^3+500000 x^4-800000 x^6\right ) \log ^4(1+x)+\left (-3125+59375 x-437500 x^2+1500000 x^3-2000000 x^4-800000 x^5+3200000 x^6\right ) \log ^5(1+x)} \, dx=\frac {25}{\left (-\frac {x^2}{5 \left (-x+4 x^2\right )}+\log (1+x)\right )^4} \]

[Out]

25/(ln(1+x)-1/5*x^2/(4*x^2-x))^4

Rubi [F]

\[ \int \frac {375000-6937500 x+52250000 x^2-201000000 x^3+396000000 x^4-320000000 x^5}{-x^5-x^6+\left (-25 x^4+75 x^5+100 x^6\right ) \log (1+x)+\left (-250 x^3+1750 x^4-2000 x^5-4000 x^6\right ) \log ^2(1+x)+\left (-1250 x^2+13750 x^3-45000 x^4+20000 x^5+80000 x^6\right ) \log ^3(1+x)+\left (-3125 x+46875 x^2-250000 x^3+500000 x^4-800000 x^6\right ) \log ^4(1+x)+\left (-3125+59375 x-437500 x^2+1500000 x^3-2000000 x^4-800000 x^5+3200000 x^6\right ) \log ^5(1+x)} \, dx=\int \frac {375000-6937500 x+52250000 x^2-201000000 x^3+396000000 x^4-320000000 x^5}{-x^5-x^6+\left (-25 x^4+75 x^5+100 x^6\right ) \log (1+x)+\left (-250 x^3+1750 x^4-2000 x^5-4000 x^6\right ) \log ^2(1+x)+\left (-1250 x^2+13750 x^3-45000 x^4+20000 x^5+80000 x^6\right ) \log ^3(1+x)+\left (-3125 x+46875 x^2-250000 x^3+500000 x^4-800000 x^6\right ) \log ^4(1+x)+\left (-3125+59375 x-437500 x^2+1500000 x^3-2000000 x^4-800000 x^5+3200000 x^6\right ) \log ^5(1+x)} \, dx \]

[In]

Int[(375000 - 6937500*x + 52250000*x^2 - 201000000*x^3 + 396000000*x^4 - 320000000*x^5)/(-x^5 - x^6 + (-25*x^4
+ 75*x^5 + 100*x^6)*Log[1 + x] + (-250*x^3 + 1750*x^4 - 2000*x^5 - 4000*x^6)*Log[1 + x]^2 + (-1250*x^2 + 1375
0*x^3 - 45000*x^4 + 20000*x^5 + 80000*x^6)*Log[1 + x]^3 + (-3125*x + 46875*x^2 - 250000*x^3 + 500000*x^4 - 800
000*x^6)*Log[1 + x]^4 + (-3125 + 59375*x - 437500*x^2 + 1500000*x^3 - 2000000*x^4 - 800000*x^5 + 3200000*x^6)*
Log[1 + x]^5),x]

[Out]

-976187500*Defer[Int][(-x - 5*Log[1 + x] + 20*x*Log[1 + x])^(-5), x] + 969250000*Defer[Int][x/(-x - 5*Log[1 +
x] + 20*x*Log[1 + x])^5, x] - 917000000*Defer[Int][x^2/(-x - 5*Log[1 + x] + 20*x*Log[1 + x])^5, x] + 716000000
*Defer[Int][x^3/(-x - 5*Log[1 + x] + 20*x*Log[1 + x])^5, x] - 320000000*Defer[Int][x^4/(-x - 5*Log[1 + x] + 20
*x*Log[1 + x])^5, x] + 976562500*Defer[Int][1/((1 + x)*(-x - 5*Log[1 + x] + 20*x*Log[1 + x])^5), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {62500 (1-4 x)^3 \left (-6+39 x-80 x^2\right )}{(1+x) (x-5 (-1+4 x) \log (1+x))^5} \, dx \\ & = 62500 \int \frac {(1-4 x)^3 \left (-6+39 x-80 x^2\right )}{(1+x) (x-5 (-1+4 x) \log (1+x))^5} \, dx \\ & = 62500 \int \left (-\frac {15619}{(-x-5 \log (1+x)+20 x \log (1+x))^5}+\frac {15508 x}{(-x-5 \log (1+x)+20 x \log (1+x))^5}-\frac {14672 x^2}{(-x-5 \log (1+x)+20 x \log (1+x))^5}+\frac {11456 x^3}{(-x-5 \log (1+x)+20 x \log (1+x))^5}-\frac {5120 x^4}{(-x-5 \log (1+x)+20 x \log (1+x))^5}+\frac {15625}{(1+x) (-x-5 \log (1+x)+20 x \log (1+x))^5}\right ) \, dx \\ & = -\left (320000000 \int \frac {x^4}{(-x-5 \log (1+x)+20 x \log (1+x))^5} \, dx\right )[phone] \int \frac {x^3}{(-x-5 \log (1+x)+20 x \log (1+x))^5} \, dx-917000000 \int \frac {x^2}{(-x-5 \log (1+x)+20 x \log (1+x))^5} \, dx+969250000 \int \frac {x}{(-x-5 \log (1+x)+20 x \log (1+x))^5} \, dx-976187500 \int \frac {1}{(-x-5 \log (1+x)+20 x \log (1+x))^5} \, dx+976562500 \int \frac {1}{(1+x) (-x-5 \log (1+x)+20 x \log (1+x))^5} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 2.34 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.85 \[ \int \frac {375000-6937500 x+52250000 x^2-201000000 x^3+396000000 x^4-320000000 x^5}{-x^5-x^6+\left (-25 x^4+75 x^5+100 x^6\right ) \log (1+x)+\left (-250 x^3+1750 x^4-2000 x^5-4000 x^6\right ) \log ^2(1+x)+\left (-1250 x^2+13750 x^3-45000 x^4+20000 x^5+80000 x^6\right ) \log ^3(1+x)+\left (-3125 x+46875 x^2-250000 x^3+500000 x^4-800000 x^6\right ) \log ^4(1+x)+\left (-3125+59375 x-437500 x^2+1500000 x^3-2000000 x^4-800000 x^5+3200000 x^6\right ) \log ^5(1+x)} \, dx=\frac {15625 (1-4 x)^4}{(x+(5-20 x) \log (1+x))^4} \]

[In]

Integrate[(375000 - 6937500*x + 52250000*x^2 - 201000000*x^3 + 396000000*x^4 - 320000000*x^5)/(-x^5 - x^6 + (-
25*x^4 + 75*x^5 + 100*x^6)*Log[1 + x] + (-250*x^3 + 1750*x^4 - 2000*x^5 - 4000*x^6)*Log[1 + x]^2 + (-1250*x^2
+ 13750*x^3 - 45000*x^4 + 20000*x^5 + 80000*x^6)*Log[1 + x]^3 + (-3125*x + 46875*x^2 - 250000*x^3 + 500000*x^4
- 800000*x^6)*Log[1 + x]^4 + (-3125 + 59375*x - 437500*x^2 + 1500000*x^3 - 2000000*x^4 - 800000*x^5 + 3200000
*x^6)*Log[1 + x]^5),x]

[Out]

(15625*(1 - 4*x)^4)/(x + (5 - 20*x)*Log[1 + x])^4

Maple [A] (verified)

Time = 0.91 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.56

method	result	size
risch	\(\frac {15625 \left (64 x^{3}-48 x^{2}+12 x -1\right ) \left (-1+4 x \right )}{\left (20 \ln \left (1+x \right ) x -5 \ln \left (1+x \right )-x \right )^{4}}\)	\(42\)
parallelrisch	\(\frac {640000000000 x^{4}-640000000000 x^{3}[phone] x^{2}-40000000000 x [phone]}{25600000000 \ln \left (1+x \right )^{4} x^{4}-5120000000 \ln \left (1+x \right )^{3} x^{4}-25600000000 \ln \left (1+x \right )^{4} x^{3}[phone] \ln \left (1+x \right )^{2} x^{4}[phone] \ln \left (1+x \right )^{3} x^{3}[phone] \ln \left (1+x \right )^{4} x^{2}-12800000 \ln \left (1+x \right ) x^{4}-192000000 \ln \left (1+x \right )^{2} x^{3}-960000000 \ln \left (1+x \right )^{3} x^{2}-1600000000 \ln \left (1+x \right )^{4} x +160000 x^{4}+3200000 x^{3} \ln \left (1+x \right )[phone] x^{2} \ln \left (1+x \right )^{2}[phone] x \ln \left (1+x \right )^{3}[phone] \ln \left (1+x \right )^{4}}\)	\(172\)
derivativedivides	\(\frac {1600000000 \ln \left (1+x \right )^{2} \left (1+x \right )^{4}-160000000 \ln \left (1+x \right ) \left (1+x \right )^{4}-8000000000 \ln \left (1+x \right )^{2} \left (1+x \right )^{3}+4000000 \left (1+x \right )^{4}[phone] \ln \left (1+x \right ) \left (1+x \right )^{3}[phone] \ln \left (1+x \right )^{2} \left (1+x \right )^{2}-20000000 \left (1+x \right )^{3}-1500000000 \ln \left (1+x \right ) \left (1+x \right )^{2}-12500000000 \left (1+x \right ) \ln \left (1+x \right )^{2}[phone] \left (1+x \right )^{2}[phone] \left (1+x \right ) \ln \left (1+x \right )[phone] \ln \left (1+x \right )^{2}-21484375-31250000 x -390625000 \ln \left (1+x \right )}{\left (20 \left (1+x \right ) \ln \left (1+x \right )-x -25 \ln \left (1+x \right )\right )^{4} \left (400 \ln \left (1+x \right )^{2}-40 \ln \left (1+x \right )+1\right )}\)	\(174\)
default	\(\frac {1600000000 \ln \left (1+x \right )^{2} \left (1+x \right )^{4}-160000000 \ln \left (1+x \right ) \left (1+x \right )^{4}-8000000000 \ln \left (1+x \right )^{2} \left (1+x \right )^{3}+4000000 \left (1+x \right )^{4}[phone] \ln \left (1+x \right ) \left (1+x \right )^{3}[phone] \ln \left (1+x \right )^{2} \left (1+x \right )^{2}-20000000 \left (1+x \right )^{3}-1500000000 \ln \left (1+x \right ) \left (1+x \right )^{2}-12500000000 \left (1+x \right ) \ln \left (1+x \right )^{2}[phone] \left (1+x \right )^{2}[phone] \left (1+x \right ) \ln \left (1+x \right )[phone] \ln \left (1+x \right )^{2}-21484375-31250000 x -390625000 \ln \left (1+x \right )}{\left (20 \left (1+x \right ) \ln \left (1+x \right )-x -25 \ln \left (1+x \right )\right )^{4} \left (400 \ln \left (1+x \right )^{2}-40 \ln \left (1+x \right )+1\right )}\)	\(174\)

[In]

int((-320000000*x^5+396000000*x^4-201000000*x^3+52250000*x^2-6937500*x+375000)/((3200000*x^6-800000*x^5-200000
0*x^4+1500000*x^3-437500*x^2+59375*x-3125)*ln(1+x)^5+(-800000*x^6+500000*x^4-250000*x^3+46875*x^2-3125*x)*ln(1
+x)^4+(80000*x^6+20000*x^5-45000*x^4+13750*x^3-1250*x^2)*ln(1+x)^3+(-4000*x^6-2000*x^5+1750*x^4-250*x^3)*ln(1+
x)^2+(100*x^6+75*x^5-25*x^4)*ln(1+x)-x^6-x^5),x,method=_RETURNVERBOSE)

[Out]

15625*(64*x^3-48*x^2+12*x-1)*(-1+4*x)/(20*ln(1+x)*x-5*ln(1+x)-x)^4

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 122 vs. \(2 (26) = 52\).

Time = 0.27 (sec) , antiderivative size = 122, normalized size of antiderivative = 4.52 \[ \int \frac {375000-6937500 x+52250000 x^2-201000000 x^3+396000000 x^4-320000000 x^5}{-x^5-x^6+\left (-25 x^4+75 x^5+100 x^6\right ) \log (1+x)+\left (-250 x^3+1750 x^4-2000 x^5-4000 x^6\right ) \log ^2(1+x)+\left (-1250 x^2+13750 x^3-45000 x^4+20000 x^5+80000 x^6\right ) \log ^3(1+x)+\left (-3125 x+46875 x^2-250000 x^3+500000 x^4-800000 x^6\right ) \log ^4(1+x)+\left (-3125+59375 x-437500 x^2+1500000 x^3-2000000 x^4-800000 x^5+3200000 x^6\right ) \log ^5(1+x)} \, dx=\frac {15625 \, {\left (256 \, x^{4} - 256 \, x^{3} + 96 \, x^{2} - 16 \, x + 1\right )}}{625 \, {\left (256 \, x^{4} - 256 \, x^{3} + 96 \, x^{2} - 16 \, x + 1\right )} \log \left (x + 1\right )^{4} + x^{4} - 500 \, {\left (64 \, x^{4} - 48 \, x^{3} + 12 \, x^{2} - x\right )} \log \left (x + 1\right )^{3} + 150 \, {\left (16 \, x^{4} - 8 \, x^{3} + x^{2}\right )} \log \left (x + 1\right )^{2} - 20 \, {\left (4 \, x^{4} - x^{3}\right )} \log \left (x + 1\right )} \]

[In]

integrate((-320000000*x^5+396000000*x^4-201000000*x^3+52250000*x^2-6937500*x+375000)/((3200000*x^6-800000*x^5-
2000000*x^4+1500000*x^3-437500*x^2+59375*x-3125)*log(1+x)^5+(-800000*x^6+500000*x^4-250000*x^3+46875*x^2-3125*
x)*log(1+x)^4+(80000*x^6+20000*x^5-45000*x^4+13750*x^3-1250*x^2)*log(1+x)^3+(-4000*x^6-2000*x^5+1750*x^4-250*x
^3)*log(1+x)^2+(100*x^6+75*x^5-25*x^4)*log(1+x)-x^6-x^5),x, algorithm="fricas")

[Out]

15625*(256*x^4 - 256*x^3 + 96*x^2 - 16*x + 1)/(625*(256*x^4 - 256*x^3 + 96*x^2 - 16*x + 1)*log(x + 1)^4 + x^4
- 500*(64*x^4 - 48*x^3 + 12*x^2 - x)*log(x + 1)^3 + 150*(16*x^4 - 8*x^3 + x^2)*log(x + 1)^2 - 20*(4*x^4 - x^3)
*log(x + 1))

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 112 vs. \(2 (19) = 38\).

Time = 0.35 (sec) , antiderivative size = 112, normalized size of antiderivative = 4.15 \[ \int \frac {375000-6937500 x+52250000 x^2-201000000 x^3+396000000 x^4-320000000 x^5}{-x^5-x^6+\left (-25 x^4+75 x^5+100 x^6\right ) \log (1+x)+\left (-250 x^3+1750 x^4-2000 x^5-4000 x^6\right ) \log ^2(1+x)+\left (-1250 x^2+13750 x^3-45000 x^4+20000 x^5+80000 x^6\right ) \log ^3(1+x)+\left (-3125 x+46875 x^2-250000 x^3+500000 x^4-800000 x^6\right ) \log ^4(1+x)+\left (-3125+59375 x-437500 x^2+1500000 x^3-2000000 x^4-800000 x^5+3200000 x^6\right ) \log ^5(1+x)} \, dx=\frac {4000000 x^{4} - 4000000 x^{3} + 1500000 x^{2} - 250000 x + 15625}{x^{4} + \left (- 80 x^{4} + 20 x^{3}\right ) \log {\left (x + 1 \right )} + \left (2400 x^{4} - 1200 x^{3} + 150 x^{2}\right ) \log {\left (x + 1 \right )}^{2} + \left (- 32000 x^{4} + 24000 x^{3} - 6000 x^{2} + 500 x\right ) \log {\left (x + 1 \right )}^{3} + \left (160000 x^{4} - 160000 x^{3} + 60000 x^{2} - 10000 x + 625\right ) \log {\left (x + 1 \right )}^{4}} \]

[In]

integrate((-320000000*x**5+396000000*x**4-201000000*x**3+52250000*x**2-6937500*x+375000)/((3200000*x**6-800000
*x**5-2000000*x**4+1500000*x**3-437500*x**2+59375*x-3125)*ln(1+x)**5+(-800000*x**6+500000*x**4-250000*x**3+468
75*x**2-3125*x)*ln(1+x)**4+(80000*x**6+20000*x**5-45000*x**4+13750*x**3-1250*x**2)*ln(1+x)**3+(-4000*x**6-2000
*x**5+1750*x**4-250*x**3)*ln(1+x)**2+(100*x**6+75*x**5-25*x**4)*ln(1+x)-x**6-x**5),x)

[Out]

(4000000*x**4 - 4000000*x**3 + 1500000*x**2 - 250000*x + 15625)/(x**4 + (-80*x**4 + 20*x**3)*log(x + 1) + (240
0*x**4 - 1200*x**3 + 150*x**2)*log(x + 1)**2 + (-32000*x**4 + 24000*x**3 - 6000*x**2 + 500*x)*log(x + 1)**3 +
(160000*x**4 - 160000*x**3 + 60000*x**2 - 10000*x + 625)*log(x + 1)**4)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 122 vs. \(2 (26) = 52\).

Time = 0.23 (sec) , antiderivative size = 122, normalized size of antiderivative = 4.52 \[ \int \frac {375000-6937500 x+52250000 x^2-201000000 x^3+396000000 x^4-320000000 x^5}{-x^5-x^6+\left (-25 x^4+75 x^5+100 x^6\right ) \log (1+x)+\left (-250 x^3+1750 x^4-2000 x^5-4000 x^6\right ) \log ^2(1+x)+\left (-1250 x^2+13750 x^3-45000 x^4+20000 x^5+80000 x^6\right ) \log ^3(1+x)+\left (-3125 x+46875 x^2-250000 x^3+500000 x^4-800000 x^6\right ) \log ^4(1+x)+\left (-3125+59375 x-437500 x^2+1500000 x^3-2000000 x^4-800000 x^5+3200000 x^6\right ) \log ^5(1+x)} \, dx=\frac {15625 \, {\left (256 \, x^{4} - 256 \, x^{3} + 96 \, x^{2} - 16 \, x + 1\right )}}{625 \, {\left (256 \, x^{4} - 256 \, x^{3} + 96 \, x^{2} - 16 \, x + 1\right )} \log \left (x + 1\right )^{4} + x^{4} - 500 \, {\left (64 \, x^{4} - 48 \, x^{3} + 12 \, x^{2} - x\right )} \log \left (x + 1\right )^{3} + 150 \, {\left (16 \, x^{4} - 8 \, x^{3} + x^{2}\right )} \log \left (x + 1\right )^{2} - 20 \, {\left (4 \, x^{4} - x^{3}\right )} \log \left (x + 1\right )} \]

[In]

integrate((-320000000*x^5+396000000*x^4-201000000*x^3+52250000*x^2-6937500*x+375000)/((3200000*x^6-800000*x^5-
2000000*x^4+1500000*x^3-437500*x^2+59375*x-3125)*log(1+x)^5+(-800000*x^6+500000*x^4-250000*x^3+46875*x^2-3125*
x)*log(1+x)^4+(80000*x^6+20000*x^5-45000*x^4+13750*x^3-1250*x^2)*log(1+x)^3+(-4000*x^6-2000*x^5+1750*x^4-250*x
^3)*log(1+x)^2+(100*x^6+75*x^5-25*x^4)*log(1+x)-x^6-x^5),x, algorithm="maxima")

[Out]

15625*(256*x^4 - 256*x^3 + 96*x^2 - 16*x + 1)/(625*(256*x^4 - 256*x^3 + 96*x^2 - 16*x + 1)*log(x + 1)^4 + x^4
- 500*(64*x^4 - 48*x^3 + 12*x^2 - x)*log(x + 1)^3 + 150*(16*x^4 - 8*x^3 + x^2)*log(x + 1)^2 - 20*(4*x^4 - x^3)
*log(x + 1))

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 277 vs. \(2 (26) = 52\).

Time = 0.31 (sec) , antiderivative size = 277, normalized size of antiderivative = 10.26 \[ \int \frac {375000-6937500 x+52250000 x^2-201000000 x^3+396000000 x^4-320000000 x^5}{-x^5-x^6+\left (-25 x^4+75 x^5+100 x^6\right ) \log (1+x)+\left (-250 x^3+1750 x^4-2000 x^5-4000 x^6\right ) \log ^2(1+x)+\left (-1250 x^2+13750 x^3-45000 x^4+20000 x^5+80000 x^6\right ) \log ^3(1+x)+\left (-3125 x+46875 x^2-250000 x^3+500000 x^4-800000 x^6\right ) \log ^4(1+x)+\left (-3125+59375 x-437500 x^2+1500000 x^3-2000000 x^4-800000 x^5+3200000 x^6\right ) \log ^5(1+x)} \, dx=\frac {15625 \, {\left (20480 \, x^{6} - 30464 \, x^{5} + 19200 \, x^{4} - 6560 \, x^{3} + 1280 \, x^{2} - 135 \, x + 6\right )}}{12800000 \, x^{6} \log \left (x + 1\right )^{4} - 2560000 \, x^{6} \log \left (x + 1\right )^{3} - 19040000 \, x^{5} \log \left (x + 1\right )^{4} + 192000 \, x^{6} \log \left (x + 1\right )^{2} + 3168000 \, x^{5} \log \left (x + 1\right )^{3} + 12000000 \, x^{4} \log \left (x + 1\right )^{4} - 6400 \, x^{6} \log \left (x + 1\right ) - 189600 \, x^{5} \log \left (x + 1\right )^{2} - 1608000 \, x^{4} \log \left (x + 1\right )^{3} - 4100000 \, x^{3} \log \left (x + 1\right )^{4} + 80 \, x^{6} + 4720 \, x^{5} \log \left (x + 1\right ) + 73200 \, x^{4} \log \left (x + 1\right )^{2} + 418000 \, x^{3} \log \left (x + 1\right )^{3} + 800000 \, x^{2} \log \left (x + 1\right )^{4} - 39 \, x^{5} - 1260 \, x^{4} \log \left (x + 1\right ) - 13050 \, x^{3} \log \left (x + 1\right )^{2} - 55500 \, x^{2} \log \left (x + 1\right )^{3} - 84375 \, x \log \left (x + 1\right )^{4} + 6 \, x^{4} + 120 \, x^{3} \log \left (x + 1\right ) + 900 \, x^{2} \log \left (x + 1\right )^{2} + 3000 \, x \log \left (x + 1\right )^{3} + 3750 \, \log \left (x + 1\right )^{4}} \]

[In]

integrate((-320000000*x^5+396000000*x^4-201000000*x^3+52250000*x^2-6937500*x+375000)/((3200000*x^6-800000*x^5-
2000000*x^4+1500000*x^3-437500*x^2+59375*x-3125)*log(1+x)^5+(-800000*x^6+500000*x^4-250000*x^3+46875*x^2-3125*
x)*log(1+x)^4+(80000*x^6+20000*x^5-45000*x^4+13750*x^3-1250*x^2)*log(1+x)^3+(-4000*x^6-2000*x^5+1750*x^4-250*x
^3)*log(1+x)^2+(100*x^6+75*x^5-25*x^4)*log(1+x)-x^6-x^5),x, algorithm="giac")

[Out]

15625*(20480*x^6 - 30464*x^5 + 19200*x^4 - 6560*x^3 + 1280*x^2 - 135*x + 6)/(12800000*x^6*log(x + 1)^4 - 25600
00*x^6*log(x + 1)^3 - 19040000*x^5*log(x + 1)^4 + 192000*x^6*log(x + 1)^2 + 3168000*x^5*log(x + 1)^3 + 1200000
0*x^4*log(x + 1)^4 - 6400*x^6*log(x + 1) - 189600*x^5*log(x + 1)^2 - 1608000*x^4*log(x + 1)^3 - 4100000*x^3*lo
g(x + 1)^4 + 80*x^6 + 4720*x^5*log(x + 1) + 73200*x^4*log(x + 1)^2 + 418000*x^3*log(x + 1)^3 + 800000*x^2*log(
x + 1)^4 - 39*x^5 - 1260*x^4*log(x + 1) - 13050*x^3*log(x + 1)^2 - 55500*x^2*log(x + 1)^3 - 84375*x*log(x + 1)
^4 + 6*x^4 + 120*x^3*log(x + 1) + 900*x^2*log(x + 1)^2 + 3000*x*log(x + 1)^3 + 3750*log(x + 1)^4)

Mupad [F(-1)]

Timed out. \[ \int \frac {375000-6937500 x+52250000 x^2-201000000 x^3+396000000 x^4-320000000 x^5}{-x^5-x^6+\left (-25 x^4+75 x^5+100 x^6\right ) \log (1+x)+\left (-250 x^3+1750 x^4-2000 x^5-4000 x^6\right ) \log ^2(1+x)+\left (-1250 x^2+13750 x^3-45000 x^4+20000 x^5+80000 x^6\right ) \log ^3(1+x)+\left (-3125 x+46875 x^2-250000 x^3+500000 x^4-800000 x^6\right ) \log ^4(1+x)+\left (-3125+59375 x-437500 x^2+1500000 x^3-2000000 x^4-800000 x^5+3200000 x^6\right ) \log ^5(1+x)} \, dx=\int \frac {320000000\,x^5-396000000\,x^4+201000000\,x^3-52250000\,x^2+6937500\,x-375000}{{\ln \left (x+1\right )}^4\,\left (800000\,x^6-500000\,x^4+250000\,x^3-46875\,x^2+3125\,x\right )+{\ln \left (x+1\right )}^2\,\left (4000\,x^6+2000\,x^5-1750\,x^4+250\,x^3\right )+{\ln \left (x+1\right )}^5\,\left (-3200000\,x^6+800000\,x^5+2000000\,x^4-1500000\,x^3+437500\,x^2-59375\,x+3125\right )-{\ln \left (x+1\right )}^3\,\left (80000\,x^6+20000\,x^5-45000\,x^4+13750\,x^3-1250\,x^2\right )-\ln \left (x+1\right )\,\left (100\,x^6+75\,x^5-25\,x^4\right )+x^5+x^6} \,d x \]

[In]

int((6937500*x - 52250000*x^2 + 201000000*x^3 - 396000000*x^4 + 320000000*x^5 - 375000)/(log(x + 1)^4*(3125*x
- 46875*x^2 + 250000*x^3 - 500000*x^4 + 800000*x^6) + log(x + 1)^2*(250*x^3 - 1750*x^4 + 2000*x^5 + 4000*x^6)
+ log(x + 1)^5*(437500*x^2 - 59375*x - 1500000*x^3 + 2000000*x^4 + 800000*x^5 - 3200000*x^6 + 3125) - log(x +
1)^3*(13750*x^3 - 1250*x^2 - 45000*x^4 + 20000*x^5 + 80000*x^6) - log(x + 1)*(75*x^5 - 25*x^4 + 100*x^6) + x^5
+ x^6),x)

[Out]

int((6937500*x - 52250000*x^2 + 201000000*x^3 - 396000000*x^4 + 320000000*x^5 - 375000)/(log(x + 1)^4*(3125*x
- 46875*x^2 + 250000*x^3 - 500000*x^4 + 800000*x^6) + log(x + 1)^2*(250*x^3 - 1750*x^4 + 2000*x^5 + 4000*x^6)
+ log(x + 1)^5*(437500*x^2 - 59375*x - 1500000*x^3 + 2000000*x^4 + 800000*x^5 - 3200000*x^6 + 3125) - log(x +
1)^3*(13750*x^3 - 1250*x^2 - 45000*x^4 + 20000*x^5 + 80000*x^6) - log(x + 1)*(75*x^5 - 25*x^4 + 100*x^6) + x^5
+ x^6), x)