3.24.99 \(\int \frac {-80000 x+120000 x^2-60000 x^3+10000 x^4+(1024-4096 x+7168 x^2-7168 x^3+4480 x^4-1792 x^5+448 x^6-64 x^7+4 x^8) \log (x)+(1024-4096 x+7168 x^2-7168 x^3+4480 x^4-1792 x^5+448 x^6-64 x^7+4 x^8) \log (2 x)}{641601 x-563904 x^2+546832 x^3-326832 x^4+149270 x^5-54208 x^6+13552 x^7-1936 x^8+121 x^9+(-25632 x+62528 x^2-69424 x^3+49424 x^4-25890 x^5+9856 x^6-2464 x^7+352 x^8-22 x^9) \log (x) \log (2 x)+(256 x-1024 x^2+1792 x^3-1792 x^4+1120 x^5-448 x^6+112 x^7-16 x^8+x^9) \log ^2(x) \log ^2(2 x)} \, dx\)

Optimal. Leaf size=21 \[ \frac {4}{11+\frac {625}{(-2+x)^4}-\log (x) \log (2 x)} \]

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Rubi [F]  time = 55.98, 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 {-80000 x+120000 x^2-60000 x^3+10000 x^4+\left (1024-4096 x+7168 x^2-7168 x^3+4480 x^4-1792 x^5+448 x^6-64 x^7+4 x^8\right ) \log (x)+\left (1024-4096 x+7168 x^2-7168 x^3+4480 x^4-1792 x^5+448 x^6-64 x^7+4 x^8\right ) \log (2 x)}{641601 x-563904 x^2+546832 x^3-326832 x^4+149270 x^5-54208 x^6+13552 x^7-1936 x^8+121 x^9+\left (-25632 x+62528 x^2-69424 x^3+49424 x^4-25890 x^5+9856 x^6-2464 x^7+352 x^8-22 x^9\right ) \log (x) \log (2 x)+\left (256 x-1024 x^2+1792 x^3-1792 x^4+1120 x^5-448 x^6+112 x^7-16 x^8+x^9\right ) \log ^2(x) \log ^2(2 x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-80000*x + 120000*x^2 - 60000*x^3 + 10000*x^4 + (1024 - 4096*x + 7168*x^2 - 7168*x^3 + 4480*x^4 - 1792*x^
5 + 448*x^6 - 64*x^7 + 4*x^8)*Log[x] + (1024 - 4096*x + 7168*x^2 - 7168*x^3 + 4480*x^4 - 1792*x^5 + 448*x^6 -
64*x^7 + 4*x^8)*Log[2*x])/(641601*x - 563904*x^2 + 546832*x^3 - 326832*x^4 + 149270*x^5 - 54208*x^6 + 13552*x^
7 - 1936*x^8 + 121*x^9 + (-25632*x + 62528*x^2 - 69424*x^3 + 49424*x^4 - 25890*x^5 + 9856*x^6 - 2464*x^7 + 352
*x^8 - 22*x^9)*Log[x]*Log[2*x] + (256*x - 1024*x^2 + 1792*x^3 - 1792*x^4 + 1120*x^5 - 448*x^6 + 112*x^7 - 16*x
^8 + x^9)*Log[x]^2*Log[2*x]^2),x]

[Out]

-80000*Defer[Int][(801 - 352*x + 264*x^2 - 88*x^3 + 11*x^4 - (-2 + x)^4*Log[x]*Log[2*x])^(-2), x] + 120000*Def
er[Int][x/(801 - 352*x + 264*x^2 - 88*x^3 + 11*x^4 - (-2 + x)^4*Log[x]*Log[2*x])^2, x] - 60000*Defer[Int][x^2/
(801 - 352*x + 264*x^2 - 88*x^3 + 11*x^4 - (-2 + x)^4*Log[x]*Log[2*x])^2, x] + 10000*Defer[Int][x^3/(801 - 352
*x + 264*x^2 - 88*x^3 + 11*x^4 - (-2 + x)^4*Log[x]*Log[2*x])^2, x] - 125056*Defer[Int][1/(Log[x]*(801 - 352*x
+ 264*x^2 - 88*x^3 + 11*x^4 - (-2 + x)^4*Log[x]*Log[2*x])^2), x] + 51264*Defer[Int][1/(x*Log[x]*(801 - 352*x +
264*x^2 - 88*x^3 + 11*x^4 - (-2 + x)^4*Log[x]*Log[2*x])^2), x] + 138848*Defer[Int][x/(Log[x]*(801 - 352*x + 2
64*x^2 - 88*x^3 + 11*x^4 - (-2 + x)^4*Log[x]*Log[2*x])^2), x] - 98848*Defer[Int][x^2/(Log[x]*(801 - 352*x + 26
4*x^2 - 88*x^3 + 11*x^4 - (-2 + x)^4*Log[x]*Log[2*x])^2), x] + 51780*Defer[Int][x^3/(Log[x]*(801 - 352*x + 264
*x^2 - 88*x^3 + 11*x^4 - (-2 + x)^4*Log[x]*Log[2*x])^2), x] - 19712*Defer[Int][x^4/(Log[x]*(801 - 352*x + 264*
x^2 - 88*x^3 + 11*x^4 - (-2 + x)^4*Log[x]*Log[2*x])^2), x] + 4928*Defer[Int][x^5/(Log[x]*(801 - 352*x + 264*x^
2 - 88*x^3 + 11*x^4 - (-2 + x)^4*Log[x]*Log[2*x])^2), x] - 704*Defer[Int][x^6/(Log[x]*(801 - 352*x + 264*x^2 -
88*x^3 + 11*x^4 - (-2 + x)^4*Log[x]*Log[2*x])^2), x] + 44*Defer[Int][x^7/(Log[x]*(801 - 352*x + 264*x^2 - 88*
x^3 + 11*x^4 - (-2 + x)^4*Log[x]*Log[2*x])^2), x] - 4096*Defer[Int][Log[x]/(801 - 352*x + 264*x^2 - 88*x^3 + 1
1*x^4 - (-2 + x)^4*Log[x]*Log[2*x])^2, x] + 1024*Defer[Int][Log[x]/(x*(801 - 352*x + 264*x^2 - 88*x^3 + 11*x^4
- (-2 + x)^4*Log[x]*Log[2*x])^2), x] + 7168*Defer[Int][(x*Log[x])/(801 - 352*x + 264*x^2 - 88*x^3 + 11*x^4 -
(-2 + x)^4*Log[x]*Log[2*x])^2, x] - 7168*Defer[Int][(x^2*Log[x])/(801 - 352*x + 264*x^2 - 88*x^3 + 11*x^4 - (-
2 + x)^4*Log[x]*Log[2*x])^2, x] + 4480*Defer[Int][(x^3*Log[x])/(801 - 352*x + 264*x^2 - 88*x^3 + 11*x^4 - (-2
+ x)^4*Log[x]*Log[2*x])^2, x] - 1792*Defer[Int][(x^4*Log[x])/(801 - 352*x + 264*x^2 - 88*x^3 + 11*x^4 - (-2 +
x)^4*Log[x]*Log[2*x])^2, x] + 448*Defer[Int][(x^5*Log[x])/(801 - 352*x + 264*x^2 - 88*x^3 + 11*x^4 - (-2 + x)^
4*Log[x]*Log[2*x])^2, x] - 64*Defer[Int][(x^6*Log[x])/(801 - 352*x + 264*x^2 - 88*x^3 + 11*x^4 - (-2 + x)^4*Lo
g[x]*Log[2*x])^2, x] + 4*Defer[Int][(x^7*Log[x])/(801 - 352*x + 264*x^2 - 88*x^3 + 11*x^4 - (-2 + x)^4*Log[x]*
Log[2*x])^2, x] - 128*Defer[Int][1/(Log[x]*(-801 + 352*x - 264*x^2 + 88*x^3 - 11*x^4 + (-2 + x)^4*Log[x]*Log[2
*x])), x] + 64*Defer[Int][1/(x*Log[x]*(-801 + 352*x - 264*x^2 + 88*x^3 - 11*x^4 + (-2 + x)^4*Log[x]*Log[2*x]))
, x] + 96*Defer[Int][x/(Log[x]*(-801 + 352*x - 264*x^2 + 88*x^3 - 11*x^4 + (-2 + x)^4*Log[x]*Log[2*x])), x] -
32*Defer[Int][x^2/(Log[x]*(-801 + 352*x - 264*x^2 + 88*x^3 - 11*x^4 + (-2 + x)^4*Log[x]*Log[2*x])), x] + 4*Def
er[Int][x^3/(Log[x]*(-801 + 352*x - 264*x^2 + 88*x^3 - 11*x^4 + (-2 + x)^4*Log[x]*Log[2*x])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 (2-x)^3 \left (-2500 x-(-2+x)^5 \log (x)-(-2+x)^5 \log (2 x)\right )}{x \left (801-352 x+264 x^2-88 x^3+11 x^4-(-2+x)^4 \log (x) \log (2 x)\right )^2} \, dx\\ &=4 \int \frac {(2-x)^3 \left (-2500 x-(-2+x)^5 \log (x)-(-2+x)^5 \log (2 x)\right )}{x \left (801-352 x+264 x^2-88 x^3+11 x^4-(-2+x)^4 \log (x) \log (2 x)\right )^2} \, dx\\ &=4 \int \left (\frac {(-2+x)^3 \left (-1602+1505 x-880 x^2+440 x^3-110 x^4+11 x^5+2500 x \log (x)-32 \log ^2(x)+80 x \log ^2(x)-80 x^2 \log ^2(x)+40 x^3 \log ^2(x)-10 x^4 \log ^2(x)+x^5 \log ^2(x)\right )}{x \log (x) \left (-801+352 x-264 x^2+88 x^3-11 x^4+16 \log (x) \log (2 x)-32 x \log (x) \log (2 x)+24 x^2 \log (x) \log (2 x)-8 x^3 \log (x) \log (2 x)+x^4 \log (x) \log (2 x)\right )^2}+\frac {(-2+x)^4}{x \log (x) \left (-801+352 x-264 x^2+88 x^3-11 x^4+16 \log (x) \log (2 x)-32 x \log (x) \log (2 x)+24 x^2 \log (x) \log (2 x)-8 x^3 \log (x) \log (2 x)+x^4 \log (x) \log (2 x)\right )}\right ) \, dx\\ &=4 \int \frac {(-2+x)^3 \left (-1602+1505 x-880 x^2+440 x^3-110 x^4+11 x^5+2500 x \log (x)-32 \log ^2(x)+80 x \log ^2(x)-80 x^2 \log ^2(x)+40 x^3 \log ^2(x)-10 x^4 \log ^2(x)+x^5 \log ^2(x)\right )}{x \log (x) \left (-801+352 x-264 x^2+88 x^3-11 x^4+16 \log (x) \log (2 x)-32 x \log (x) \log (2 x)+24 x^2 \log (x) \log (2 x)-8 x^3 \log (x) \log (2 x)+x^4 \log (x) \log (2 x)\right )^2} \, dx+4 \int \frac {(-2+x)^4}{x \log (x) \left (-801+352 x-264 x^2+88 x^3-11 x^4+16 \log (x) \log (2 x)-32 x \log (x) \log (2 x)+24 x^2 \log (x) \log (2 x)-8 x^3 \log (x) \log (2 x)+x^4 \log (x) \log (2 x)\right )} \, dx\\ &=4 \int \frac {(2-x)^3 \left (1602-1505 x+880 x^2-440 x^3+110 x^4-11 x^5-2500 x \log (x)-(-2+x)^5 \log ^2(x)\right )}{x \log (x) \left (801-352 x+264 x^2-88 x^3+11 x^4-(-2+x)^4 \log (x) \log (2 x)\right )^2} \, dx+4 \int \frac {(2-x)^4}{x \log (x) \left (-801+352 x-264 x^2+88 x^3-11 x^4+(-2+x)^4 \log (x) \log (2 x)\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 5.21, size = 41, normalized size = 1.95 \begin {gather*} -\frac {4 (-2+x)^4}{-801+352 x-264 x^2+88 x^3-11 x^4+(-2+x)^4 \log (x) \log (2 x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-80000*x + 120000*x^2 - 60000*x^3 + 10000*x^4 + (1024 - 4096*x + 7168*x^2 - 7168*x^3 + 4480*x^4 - 1
792*x^5 + 448*x^6 - 64*x^7 + 4*x^8)*Log[x] + (1024 - 4096*x + 7168*x^2 - 7168*x^3 + 4480*x^4 - 1792*x^5 + 448*
x^6 - 64*x^7 + 4*x^8)*Log[2*x])/(641601*x - 563904*x^2 + 546832*x^3 - 326832*x^4 + 149270*x^5 - 54208*x^6 + 13
552*x^7 - 1936*x^8 + 121*x^9 + (-25632*x + 62528*x^2 - 69424*x^3 + 49424*x^4 - 25890*x^5 + 9856*x^6 - 2464*x^7
+ 352*x^8 - 22*x^9)*Log[x]*Log[2*x] + (256*x - 1024*x^2 + 1792*x^3 - 1792*x^4 + 1120*x^5 - 448*x^6 + 112*x^7
- 16*x^8 + x^9)*Log[x]^2*Log[2*x]^2),x]

[Out]

(-4*(-2 + x)^4)/(-801 + 352*x - 264*x^2 + 88*x^3 - 11*x^4 + (-2 + x)^4*Log[x]*Log[2*x])

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fricas [B]  time = 0.59, size = 90, normalized size = 4.29 \begin {gather*} \frac {4 \, {\left (x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16\right )}}{11 \, x^{4} - 88 \, x^{3} - {\left (x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16\right )} \log \relax (2) \log \relax (x) - {\left (x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16\right )} \log \relax (x)^{2} + 264 \, x^{2} - 352 \, x + 801} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^8-64*x^7+448*x^6-1792*x^5+4480*x^4-7168*x^3+7168*x^2-4096*x+1024)*log(2*x)+(4*x^8-64*x^7+448*x
^6-1792*x^5+4480*x^4-7168*x^3+7168*x^2-4096*x+1024)*log(x)+10000*x^4-60000*x^3+120000*x^2-80000*x)/((x^9-16*x^
8+112*x^7-448*x^6+1120*x^5-1792*x^4+1792*x^3-1024*x^2+256*x)*log(x)^2*log(2*x)^2+(-22*x^9+352*x^8-2464*x^7+985
6*x^6-25890*x^5+49424*x^4-69424*x^3+62528*x^2-25632*x)*log(x)*log(2*x)+121*x^9-1936*x^8+13552*x^7-54208*x^6+14
9270*x^5-326832*x^4+546832*x^3-563904*x^2+641601*x),x, algorithm="fricas")

[Out]

4*(x^4 - 8*x^3 + 24*x^2 - 32*x + 16)/(11*x^4 - 88*x^3 - (x^4 - 8*x^3 + 24*x^2 - 32*x + 16)*log(2)*log(x) - (x^
4 - 8*x^3 + 24*x^2 - 32*x + 16)*log(x)^2 + 264*x^2 - 352*x + 801)

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giac [B]  time = 0.65, size = 120, normalized size = 5.71 \begin {gather*} -\frac {4 \, {\left (x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16\right )}}{x^{4} \log \relax (2) \log \relax (x) + x^{4} \log \relax (x)^{2} - 8 \, x^{3} \log \relax (2) \log \relax (x) - 8 \, x^{3} \log \relax (x)^{2} - 11 \, x^{4} + 24 \, x^{2} \log \relax (2) \log \relax (x) + 24 \, x^{2} \log \relax (x)^{2} + 88 \, x^{3} - 32 \, x \log \relax (2) \log \relax (x) - 32 \, x \log \relax (x)^{2} - 264 \, x^{2} + 16 \, \log \relax (2) \log \relax (x) + 16 \, \log \relax (x)^{2} + 352 \, x - 801} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^8-64*x^7+448*x^6-1792*x^5+4480*x^4-7168*x^3+7168*x^2-4096*x+1024)*log(2*x)+(4*x^8-64*x^7+448*x
^6-1792*x^5+4480*x^4-7168*x^3+7168*x^2-4096*x+1024)*log(x)+10000*x^4-60000*x^3+120000*x^2-80000*x)/((x^9-16*x^
8+112*x^7-448*x^6+1120*x^5-1792*x^4+1792*x^3-1024*x^2+256*x)*log(x)^2*log(2*x)^2+(-22*x^9+352*x^8-2464*x^7+985
6*x^6-25890*x^5+49424*x^4-69424*x^3+62528*x^2-25632*x)*log(x)*log(2*x)+121*x^9-1936*x^8+13552*x^7-54208*x^6+14
9270*x^5-326832*x^4+546832*x^3-563904*x^2+641601*x),x, algorithm="giac")

[Out]

-4*(x^4 - 8*x^3 + 24*x^2 - 32*x + 16)/(x^4*log(2)*log(x) + x^4*log(x)^2 - 8*x^3*log(2)*log(x) - 8*x^3*log(x)^2
- 11*x^4 + 24*x^2*log(2)*log(x) + 24*x^2*log(x)^2 + 88*x^3 - 32*x*log(2)*log(x) - 32*x*log(x)^2 - 264*x^2 + 1
6*log(2)*log(x) + 16*log(x)^2 + 352*x - 801)

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maple [C]  time = 0.72, size = 139, normalized size = 6.62

method	result	size
risch	\(-\frac {8 i \left (x^{4}-8 x^{3}+24 x^{2}-32 x +16\right )}{-1602 i+32 i \ln \relax (x )^{2}+2 i \ln \relax (2) x^{4} \ln \relax (x )-16 i \ln \relax (2) x^{3} \ln \relax (x )+48 i \ln \relax (2) x^{2} \ln \relax (x )-64 i \ln \relax (2) x \ln \relax (x )+48 i x^{2} \ln \relax (x )^{2}+32 i \ln \relax (2) \ln \relax (x )-64 i x \ln \relax (x )^{2}+2 i x^{4} \ln \relax (x )^{2}-16 i x^{3} \ln \relax (x )^{2}+704 i x -22 i x^{4}+176 i x^{3}-528 i x^{2}}\)	\(139\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x^8-64*x^7+448*x^6-1792*x^5+4480*x^4-7168*x^3+7168*x^2-4096*x+1024)*ln(2*x)+(4*x^8-64*x^7+448*x^6-1792
*x^5+4480*x^4-7168*x^3+7168*x^2-4096*x+1024)*ln(x)+10000*x^4-60000*x^3+120000*x^2-80000*x)/((x^9-16*x^8+112*x^
7-448*x^6+1120*x^5-1792*x^4+1792*x^3-1024*x^2+256*x)*ln(x)^2*ln(2*x)^2+(-22*x^9+352*x^8-2464*x^7+9856*x^6-2589
0*x^5+49424*x^4-69424*x^3+62528*x^2-25632*x)*ln(x)*ln(2*x)+121*x^9-1936*x^8+13552*x^7-54208*x^6+149270*x^5-326
832*x^4+546832*x^3-563904*x^2+641601*x),x,method=_RETURNVERBOSE)

[Out]

-8*I*(x^4-8*x^3+24*x^2-32*x+16)/(-1602*I+32*I*ln(x)^2+2*I*ln(2)*x^4*ln(x)-16*I*ln(2)*x^3*ln(x)+48*I*ln(2)*x^2*
ln(x)-64*I*ln(2)*x*ln(x)+48*I*x^2*ln(x)^2+32*I*ln(2)*ln(x)-64*I*x*ln(x)^2+2*I*x^4*ln(x)^2-16*I*x^3*ln(x)^2+704
*I*x-22*I*x^4+176*I*x^3-528*I*x^2)

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maxima [B]  time = 0.70, size = 100, normalized size = 4.76 \begin {gather*} \frac {4 \, {\left (x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16\right )}}{11 \, x^{4} - 88 \, x^{3} - {\left (x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16\right )} \log \relax (x)^{2} + 264 \, x^{2} - {\left (x^{4} \log \relax (2) - 8 \, x^{3} \log \relax (2) + 24 \, x^{2} \log \relax (2) - 32 \, x \log \relax (2) + 16 \, \log \relax (2)\right )} \log \relax (x) - 352 \, x + 801} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^8-64*x^7+448*x^6-1792*x^5+4480*x^4-7168*x^3+7168*x^2-4096*x+1024)*log(2*x)+(4*x^8-64*x^7+448*x
^6-1792*x^5+4480*x^4-7168*x^3+7168*x^2-4096*x+1024)*log(x)+10000*x^4-60000*x^3+120000*x^2-80000*x)/((x^9-16*x^
8+112*x^7-448*x^6+1120*x^5-1792*x^4+1792*x^3-1024*x^2+256*x)*log(x)^2*log(2*x)^2+(-22*x^9+352*x^8-2464*x^7+985
6*x^6-25890*x^5+49424*x^4-69424*x^3+62528*x^2-25632*x)*log(x)*log(2*x)+121*x^9-1936*x^8+13552*x^7-54208*x^6+14
9270*x^5-326832*x^4+546832*x^3-563904*x^2+641601*x),x, algorithm="maxima")

[Out]

4*(x^4 - 8*x^3 + 24*x^2 - 32*x + 16)/(11*x^4 - 88*x^3 - (x^4 - 8*x^3 + 24*x^2 - 32*x + 16)*log(x)^2 + 264*x^2
- (x^4*log(2) - 8*x^3*log(2) + 24*x^2*log(2) - 32*x*log(2) + 16*log(2))*log(x) - 352*x + 801)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {\ln \left (2\,x\right )\,\left (4\,x^8-64\,x^7+448\,x^6-1792\,x^5+4480\,x^4-7168\,x^3+7168\,x^2-4096\,x+1024\right )-80000\,x+120000\,x^2-60000\,x^3+10000\,x^4+\ln \relax (x)\,\left (4\,x^8-64\,x^7+448\,x^6-1792\,x^5+4480\,x^4-7168\,x^3+7168\,x^2-4096\,x+1024\right )}{641601\,x-563904\,x^2+546832\,x^3-326832\,x^4+149270\,x^5-54208\,x^6+13552\,x^7-1936\,x^8+121\,x^9-\ln \left (2\,x\right )\,\ln \relax (x)\,\left (22\,x^9-352\,x^8+2464\,x^7-9856\,x^6+25890\,x^5-49424\,x^4+69424\,x^3-62528\,x^2+25632\,x\right )+{\ln \left (2\,x\right )}^2\,{\ln \relax (x)}^2\,\left (x^9-16\,x^8+112\,x^7-448\,x^6+1120\,x^5-1792\,x^4+1792\,x^3-1024\,x^2+256\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(2*x)*(7168*x^2 - 4096*x - 7168*x^3 + 4480*x^4 - 1792*x^5 + 448*x^6 - 64*x^7 + 4*x^8 + 1024) - 80000*x
+ 120000*x^2 - 60000*x^3 + 10000*x^4 + log(x)*(7168*x^2 - 4096*x - 7168*x^3 + 4480*x^4 - 1792*x^5 + 448*x^6 -
64*x^7 + 4*x^8 + 1024))/(641601*x - 563904*x^2 + 546832*x^3 - 326832*x^4 + 149270*x^5 - 54208*x^6 + 13552*x^7
- 1936*x^8 + 121*x^9 - log(2*x)*log(x)*(25632*x - 62528*x^2 + 69424*x^3 - 49424*x^4 + 25890*x^5 - 9856*x^6 +
2464*x^7 - 352*x^8 + 22*x^9) + log(2*x)^2*log(x)^2*(256*x - 1024*x^2 + 1792*x^3 - 1792*x^4 + 1120*x^5 - 448*x^
6 + 112*x^7 - 16*x^8 + x^9)),x)

[Out]

int((log(2*x)*(7168*x^2 - 4096*x - 7168*x^3 + 4480*x^4 - 1792*x^5 + 448*x^6 - 64*x^7 + 4*x^8 + 1024) - 80000*x
+ 120000*x^2 - 60000*x^3 + 10000*x^4 + log(x)*(7168*x^2 - 4096*x - 7168*x^3 + 4480*x^4 - 1792*x^5 + 448*x^6 -
64*x^7 + 4*x^8 + 1024))/(641601*x - 563904*x^2 + 546832*x^3 - 326832*x^4 + 149270*x^5 - 54208*x^6 + 13552*x^7
- 1936*x^8 + 121*x^9 - log(2*x)*log(x)*(25632*x - 62528*x^2 + 69424*x^3 - 49424*x^4 + 25890*x^5 - 9856*x^6 +
2464*x^7 - 352*x^8 + 22*x^9) + log(2*x)^2*log(x)^2*(256*x - 1024*x^2 + 1792*x^3 - 1792*x^4 + 1120*x^5 - 448*x^
6 + 112*x^7 - 16*x^8 + x^9)), x)

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sympy [B]  time = 1.10, size = 102, normalized size = 4.86 \begin {gather*} \frac {- 4 x^{4} + 32 x^{3} - 96 x^{2} + 128 x - 64}{- 11 x^{4} + 88 x^{3} - 264 x^{2} + 352 x + \left (x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 16\right ) \log {\relax (x )}^{2} + \left (x^{4} \log {\relax (2 )} - 8 x^{3} \log {\relax (2 )} + 24 x^{2} \log {\relax (2 )} - 32 x \log {\relax (2 )} + 16 \log {\relax (2 )}\right ) \log {\relax (x )} - 801} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x**8-64*x**7+448*x**6-1792*x**5+4480*x**4-7168*x**3+7168*x**2-4096*x+1024)*ln(2*x)+(4*x**8-64*x*
*7+448*x**6-1792*x**5+4480*x**4-7168*x**3+7168*x**2-4096*x+1024)*ln(x)+10000*x**4-60000*x**3+120000*x**2-80000
*x)/((x**9-16*x**8+112*x**7-448*x**6+1120*x**5-1792*x**4+1792*x**3-1024*x**2+256*x)*ln(x)**2*ln(2*x)**2+(-22*x
**9+352*x**8-2464*x**7+9856*x**6-25890*x**5+49424*x**4-69424*x**3+62528*x**2-25632*x)*ln(x)*ln(2*x)+121*x**9-1
936*x**8+13552*x**7-54208*x**6+149270*x**5-326832*x**4+546832*x**3-563904*x**2+641601*x),x)

[Out]

(-4*x**4 + 32*x**3 - 96*x**2 + 128*x - 64)/(-11*x**4 + 88*x**3 - 264*x**2 + 352*x + (x**4 - 8*x**3 + 24*x**2 -
32*x + 16)*log(x)**2 + (x**4*log(2) - 8*x**3*log(2) + 24*x**2*log(2) - 32*x*log(2) + 16*log(2))*log(x) - 801)

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