3.82.28 \(\int \frac {512-100 x+(2304+50 x) \log (x)+4608 \log ^2(x)+5376 \log ^3(x)+4032 \log ^4(x)+2016 \log ^5(x)+672 \log ^6(x)+144 \log ^7(x)+18 \log ^8(x)+\log ^9(x)}{512+2304 \log (x)+4608 \log ^2(x)+5376 \log ^3(x)+4032 \log ^4(x)+2016 \log ^5(x)+672 \log ^6(x)+144 \log ^7(x)+18 \log ^8(x)+\log ^9(x)} \, dx\)

Optimal. Leaf size=16 \[ \frac {3}{2}+x+\frac {25 x^2}{(2+\log (x))^8} \]

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Rubi [A]  time = 0.66, antiderivative size = 13, normalized size of antiderivative = 0.81, number of steps used = 22, number of rules used = 5, integrand size = 114, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.044, Rules used = {6688, 6742, 2306, 2309, 2178} \begin {gather*} \frac {25 x^2}{(\log (x)+2)^8}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(512 - 100*x + (2304 + 50*x)*Log[x] + 4608*Log[x]^2 + 5376*Log[x]^3 + 4032*Log[x]^4 + 2016*Log[x]^5 + 672*
Log[x]^6 + 144*Log[x]^7 + 18*Log[x]^8 + Log[x]^9)/(512 + 2304*Log[x] + 4608*Log[x]^2 + 5376*Log[x]^3 + 4032*Lo
g[x]^4 + 2016*Log[x]^5 + 672*Log[x]^6 + 144*Log[x]^7 + 18*Log[x]^8 + Log[x]^9),x]

[Out]

x + (25*x^2)/(2 + Log[x])^8

Rule 2178

Int[(F_)^((g_.)*((e_.) + (f_.)*(x_)))/((c_.) + (d_.)*(x_)), x_Symbol] :> Simp[(F^(g*(e - (c*f)/d))*ExpIntegral
Ei[(f*g*(c + d*x)*Log[F])/d])/d, x] /; FreeQ[{F, c, d, e, f, g}, x] &&  !$UseGamma === True

Rule 2306

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_)*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[((d*x)^(m + 1)*(a + b*Log
[c*x^n])^(p + 1))/(b*d*n*(p + 1)), x] - Dist[(m + 1)/(b*n*(p + 1)), Int[(d*x)^m*(a + b*Log[c*x^n])^(p + 1), x]
, x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1] && LtQ[p, -1]

Rule 2309

Int[((a_.) + Log[(c_.)*(x_)]*(b_.))^(p_)*(x_)^(m_.), x_Symbol] :> Dist[1/c^(m + 1), Subst[Int[E^((m + 1)*x)*(a
+ b*x)^p, x], x, Log[c*x]], x] /; FreeQ[{a, b, c, p}, x] && IntegerQ[m]

Rule 6688

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

Rule 6742

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {512-100 x+(2304+50 x) \log (x)+4608 \log ^2(x)+5376 \log ^3(x)+4032 \log ^4(x)+2016 \log ^5(x)+672 \log ^6(x)+144 \log ^7(x)+18 \log ^8(x)+\log ^9(x)}{(2+\log (x))^9} \, dx\\ &=\int \left (1-\frac {200 x}{(2+\log (x))^9}+\frac {50 x}{(2+\log (x))^8}\right ) \, dx\\ &=x+50 \int \frac {x}{(2+\log (x))^8} \, dx-200 \int \frac {x}{(2+\log (x))^9} \, dx\\ &=x+\frac {25 x^2}{(2+\log (x))^8}-\frac {50 x^2}{7 (2+\log (x))^7}+\frac {100}{7} \int \frac {x}{(2+\log (x))^7} \, dx-50 \int \frac {x}{(2+\log (x))^8} \, dx\\ &=x+\frac {25 x^2}{(2+\log (x))^8}-\frac {50 x^2}{21 (2+\log (x))^6}+\frac {100}{21} \int \frac {x}{(2+\log (x))^6} \, dx-\frac {100}{7} \int \frac {x}{(2+\log (x))^7} \, dx\\ &=x+\frac {25 x^2}{(2+\log (x))^8}-\frac {20 x^2}{21 (2+\log (x))^5}+\frac {40}{21} \int \frac {x}{(2+\log (x))^5} \, dx-\frac {100}{21} \int \frac {x}{(2+\log (x))^6} \, dx\\ &=x+\frac {25 x^2}{(2+\log (x))^8}-\frac {10 x^2}{21 (2+\log (x))^4}+\frac {20}{21} \int \frac {x}{(2+\log (x))^4} \, dx-\frac {40}{21} \int \frac {x}{(2+\log (x))^5} \, dx\\ &=x+\frac {25 x^2}{(2+\log (x))^8}-\frac {20 x^2}{63 (2+\log (x))^3}+\frac {40}{63} \int \frac {x}{(2+\log (x))^3} \, dx-\frac {20}{21} \int \frac {x}{(2+\log (x))^4} \, dx\\ &=x+\frac {25 x^2}{(2+\log (x))^8}-\frac {20 x^2}{63 (2+\log (x))^2}-\frac {40}{63} \int \frac {x}{(2+\log (x))^3} \, dx+\frac {40}{63} \int \frac {x}{(2+\log (x))^2} \, dx\\ &=x+\frac {25 x^2}{(2+\log (x))^8}-\frac {40 x^2}{63 (2+\log (x))}-\frac {40}{63} \int \frac {x}{(2+\log (x))^2} \, dx+\frac {80}{63} \int \frac {x}{2+\log (x)} \, dx\\ &=x+\frac {25 x^2}{(2+\log (x))^8}-\frac {80}{63} \int \frac {x}{2+\log (x)} \, dx+\frac {80}{63} \operatorname {Subst}\left (\int \frac {e^{2 x}}{2+x} \, dx,x,\log (x)\right )\\ &=x+\frac {80 \text {Ei}(2 (2+\log (x)))}{63 e^4}+\frac {25 x^2}{(2+\log (x))^8}-\frac {80}{63} \operatorname {Subst}\left (\int \frac {e^{2 x}}{2+x} \, dx,x,\log (x)\right )\\ &=x+\frac {25 x^2}{(2+\log (x))^8}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.46, size = 13, normalized size = 0.81 \begin {gather*} x+\frac {25 x^2}{(2+\log (x))^8} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(512 - 100*x + (2304 + 50*x)*Log[x] + 4608*Log[x]^2 + 5376*Log[x]^3 + 4032*Log[x]^4 + 2016*Log[x]^5
+ 672*Log[x]^6 + 144*Log[x]^7 + 18*Log[x]^8 + Log[x]^9)/(512 + 2304*Log[x] + 4608*Log[x]^2 + 5376*Log[x]^3 + 4
032*Log[x]^4 + 2016*Log[x]^5 + 672*Log[x]^6 + 144*Log[x]^7 + 18*Log[x]^8 + Log[x]^9),x]

[Out]

x + (25*x^2)/(2 + Log[x])^8

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fricas [B]  time = 0.97, size = 111, normalized size = 6.94 \begin {gather*} \frac {x \log \relax (x)^{8} + 16 \, x \log \relax (x)^{7} + 112 \, x \log \relax (x)^{6} + 448 \, x \log \relax (x)^{5} + 1120 \, x \log \relax (x)^{4} + 1792 \, x \log \relax (x)^{3} + 1792 \, x \log \relax (x)^{2} + 25 \, x^{2} + 1024 \, x \log \relax (x) + 256 \, x}{\log \relax (x)^{8} + 16 \, \log \relax (x)^{7} + 112 \, \log \relax (x)^{6} + 448 \, \log \relax (x)^{5} + 1120 \, \log \relax (x)^{4} + 1792 \, \log \relax (x)^{3} + 1792 \, \log \relax (x)^{2} + 1024 \, \log \relax (x) + 256} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(x)^9+18*log(x)^8+144*log(x)^7+672*log(x)^6+2016*log(x)^5+4032*log(x)^4+5376*log(x)^3+4608*log(x
)^2+(50*x+2304)*log(x)-100*x+512)/(log(x)^9+18*log(x)^8+144*log(x)^7+672*log(x)^6+2016*log(x)^5+4032*log(x)^4+
5376*log(x)^3+4608*log(x)^2+2304*log(x)+512),x, algorithm="fricas")

[Out]

(x*log(x)^8 + 16*x*log(x)^7 + 112*x*log(x)^6 + 448*x*log(x)^5 + 1120*x*log(x)^4 + 1792*x*log(x)^3 + 1792*x*log
(x)^2 + 25*x^2 + 1024*x*log(x) + 256*x)/(log(x)^8 + 16*log(x)^7 + 112*log(x)^6 + 448*log(x)^5 + 1120*log(x)^4
+ 1792*log(x)^3 + 1792*log(x)^2 + 1024*log(x) + 256)

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giac [B]  time = 0.24, size = 542, normalized size = 33.88 \begin {gather*} \frac {x \log \relax (x)^{8}}{\log \relax (x)^{8} + 16 \, \log \relax (x)^{7} + 112 \, \log \relax (x)^{6} + 448 \, \log \relax (x)^{5} + 1120 \, \log \relax (x)^{4} + 1792 \, \log \relax (x)^{3} + 1792 \, \log \relax (x)^{2} + 1024 \, \log \relax (x) + 256} + \frac {16 \, x \log \relax (x)^{7}}{\log \relax (x)^{8} + 16 \, \log \relax (x)^{7} + 112 \, \log \relax (x)^{6} + 448 \, \log \relax (x)^{5} + 1120 \, \log \relax (x)^{4} + 1792 \, \log \relax (x)^{3} + 1792 \, \log \relax (x)^{2} + 1024 \, \log \relax (x) + 256} + \frac {112 \, x \log \relax (x)^{6}}{\log \relax (x)^{8} + 16 \, \log \relax (x)^{7} + 112 \, \log \relax (x)^{6} + 448 \, \log \relax (x)^{5} + 1120 \, \log \relax (x)^{4} + 1792 \, \log \relax (x)^{3} + 1792 \, \log \relax (x)^{2} + 1024 \, \log \relax (x) + 256} + \frac {448 \, x \log \relax (x)^{5}}{\log \relax (x)^{8} + 16 \, \log \relax (x)^{7} + 112 \, \log \relax (x)^{6} + 448 \, \log \relax (x)^{5} + 1120 \, \log \relax (x)^{4} + 1792 \, \log \relax (x)^{3} + 1792 \, \log \relax (x)^{2} + 1024 \, \log \relax (x) + 256} + \frac {1120 \, x \log \relax (x)^{4}}{\log \relax (x)^{8} + 16 \, \log \relax (x)^{7} + 112 \, \log \relax (x)^{6} + 448 \, \log \relax (x)^{5} + 1120 \, \log \relax (x)^{4} + 1792 \, \log \relax (x)^{3} + 1792 \, \log \relax (x)^{2} + 1024 \, \log \relax (x) + 256} + \frac {1792 \, x \log \relax (x)^{3}}{\log \relax (x)^{8} + 16 \, \log \relax (x)^{7} + 112 \, \log \relax (x)^{6} + 448 \, \log \relax (x)^{5} + 1120 \, \log \relax (x)^{4} + 1792 \, \log \relax (x)^{3} + 1792 \, \log \relax (x)^{2} + 1024 \, \log \relax (x) + 256} + \frac {1792 \, x \log \relax (x)^{2}}{\log \relax (x)^{8} + 16 \, \log \relax (x)^{7} + 112 \, \log \relax (x)^{6} + 448 \, \log \relax (x)^{5} + 1120 \, \log \relax (x)^{4} + 1792 \, \log \relax (x)^{3} + 1792 \, \log \relax (x)^{2} + 1024 \, \log \relax (x) + 256} + \frac {25 \, x^{2}}{\log \relax (x)^{8} + 16 \, \log \relax (x)^{7} + 112 \, \log \relax (x)^{6} + 448 \, \log \relax (x)^{5} + 1120 \, \log \relax (x)^{4} + 1792 \, \log \relax (x)^{3} + 1792 \, \log \relax (x)^{2} + 1024 \, \log \relax (x) + 256} + \frac {1024 \, x \log \relax (x)}{\log \relax (x)^{8} + 16 \, \log \relax (x)^{7} + 112 \, \log \relax (x)^{6} + 448 \, \log \relax (x)^{5} + 1120 \, \log \relax (x)^{4} + 1792 \, \log \relax (x)^{3} + 1792 \, \log \relax (x)^{2} + 1024 \, \log \relax (x) + 256} + \frac {256 \, x}{\log \relax (x)^{8} + 16 \, \log \relax (x)^{7} + 112 \, \log \relax (x)^{6} + 448 \, \log \relax (x)^{5} + 1120 \, \log \relax (x)^{4} + 1792 \, \log \relax (x)^{3} + 1792 \, \log \relax (x)^{2} + 1024 \, \log \relax (x) + 256} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(x)^9+18*log(x)^8+144*log(x)^7+672*log(x)^6+2016*log(x)^5+4032*log(x)^4+5376*log(x)^3+4608*log(x
)^2+(50*x+2304)*log(x)-100*x+512)/(log(x)^9+18*log(x)^8+144*log(x)^7+672*log(x)^6+2016*log(x)^5+4032*log(x)^4+
5376*log(x)^3+4608*log(x)^2+2304*log(x)+512),x, algorithm="giac")

[Out]

x*log(x)^8/(log(x)^8 + 16*log(x)^7 + 112*log(x)^6 + 448*log(x)^5 + 1120*log(x)^4 + 1792*log(x)^3 + 1792*log(x)
^2 + 1024*log(x) + 256) + 16*x*log(x)^7/(log(x)^8 + 16*log(x)^7 + 112*log(x)^6 + 448*log(x)^5 + 1120*log(x)^4
+ 1792*log(x)^3 + 1792*log(x)^2 + 1024*log(x) + 256) + 112*x*log(x)^6/(log(x)^8 + 16*log(x)^7 + 112*log(x)^6 +
448*log(x)^5 + 1120*log(x)^4 + 1792*log(x)^3 + 1792*log(x)^2 + 1024*log(x) + 256) + 448*x*log(x)^5/(log(x)^8
+ 16*log(x)^7 + 112*log(x)^6 + 448*log(x)^5 + 1120*log(x)^4 + 1792*log(x)^3 + 1792*log(x)^2 + 1024*log(x) + 25
6) + 1120*x*log(x)^4/(log(x)^8 + 16*log(x)^7 + 112*log(x)^6 + 448*log(x)^5 + 1120*log(x)^4 + 1792*log(x)^3 + 1
792*log(x)^2 + 1024*log(x) + 256) + 1792*x*log(x)^3/(log(x)^8 + 16*log(x)^7 + 112*log(x)^6 + 448*log(x)^5 + 11
20*log(x)^4 + 1792*log(x)^3 + 1792*log(x)^2 + 1024*log(x) + 256) + 1792*x*log(x)^2/(log(x)^8 + 16*log(x)^7 + 1
12*log(x)^6 + 448*log(x)^5 + 1120*log(x)^4 + 1792*log(x)^3 + 1792*log(x)^2 + 1024*log(x) + 256) + 25*x^2/(log(
x)^8 + 16*log(x)^7 + 112*log(x)^6 + 448*log(x)^5 + 1120*log(x)^4 + 1792*log(x)^3 + 1792*log(x)^2 + 1024*log(x)
+ 256) + 1024*x*log(x)/(log(x)^8 + 16*log(x)^7 + 112*log(x)^6 + 448*log(x)^5 + 1120*log(x)^4 + 1792*log(x)^3
+ 1792*log(x)^2 + 1024*log(x) + 256) + 256*x/(log(x)^8 + 16*log(x)^7 + 112*log(x)^6 + 448*log(x)^5 + 1120*log(
x)^4 + 1792*log(x)^3 + 1792*log(x)^2 + 1024*log(x) + 256)

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maple [A]  time = 0.06, size = 14, normalized size = 0.88

method	result	size
risch	\(x +\frac {25 x^{2}}{\left (\ln \relax (x )+2\right )^{8}}\)	\(14\)
norman	\(\frac {x \ln \relax (x )^{8}+256 x +25 x^{2}+1024 x \ln \relax (x )+1792 x \ln \relax (x )^{2}+1792 x \ln \relax (x )^{3}+1120 x \ln \relax (x )^{4}+448 x \ln \relax (x )^{5}+112 x \ln \relax (x )^{6}+16 x \ln \relax (x )^{7}}{\left (\ln \relax (x )+2\right )^{8}}\)	\(70\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((ln(x)^9+18*ln(x)^8+144*ln(x)^7+672*ln(x)^6+2016*ln(x)^5+4032*ln(x)^4+5376*ln(x)^3+4608*ln(x)^2+(50*x+2304
)*ln(x)-100*x+512)/(ln(x)^9+18*ln(x)^8+144*ln(x)^7+672*ln(x)^6+2016*ln(x)^5+4032*ln(x)^4+5376*ln(x)^3+4608*ln(
x)^2+2304*ln(x)+512),x,method=_RETURNVERBOSE)

[Out]

x+25/(ln(x)+2)^8*x^2

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {630 \, x \log \relax (x)^{8} - 8 \, {\left (25 \, x^{2} - 1261 \, x\right )} \log \relax (x)^{7} - 20 \, {\left (145 \, x^{2} - 3534 \, x\right )} \log \relax (x)^{6} - 4 \, {\left (4525 \, x^{2} - 70756 \, x\right )} \log \relax (x)^{5} - 6 \, {\left (10525 \, x^{2} - 118088 \, x\right )} \log \relax (x)^{4} - 4 \, {\left (33375 \, x^{2} - 283984 \, x\right )} \log \relax (x)^{3} - 50 \, {\left (3451 \, x^{2} - 22816 \, x\right )} \log \relax (x)^{2} - 39625 \, x^{2} - 10 \, {\left (13045 \, x^{2} - 66496 \, x\right )} \log \relax (x) + 221312 \, x}{630 \, {\left (\log \relax (x)^{8} + 16 \, \log \relax (x)^{7} + 112 \, \log \relax (x)^{6} + 448 \, \log \relax (x)^{5} + 1120 \, \log \relax (x)^{4} + 1792 \, \log \relax (x)^{3} + 1792 \, \log \relax (x)^{2} + 1024 \, \log \relax (x) + 256\right )}} - \frac {512 \, e^{\left (-2\right )} E_{9}\left (-\log \relax (x) - 2\right )}{{\left (\log \relax (x) + 2\right )}^{8}} + \frac {100 \, e^{\left (-4\right )} E_{9}\left (-2 \, \log \relax (x) - 4\right )}{{\left (\log \relax (x) + 2\right )}^{8}} + \int \frac {4 \, {\left (50 \, x - 1\right )}}{315 \, {\left (\log \relax (x) + 2\right )}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(x)^9+18*log(x)^8+144*log(x)^7+672*log(x)^6+2016*log(x)^5+4032*log(x)^4+5376*log(x)^3+4608*log(x
)^2+(50*x+2304)*log(x)-100*x+512)/(log(x)^9+18*log(x)^8+144*log(x)^7+672*log(x)^6+2016*log(x)^5+4032*log(x)^4+
5376*log(x)^3+4608*log(x)^2+2304*log(x)+512),x, algorithm="maxima")

[Out]

1/630*(630*x*log(x)^8 - 8*(25*x^2 - 1261*x)*log(x)^7 - 20*(145*x^2 - 3534*x)*log(x)^6 - 4*(4525*x^2 - 70756*x)
*log(x)^5 - 6*(10525*x^2 - 118088*x)*log(x)^4 - 4*(33375*x^2 - 283984*x)*log(x)^3 - 50*(3451*x^2 - 22816*x)*lo
g(x)^2 - 39625*x^2 - 10*(13045*x^2 - 66496*x)*log(x) + 221312*x)/(log(x)^8 + 16*log(x)^7 + 112*log(x)^6 + 448*
log(x)^5 + 1120*log(x)^4 + 1792*log(x)^3 + 1792*log(x)^2 + 1024*log(x) + 256) - 512*e^(-2)*exp_integral_e(9, -
log(x) - 2)/(log(x) + 2)^8 + 100*e^(-4)*exp_integral_e(9, -2*log(x) - 4)/(log(x) + 2)^8 + integrate(4/315*(50*
x - 1)/(log(x) + 2), x)

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mupad [B]  time = 5.40, size = 337, normalized size = 21.06 \begin {gather*} x-\frac {\frac {25\,x^2\,\ln \relax (x)}{4}-\frac {25\,x^2}{2}}{{\ln \relax (x)}^8+16\,{\ln \relax (x)}^7+112\,{\ln \relax (x)}^6+448\,{\ln \relax (x)}^5+1120\,{\ln \relax (x)}^4+1792\,{\ln \relax (x)}^3+1792\,{\ln \relax (x)}^2+1024\,\ln \relax (x)+256}-\frac {\frac {5\,x^2\,\ln \relax (x)}{21}-\frac {5\,x^2}{42}}{{\ln \relax (x)}^5+10\,{\ln \relax (x)}^4+40\,{\ln \relax (x)}^3+80\,{\ln \relax (x)}^2+80\,\ln \relax (x)+32}-\frac {\frac {5\,x^2\,\ln \relax (x)}{63}+\frac {5\,x^2}{63}}{{\ln \relax (x)}^2+4\,\ln \relax (x)+4}-\frac {\frac {25\,x^2\,\ln \relax (x)}{14}-\frac {75\,x^2}{28}}{{\ln \relax (x)}^7+14\,{\ln \relax (x)}^6+84\,{\ln \relax (x)}^5+280\,{\ln \relax (x)}^4+560\,{\ln \relax (x)}^3+672\,{\ln \relax (x)}^2+448\,\ln \relax (x)+128}-\frac {\frac {10\,x^2\,\ln \relax (x)}{63}+\frac {5\,x^2}{21}}{\ln \relax (x)+2}+\frac {10\,x^2}{63}-\frac {\frac {25\,x^2\,\ln \relax (x)}{42}-\frac {25\,x^2}{42}}{{\ln \relax (x)}^6+12\,{\ln \relax (x)}^5+60\,{\ln \relax (x)}^4+160\,{\ln \relax (x)}^3+240\,{\ln \relax (x)}^2+192\,\ln \relax (x)+64}-\frac {\frac {5\,x^2\,\ln \relax (x)}{63}+\frac {5\,x^2}{126}}{{\ln \relax (x)}^3+6\,{\ln \relax (x)}^2+12\,\ln \relax (x)+8}-\frac {5\,x^2\,\ln \relax (x)}{42\,\left ({\ln \relax (x)}^4+8\,{\ln \relax (x)}^3+24\,{\ln \relax (x)}^2+32\,\ln \relax (x)+16\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4608*log(x)^2 - 100*x + 5376*log(x)^3 + 4032*log(x)^4 + 2016*log(x)^5 + 672*log(x)^6 + 144*log(x)^7 + 18*
log(x)^8 + log(x)^9 + log(x)*(50*x + 2304) + 512)/(2304*log(x) + 4608*log(x)^2 + 5376*log(x)^3 + 4032*log(x)^4
+ 2016*log(x)^5 + 672*log(x)^6 + 144*log(x)^7 + 18*log(x)^8 + log(x)^9 + 512),x)

[Out]

x - ((25*x^2*log(x))/4 - (25*x^2)/2)/(1024*log(x) + 1792*log(x)^2 + 1792*log(x)^3 + 1120*log(x)^4 + 448*log(x)
^5 + 112*log(x)^6 + 16*log(x)^7 + log(x)^8 + 256) - ((5*x^2*log(x))/21 - (5*x^2)/42)/(80*log(x) + 80*log(x)^2
+ 40*log(x)^3 + 10*log(x)^4 + log(x)^5 + 32) - ((5*x^2*log(x))/63 + (5*x^2)/63)/(4*log(x) + log(x)^2 + 4) - ((
25*x^2*log(x))/14 - (75*x^2)/28)/(448*log(x) + 672*log(x)^2 + 560*log(x)^3 + 280*log(x)^4 + 84*log(x)^5 + 14*l
og(x)^6 + log(x)^7 + 128) - ((10*x^2*log(x))/63 + (5*x^2)/21)/(log(x) + 2) + (10*x^2)/63 - ((25*x^2*log(x))/42
- (25*x^2)/42)/(192*log(x) + 240*log(x)^2 + 160*log(x)^3 + 60*log(x)^4 + 12*log(x)^5 + log(x)^6 + 64) - ((5*x
^2*log(x))/63 + (5*x^2)/126)/(12*log(x) + 6*log(x)^2 + log(x)^3 + 8) - (5*x^2*log(x))/(42*(32*log(x) + 24*log(
x)^2 + 8*log(x)^3 + log(x)^4 + 16))

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sympy [B]  time = 0.23, size = 58, normalized size = 3.62 \begin {gather*} \frac {25 x^{2}}{\log {\relax (x )}^{8} + 16 \log {\relax (x )}^{7} + 112 \log {\relax (x )}^{6} + 448 \log {\relax (x )}^{5} + 1120 \log {\relax (x )}^{4} + 1792 \log {\relax (x )}^{3} + 1792 \log {\relax (x )}^{2} + 1024 \log {\relax (x )} + 256} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((ln(x)**9+18*ln(x)**8+144*ln(x)**7+672*ln(x)**6+2016*ln(x)**5+4032*ln(x)**4+5376*ln(x)**3+4608*ln(x)
**2+(50*x+2304)*ln(x)-100*x+512)/(ln(x)**9+18*ln(x)**8+144*ln(x)**7+672*ln(x)**6+2016*ln(x)**5+4032*ln(x)**4+5
376*ln(x)**3+4608*ln(x)**2+2304*ln(x)+512),x)

[Out]

25*x**2/(log(x)**8 + 16*log(x)**7 + 112*log(x)**6 + 448*log(x)**5 + 1120*log(x)**4 + 1792*log(x)**3 + 1792*log
(x)**2 + 1024*log(x) + 256) + x

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