3.98.93 \(\int \frac {-7742196 x^8+7779240 x^7 \log ^2(2)+(-7461720 x^8+7482888 x^7 \log ^2(2)) \log (-x+\log ^2(2))+(-2874816 x^8+2878848 x^7 \log ^2(2)) \log ^2(-x+\log ^2(2))+(-553472 x^8+553728 x^7 \log ^2(2)) \log ^3(-x+\log ^2(2))+(-53248 x^8+53248 x^7 \log ^2(2)) \log ^4(-x+\log ^2(2))+(-2048 x^8+2048 x^7 \log ^2(2)) \log ^5(-x+\log ^2(2))}{-3125 x+3125 \log ^2(2)+(-3125 x+3125 \log ^2(2)) \log (-x+\log ^2(2))+(-1250 x+1250 \log ^2(2)) \log ^2(-x+\log ^2(2))+(-250 x+250 \log ^2(2)) \log ^3(-x+\log ^2(2))+(-25 x+25 \log ^2(2)) \log ^4(-x+\log ^2(2))+(-x+\log ^2(2)) \log ^5(-x+\log ^2(2))} \, dx\)
Optimal. Leaf size=31 \[ x^8 \left (5+\frac {-x+\frac {x}{5+\log \left (-x+\log ^2(2)\right )}}{x}\right )^4 \]
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Rubi [B] time = 27.73, antiderivative size = 1640, normalized size of antiderivative = 52.90,
number of steps used = 1467, number of rules used = 17, integrand size = 267, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.064, Rules
used = {6688, 12, 6742, 2411, 2353, 2306, 2309, 2178, 2297, 2299, 2302, 30, 2418, 2400, 2399,
2389, 2390}
result too large to display
Antiderivative was successfully verified.
[In]
Int[(-7742196*x^8 + 7779240*x^7*Log[2]^2 + (-7461720*x^8 + 7482888*x^7*Log[2]^2)*Log[-x + Log[2]^2] + (-287481
6*x^8 + 2878848*x^7*Log[2]^2)*Log[-x + Log[2]^2]^2 + (-553472*x^8 + 553728*x^7*Log[2]^2)*Log[-x + Log[2]^2]^3
+ (-53248*x^8 + 53248*x^7*Log[2]^2)*Log[-x + Log[2]^2]^4 + (-2048*x^8 + 2048*x^7*Log[2]^2)*Log[-x + Log[2]^2]^
5)/(-3125*x + 3125*Log[2]^2 + (-3125*x + 3125*Log[2]^2)*Log[-x + Log[2]^2] + (-1250*x + 1250*Log[2]^2)*Log[-x
+ Log[2]^2]^2 + (-250*x + 250*Log[2]^2)*Log[-x + Log[2]^2]^3 + (-25*x + 25*Log[2]^2)*Log[-x + Log[2]^2]^4 + (-
x + Log[2]^2)*Log[-x + Log[2]^2]^5),x]
[Out]
256*x^8 + Log[2]^16/(5 + Log[-x + Log[2]^2])^4 + (8*Log[2]^14*(x - Log[2]^2))/(5 + Log[-x + Log[2]^2])^4 + (28
*Log[2]^12*(x - Log[2]^2)^2)/(5 + Log[-x + Log[2]^2])^4 + (56*Log[2]^10*(x - Log[2]^2)^3)/(5 + Log[-x + Log[2]
^2])^4 + (70*Log[2]^8*(x - Log[2]^2)^4)/(5 + Log[-x + Log[2]^2])^4 + (56*Log[2]^6*(x - Log[2]^2)^5)/(5 + Log[-
x + Log[2]^2])^4 + (28*Log[2]^4*(x - Log[2]^2)^6)/(5 + Log[-x + Log[2]^2])^4 + (8*Log[2]^2*(x - Log[2]^2)^7)/(
5 + Log[-x + Log[2]^2])^4 + (x - Log[2]^2)^8/(5 + Log[-x + Log[2]^2])^4 + (16*Log[2]^16)/(5 + Log[-x + Log[2]^
2])^3 + (40*x^7*(x - Log[2]^2))/(3*(5 + Log[-x + Log[2]^2])^3) + (16*x^6*Log[2]^2*(x - Log[2]^2))/(5 + Log[-x
+ Log[2]^2])^3 + (16*x^5*Log[2]^4*(x - Log[2]^2))/(5 + Log[-x + Log[2]^2])^3 + (16*x^4*Log[2]^6*(x - Log[2]^2)
)/(5 + Log[-x + Log[2]^2])^3 + (16*x^3*Log[2]^8*(x - Log[2]^2))/(5 + Log[-x + Log[2]^2])^3 + (16*x^2*Log[2]^10
*(x - Log[2]^2))/(5 + Log[-x + Log[2]^2])^3 + (16*x*Log[2]^12*(x - Log[2]^2))/(5 + Log[-x + Log[2]^2])^3 + (56
*Log[2]^14*(x - Log[2]^2))/(3*(5 + Log[-x + Log[2]^2])^3) + (56*Log[2]^12*(x - Log[2]^2)^2)/(3*(5 + Log[-x + L
og[2]^2])^3) + (56*Log[2]^10*(x - Log[2]^2)^3)/(5 + Log[-x + Log[2]^2])^3 + (280*Log[2]^8*(x - Log[2]^2)^4)/(3
*(5 + Log[-x + Log[2]^2])^3) + (280*Log[2]^6*(x - Log[2]^2)^5)/(3*(5 + Log[-x + Log[2]^2])^3) + (56*Log[2]^4*(
x - Log[2]^2)^6)/(5 + Log[-x + Log[2]^2])^3 + (56*Log[2]^2*(x - Log[2]^2)^7)/(3*(5 + Log[-x + Log[2]^2])^3) +
(8*(x - Log[2]^2)^8)/(3*(5 + Log[-x + Log[2]^2])^3) + (96*Log[2]^16)/(5 + Log[-x + Log[2]^2])^2 + (256*x^7*(x
- Log[2]^2))/(3*(5 + Log[-x + Log[2]^2])^2) + (316*x^6*Log[2]^2*(x - Log[2]^2))/(3*(5 + Log[-x + Log[2]^2])^2)
+ (96*x^5*Log[2]^4*(x - Log[2]^2))/(5 + Log[-x + Log[2]^2])^2 + (96*x^4*Log[2]^6*(x - Log[2]^2))/(5 + Log[-x
+ Log[2]^2])^2 + (96*x^3*Log[2]^8*(x - Log[2]^2))/(5 + Log[-x + Log[2]^2])^2 + (96*x^2*Log[2]^10*(x - Log[2]^2
))/(5 + Log[-x + Log[2]^2])^2 + (96*x*Log[2]^12*(x - Log[2]^2))/(5 + Log[-x + Log[2]^2])^2 + (292*Log[2]^14*(x
- Log[2]^2))/(3*(5 + Log[-x + Log[2]^2])^2) + (56*Log[2]^12*(x - Log[2]^2)^2)/(3*(5 + Log[-x + Log[2]^2])^2)
+ (84*Log[2]^10*(x - Log[2]^2)^3)/(5 + Log[-x + Log[2]^2])^2 + (560*Log[2]^8*(x - Log[2]^2)^4)/(3*(5 + Log[-x
+ Log[2]^2])^2) + (700*Log[2]^6*(x - Log[2]^2)^5)/(3*(5 + Log[-x + Log[2]^2])^2) + (168*Log[2]^4*(x - Log[2]^2
)^6)/(5 + Log[-x + Log[2]^2])^2 + (196*Log[2]^2*(x - Log[2]^2)^7)/(3*(5 + Log[-x + Log[2]^2])^2) + (32*(x - Lo
g[2]^2)^8)/(3*(5 + Log[-x + Log[2]^2])^2) + (256*Log[2]^16)/(5 + Log[-x + Log[2]^2]) + (512*x^7*(x - Log[2]^2)
)/(3*(5 + Log[-x + Log[2]^2])) + (396*x^6*Log[2]^2*(x - Log[2]^2))/(5 + Log[-x + Log[2]^2]) + (200*x^5*Log[2]^
4*(x - Log[2]^2))/(5 + Log[-x + Log[2]^2]) + (256*x^4*Log[2]^6*(x - Log[2]^2))/(5 + Log[-x + Log[2]^2]) + (256
*x^3*Log[2]^8*(x - Log[2]^2))/(5 + Log[-x + Log[2]^2]) + (256*x^2*Log[2]^10*(x - Log[2]^2))/(5 + Log[-x + Log[
2]^2]) + (256*x*Log[2]^12*(x - Log[2]^2))/(5 + Log[-x + Log[2]^2]) + (772*Log[2]^14*(x - Log[2]^2))/(3*(5 + Lo
g[-x + Log[2]^2])) + (112*Log[2]^12*(x - Log[2]^2)^2)/(3*(5 + Log[-x + Log[2]^2])) + (252*Log[2]^10*(x - Log[2
]^2)^3)/(5 + Log[-x + Log[2]^2]) + (2240*Log[2]^8*(x - Log[2]^2)^4)/(3*(5 + Log[-x + Log[2]^2])) + (3500*Log[2
]^6*(x - Log[2]^2)^5)/(3*(5 + Log[-x + Log[2]^2])) + (1008*Log[2]^4*(x - Log[2]^2)^6)/(5 + Log[-x + Log[2]^2])
+ (1372*Log[2]^2*(x - Log[2]^2)^7)/(3*(5 + Log[-x + Log[2]^2])) + (256*(x - Log[2]^2)^8)/(3*(5 + Log[-x + Log
[2]^2]))
Rule 12
Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] && !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]
Rule 30
Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]
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 2297
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_), x_Symbol] :> Simp[(x*(a + b*Log[c*x^n])^(p + 1))/(b*n*(p + 1))
, x] - Dist[1/(b*n*(p + 1)), Int[(a + b*Log[c*x^n])^(p + 1), x], x] /; FreeQ[{a, b, c, n}, x] && LtQ[p, -1] &&
IntegerQ[2*p]
Rule 2299
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_), x_Symbol] :> Dist[1/(n*c^(1/n)), Subst[Int[E^(x/n)*(a + b*x)^p
, x], x, Log[c*x^n]], x] /; FreeQ[{a, b, c, p}, x] && IntegerQ[1/n]
Rule 2302
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)/(x_), x_Symbol] :> Dist[1/(b*n), Subst[Int[x^p, x], x, a + b*L
og[c*x^n]], x] /; FreeQ[{a, b, c, n, p}, x]
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 2353
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((f_.)*(x_))^(m_.)*((d_) + (e_.)*(x_)^(r_.))^(q_.), x_Symbol]
:> With[{u = ExpandIntegrand[(a + b*Log[c*x^n])^p, (f*x)^m*(d + e*x^r)^q, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[
{a, b, c, d, e, f, m, n, p, q, r}, x] && IntegerQ[q] && (GtQ[q, 0] || (IGtQ[p, 0] && IntegerQ[m] && IntegerQ[r
]))
Rule 2389
Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.), x_Symbol] :> Dist[1/e, Subst[Int[(a + b*Log[c*
x^n])^p, x], x, d + e*x], x] /; FreeQ[{a, b, c, d, e, n, p}, x]
Rule 2390
Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.)*((f_) + (g_.)*(x_))^(q_.), x_Symbol] :> Dist[1/
e, Subst[Int[((f*x)/d)^q*(a + b*Log[c*x^n])^p, x], x, d + e*x], x] /; FreeQ[{a, b, c, d, e, f, g, n, p, q}, x]
&& EqQ[e*f - d*g, 0]
Rule 2399
Int[((f_.) + (g_.)*(x_))^(q_.)/((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.)), x_Symbol] :> Int[ExpandIn
tegrand[(f + g*x)^q/(a + b*Log[c*(d + e*x)^n]), x], x] /; FreeQ[{a, b, c, d, e, f, g, n}, x] && NeQ[e*f - d*g,
0] && IGtQ[q, 0]
Rule 2400
Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_)*((f_.) + (g_.)*(x_))^(q_.), x_Symbol] :> Simp[((
d + e*x)*(f + g*x)^q*(a + b*Log[c*(d + e*x)^n])^(p + 1))/(b*e*n*(p + 1)), x] + (-Dist[(q + 1)/(b*n*(p + 1)), I
nt[(f + g*x)^q*(a + b*Log[c*(d + e*x)^n])^(p + 1), x], x] + Dist[(q*(e*f - d*g))/(b*e*n*(p + 1)), Int[(f + g*x
)^(q - 1)*(a + b*Log[c*(d + e*x)^n])^(p + 1), x], x]) /; FreeQ[{a, b, c, d, e, f, g, n}, x] && NeQ[e*f - d*g,
0] && LtQ[p, -1] && GtQ[q, 0]
Rule 2411
Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.)*((f_.) + (g_.)*(x_))^(q_.)*((h_.) + (i_.)*(x_))
^(r_.), x_Symbol] :> Dist[1/e, Subst[Int[((g*x)/e)^q*((e*h - d*i)/e + (i*x)/e)^r*(a + b*Log[c*x^n])^p, x], x,
d + e*x], x] /; FreeQ[{a, b, c, d, e, f, g, h, i, n, p, q, r}, x] && EqQ[e*f - d*g, 0] && (IGtQ[p, 0] || IGtQ[
r, 0]) && IntegerQ[2*r]
Rule 2418
Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.)*(RFx_), x_Symbol] :> With[{u = ExpandIntegrand[
(a + b*Log[c*(d + e*x)^n])^p, RFx, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[{a, b, c, d, e, n}, x] && RationalFunct
ionQ[RFx, x] && IntegerQ[p]
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 {4 x^7 \left (21+4 \log \left (-x+\log ^2(2)\right )\right )^3 \left (209 x-210 \log ^2(2)+82 \left (x-\log ^2(2)\right ) \log \left (-x+\log ^2(2)\right )+8 \left (x-\log ^2(2)\right ) \log ^2\left (-x+\log ^2(2)\right )\right )}{\left (x-\log ^2(2)\right ) \left (5+\log \left (-x+\log ^2(2)\right )\right )^5} \, dx\\ &=4 \int \frac {x^7 \left (21+4 \log \left (-x+\log ^2(2)\right )\right )^3 \left (209 x-210 \log ^2(2)+82 \left (x-\log ^2(2)\right ) \log \left (-x+\log ^2(2)\right )+8 \left (x-\log ^2(2)\right ) \log ^2\left (-x+\log ^2(2)\right )\right )}{\left (x-\log ^2(2)\right ) \left (5+\log \left (-x+\log ^2(2)\right )\right )^5} \, dx\\ &=4 \int \left (512 x^7-\frac {x^8}{\left (x-\log ^2(2)\right ) \left (5+\log \left (-x+\log ^2(2)\right )\right )^5}-\frac {2 x^7 \left (5 x+\log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (5+\log \left (-x+\log ^2(2)\right )\right )^4}-\frac {16 x^7 \left (x+2 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (5+\log \left (-x+\log ^2(2)\right )\right )^3}+\frac {64 x^7 \left (2 x-3 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (5+\log \left (-x+\log ^2(2)\right )\right )^2}+\frac {512 x^7}{5+\log \left (-x+\log ^2(2)\right )}\right ) \, dx\\ &=256 x^8-4 \int \frac {x^8}{\left (x-\log ^2(2)\right ) \left (5+\log \left (-x+\log ^2(2)\right )\right )^5} \, dx-8 \int \frac {x^7 \left (5 x+\log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (5+\log \left (-x+\log ^2(2)\right )\right )^4} \, dx-64 \int \frac {x^7 \left (x+2 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (5+\log \left (-x+\log ^2(2)\right )\right )^3} \, dx+256 \int \frac {x^7 \left (2 x-3 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (5+\log \left (-x+\log ^2(2)\right )\right )^2} \, dx+2048 \int \frac {x^7}{5+\log \left (-x+\log ^2(2)\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [B] time = 2.45, size = 122, normalized size = 3.94 \begin {gather*} \frac {194481 x^8-160000 \log ^{16}(2)+16 \left (9261 x^8-8000 \log ^{16}(2)\right ) \log \left (-x+\log ^2(2)\right )+96 \left (441 x^8-400 \log ^{16}(2)\right ) \log ^2\left (-x+\log ^2(2)\right )+256 \left (21 x^8-20 \log ^{16}(2)\right ) \log ^3\left (-x+\log ^2(2)\right )+256 \left (x^8-\log ^{16}(2)\right ) \log ^4\left (-x+\log ^2(2)\right )}{\left (5+\log \left (-x+\log ^2(2)\right )\right )^4} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-7742196*x^8 + 7779240*x^7*Log[2]^2 + (-7461720*x^8 + 7482888*x^7*Log[2]^2)*Log[-x + Log[2]^2] + (-
2874816*x^8 + 2878848*x^7*Log[2]^2)*Log[-x + Log[2]^2]^2 + (-553472*x^8 + 553728*x^7*Log[2]^2)*Log[-x + Log[2]
^2]^3 + (-53248*x^8 + 53248*x^7*Log[2]^2)*Log[-x + Log[2]^2]^4 + (-2048*x^8 + 2048*x^7*Log[2]^2)*Log[-x + Log[
2]^2]^5)/(-3125*x + 3125*Log[2]^2 + (-3125*x + 3125*Log[2]^2)*Log[-x + Log[2]^2] + (-1250*x + 1250*Log[2]^2)*L
og[-x + Log[2]^2]^2 + (-250*x + 250*Log[2]^2)*Log[-x + Log[2]^2]^3 + (-25*x + 25*Log[2]^2)*Log[-x + Log[2]^2]^
4 + (-x + Log[2]^2)*Log[-x + Log[2]^2]^5),x]
[Out]
(194481*x^8 - 160000*Log[2]^16 + 16*(9261*x^8 - 8000*Log[2]^16)*Log[-x + Log[2]^2] + 96*(441*x^8 - 400*Log[2]^
16)*Log[-x + Log[2]^2]^2 + 256*(21*x^8 - 20*Log[2]^16)*Log[-x + Log[2]^2]^3 + 256*(x^8 - Log[2]^16)*Log[-x + L
og[2]^2]^4)/(5 + Log[-x + Log[2]^2])^4
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fricas [B] time = 0.81, size = 121, normalized size = 3.90 \begin {gather*} \frac {256 \, x^{8} \log \left (\log \relax (2)^{2} - x\right )^{4} + 5376 \, x^{8} \log \left (\log \relax (2)^{2} - x\right )^{3} + 42336 \, x^{8} \log \left (\log \relax (2)^{2} - x\right )^{2} + 148176 \, x^{8} \log \left (\log \relax (2)^{2} - x\right ) + 194481 \, x^{8}}{\log \left (\log \relax (2)^{2} - x\right )^{4} + 20 \, \log \left (\log \relax (2)^{2} - x\right )^{3} + 150 \, \log \left (\log \relax (2)^{2} - x\right )^{2} + 500 \, \log \left (\log \relax (2)^{2} - x\right ) + 625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((2048*x^7*log(2)^2-2048*x^8)*log(log(2)^2-x)^5+(53248*x^7*log(2)^2-53248*x^8)*log(log(2)^2-x)^4+(55
3728*x^7*log(2)^2-553472*x^8)*log(log(2)^2-x)^3+(2878848*x^7*log(2)^2-2874816*x^8)*log(log(2)^2-x)^2+(7482888*
x^7*log(2)^2-7461720*x^8)*log(log(2)^2-x)+7779240*x^7*log(2)^2-7742196*x^8)/((log(2)^2-x)*log(log(2)^2-x)^5+(2
5*log(2)^2-25*x)*log(log(2)^2-x)^4+(250*log(2)^2-250*x)*log(log(2)^2-x)^3+(1250*log(2)^2-1250*x)*log(log(2)^2-
x)^2+(3125*log(2)^2-3125*x)*log(log(2)^2-x)+3125*log(2)^2-3125*x),x, algorithm="fricas")
[Out]
(256*x^8*log(log(2)^2 - x)^4 + 5376*x^8*log(log(2)^2 - x)^3 + 42336*x^8*log(log(2)^2 - x)^2 + 148176*x^8*log(l
og(2)^2 - x) + 194481*x^8)/(log(log(2)^2 - x)^4 + 20*log(log(2)^2 - x)^3 + 150*log(log(2)^2 - x)^2 + 500*log(l
og(2)^2 - x) + 625)
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giac [B] time = 0.35, size = 111, normalized size = 3.58 \begin {gather*} 256 \, x^{8} + \frac {256 \, x^{8} \log \left (\log \relax (2)^{2} - x\right )^{3} + 3936 \, x^{8} \log \left (\log \relax (2)^{2} - x\right )^{2} + 20176 \, x^{8} \log \left (\log \relax (2)^{2} - x\right ) + 34481 \, x^{8}}{\log \left (\log \relax (2)^{2} - x\right )^{4} + 20 \, \log \left (\log \relax (2)^{2} - x\right )^{3} + 150 \, \log \left (\log \relax (2)^{2} - x\right )^{2} + 500 \, \log \left (\log \relax (2)^{2} - x\right ) + 625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((2048*x^7*log(2)^2-2048*x^8)*log(log(2)^2-x)^5+(53248*x^7*log(2)^2-53248*x^8)*log(log(2)^2-x)^4+(55
3728*x^7*log(2)^2-553472*x^8)*log(log(2)^2-x)^3+(2878848*x^7*log(2)^2-2874816*x^8)*log(log(2)^2-x)^2+(7482888*
x^7*log(2)^2-7461720*x^8)*log(log(2)^2-x)+7779240*x^7*log(2)^2-7742196*x^8)/((log(2)^2-x)*log(log(2)^2-x)^5+(2
5*log(2)^2-25*x)*log(log(2)^2-x)^4+(250*log(2)^2-250*x)*log(log(2)^2-x)^3+(1250*log(2)^2-1250*x)*log(log(2)^2-
x)^2+(3125*log(2)^2-3125*x)*log(log(2)^2-x)+3125*log(2)^2-3125*x),x, algorithm="giac")
[Out]
256*x^8 + (256*x^8*log(log(2)^2 - x)^3 + 3936*x^8*log(log(2)^2 - x)^2 + 20176*x^8*log(log(2)^2 - x) + 34481*x^
8)/(log(log(2)^2 - x)^4 + 20*log(log(2)^2 - x)^3 + 150*log(log(2)^2 - x)^2 + 500*log(log(2)^2 - x) + 625)
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maple [A] time = 0.09, size = 63, normalized size = 2.03
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\(256 x^{8}+\frac {x^{8} \left (256 \ln \left (\ln \relax (2)^{2}-x \right )^{3}+3936 \ln \left (\ln \relax (2)^{2}-x \right )^{2}+20176 \ln \left (\ln \relax (2)^{2}-x \right )+34481\right )}{\left (5+\ln \left (\ln \relax (2)^{2}-x \right )\right )^{4}}\) |
\(63\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((2048*x^7*ln(2)^2-2048*x^8)*ln(ln(2)^2-x)^5+(53248*x^7*ln(2)^2-53248*x^8)*ln(ln(2)^2-x)^4+(553728*x^7*ln(
2)^2-553472*x^8)*ln(ln(2)^2-x)^3+(2878848*x^7*ln(2)^2-2874816*x^8)*ln(ln(2)^2-x)^2+(7482888*x^7*ln(2)^2-746172
0*x^8)*ln(ln(2)^2-x)+7779240*x^7*ln(2)^2-7742196*x^8)/((ln(2)^2-x)*ln(ln(2)^2-x)^5+(25*ln(2)^2-25*x)*ln(ln(2)^
2-x)^4+(250*ln(2)^2-250*x)*ln(ln(2)^2-x)^3+(1250*ln(2)^2-1250*x)*ln(ln(2)^2-x)^2+(3125*ln(2)^2-3125*x)*ln(ln(2
)^2-x)+3125*ln(2)^2-3125*x),x,method=_RETURNVERBOSE)
[Out]
256*x^8+x^8*(256*ln(ln(2)^2-x)^3+3936*ln(ln(2)^2-x)^2+20176*ln(ln(2)^2-x)+34481)/(5+ln(ln(2)^2-x))^4
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maxima [B] time = 0.51, size = 121, normalized size = 3.90 \begin {gather*} \frac {256 \, x^{8} \log \left (\log \relax (2)^{2} - x\right )^{4} + 5376 \, x^{8} \log \left (\log \relax (2)^{2} - x\right )^{3} + 42336 \, x^{8} \log \left (\log \relax (2)^{2} - x\right )^{2} + 148176 \, x^{8} \log \left (\log \relax (2)^{2} - x\right ) + 194481 \, x^{8}}{\log \left (\log \relax (2)^{2} - x\right )^{4} + 20 \, \log \left (\log \relax (2)^{2} - x\right )^{3} + 150 \, \log \left (\log \relax (2)^{2} - x\right )^{2} + 500 \, \log \left (\log \relax (2)^{2} - x\right ) + 625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((2048*x^7*log(2)^2-2048*x^8)*log(log(2)^2-x)^5+(53248*x^7*log(2)^2-53248*x^8)*log(log(2)^2-x)^4+(55
3728*x^7*log(2)^2-553472*x^8)*log(log(2)^2-x)^3+(2878848*x^7*log(2)^2-2874816*x^8)*log(log(2)^2-x)^2+(7482888*
x^7*log(2)^2-7461720*x^8)*log(log(2)^2-x)+7779240*x^7*log(2)^2-7742196*x^8)/((log(2)^2-x)*log(log(2)^2-x)^5+(2
5*log(2)^2-25*x)*log(log(2)^2-x)^4+(250*log(2)^2-250*x)*log(log(2)^2-x)^3+(1250*log(2)^2-1250*x)*log(log(2)^2-
x)^2+(3125*log(2)^2-3125*x)*log(log(2)^2-x)+3125*log(2)^2-3125*x),x, algorithm="maxima")
[Out]
(256*x^8*log(log(2)^2 - x)^4 + 5376*x^8*log(log(2)^2 - x)^3 + 42336*x^8*log(log(2)^2 - x)^2 + 148176*x^8*log(l
og(2)^2 - x) + 194481*x^8)/(log(log(2)^2 - x)^4 + 20*log(log(2)^2 - x)^3 + 150*log(log(2)^2 - x)^2 + 500*log(l
og(2)^2 - x) + 625)
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mupad [B] time = 6.18, size = 1087, normalized size = 35.06 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(7779240*x^7*log(2)^2 + log(log(2)^2 - x)*(7482888*x^7*log(2)^2 - 7461720*x^8) + log(log(2)^2 - x)^5*(204
8*x^7*log(2)^2 - 2048*x^8) + log(log(2)^2 - x)^4*(53248*x^7*log(2)^2 - 53248*x^8) + log(log(2)^2 - x)^3*(55372
8*x^7*log(2)^2 - 553472*x^8) + log(log(2)^2 - x)^2*(2878848*x^7*log(2)^2 - 2874816*x^8) - 7742196*x^8)/(3125*x
+ log(log(2)^2 - x)*(3125*x - 3125*log(2)^2) + log(log(2)^2 - x)^5*(x - log(2)^2) + log(log(2)^2 - x)^4*(25*x
- 25*log(2)^2) + log(log(2)^2 - x)^3*(250*x - 250*log(2)^2) + log(log(2)^2 - x)^2*(1250*x - 1250*log(2)^2) -
3125*log(2)^2),x)
[Out]
(83397377*x^6*log(2)^4)/3 - (72798895*x^7*log(2)^2)/3 - 13680940*x^5*log(2)^6 + 2413670*x^4*log(2)^8 - ((256*l
og(log(2)^2 - x)^4*(x - log(2)^2)*(42*x^5*log(2)^4 - 105*x^6*log(2)^2 + 64*x^7))/3 - (x^5*log(log(2)^2 - x)*(2
4965017*x^2*log(2)^2 - 20865859*x*log(2)^4 + 5685162*log(2)^6 - 9784128*x^3))/3 - (x^5*(32678991*x^2*log(2)^2
- 26979281*x*log(2)^4 + 7241010*log(2)^6 - 12939712*x^3))/3 + (32*log(log(2)^2 - x)^3*(x - log(2)^2)*(6846*x^5
*log(2)^4 - 17507*x^6*log(2)^2 + 10880*x^7))/3 + (112*log(log(2)^2 - x)^2*(x - log(2)^2)*(14946*x^5*log(2)^4 -
39069*x^6*log(2)^2 + 24736*x^7))/3)/(10*log(log(2)^2 - x) + log(log(2)^2 - x)^2 + 25) + log(log(2)^2 - x)*((4
6356688*x^6*log(2)^4)/3 - 13219344*x^7*log(2)^2 - 7784896*x^5*log(2)^6 + 1412320*x^4*log(2)^8 + (12419072*x^8)
/3) + ((log(log(2)^2 - x)*(x - log(2)^2)*(183506575*x^6*log(2)^2 - 128543058*x^5*log(2)^4 + 28425810*x^4*log(2
)^6 - 83813888*x^7))/3 - (2*x^4*(205747241*x^2*log(2)^4 - 178617825*x^3*log(2)^2 - 101882949*x*log(2)^6 + 1810
2525*log(2)^8 + 56650912*x^4))/3 + (256*log(log(2)^2 - x)^4*(x - log(2)^2)*(1183*x^6*log(2)^2 - 882*x^5*log(2)
^4 + 210*x^4*log(2)^6 - 512*x^7))/3 + (32*log(log(2)^2 - x)^3*(x - log(2)^2)*(202069*x^6*log(2)^2 - 147462*x^5
*log(2)^4 + 34230*x^4*log(2)^6 - 89088*x^7))/3 + (16*log(log(2)^2 - x)^2*(x - log(2)^2)*(3231487*x^6*log(2)^2
- 2309706*x^5*log(2)^4 + 523110*x^4*log(2)^6 - 1450496*x^7))/3)/(log(log(2)^2 - x) + 5) + log(log(2)^2 - x)^3*
((528640*x^6*log(2)^4)/3 - 144640*x^7*log(2)^2 - 93184*x^5*log(2)^6 + 17920*x^4*log(2)^8 + (131072*x^8)/3) + l
og(log(2)^2 - x)^2*(2859808*x^6*log(2)^4 - 2396896*x^7*log(2)^2 - 1475712*x^5*log(2)^6 + 275520*x^4*log(2)^8 +
737280*x^8) + (23204096*x^8)/3 - ((2*x^6*(1206835*log(2)^4 - 2684392*x*log(2)^2 + 1474911*x^2))/3 + (2*x^6*lo
g(log(2)^2 - x)*(947527*log(2)^4 - 2088959*x*log(2)^2 + 1140424*x^2))/3 + (32*x^6*log(log(2)^2 - x)^2*(17437*l
og(2)^4 - 38091*x*log(2)^2 + 20648*x^2))/3 - (512*log(log(2)^2 - x)^4*(x - log(2)^2)*(7*x^6*log(2)^2 - 8*x^7))
/3 - (64*log(log(2)^2 - x)^3*(x - log(2)^2)*(1141*x^6*log(2)^2 - 1328*x^7))/3)/(75*log(log(2)^2 - x) + 15*log(
log(2)^2 - x)^2 + log(log(2)^2 - x)^3 + 125) - (x^7*(335549*x - 344810*log(2)^2) + 512*x^7*log(log(2)^2 - x)^4
*(x - log(2)^2) + 2*x^7*log(log(2)^2 - x)*(132715*x - 135361*log(2)^2) + 64*x^7*log(log(2)^2 - x)^3*(162*x - 1
63*log(2)^2) + 16*x^7*log(log(2)^2 - x)^2*(4919*x - 4982*log(2)^2))/(500*log(log(2)^2 - x) + 150*log(log(2)^2
- x)^2 + 20*log(log(2)^2 - x)^3 + log(log(2)^2 - x)^4 + 625)
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sympy [B] time = 0.26, size = 99, normalized size = 3.19 \begin {gather*} 256 x^{8} + \frac {256 x^{8} \log {\left (- x + \log {\relax (2 )}^{2} \right )}^{3} + 3936 x^{8} \log {\left (- x + \log {\relax (2 )}^{2} \right )}^{2} + 20176 x^{8} \log {\left (- x + \log {\relax (2 )}^{2} \right )} + 34481 x^{8}}{\log {\left (- x + \log {\relax (2 )}^{2} \right )}^{4} + 20 \log {\left (- x + \log {\relax (2 )}^{2} \right )}^{3} + 150 \log {\left (- x + \log {\relax (2 )}^{2} \right )}^{2} + 500 \log {\left (- x + \log {\relax (2 )}^{2} \right )} + 625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((2048*x**7*ln(2)**2-2048*x**8)*ln(ln(2)**2-x)**5+(53248*x**7*ln(2)**2-53248*x**8)*ln(ln(2)**2-x)**4
+(553728*x**7*ln(2)**2-553472*x**8)*ln(ln(2)**2-x)**3+(2878848*x**7*ln(2)**2-2874816*x**8)*ln(ln(2)**2-x)**2+(
7482888*x**7*ln(2)**2-7461720*x**8)*ln(ln(2)**2-x)+7779240*x**7*ln(2)**2-7742196*x**8)/((ln(2)**2-x)*ln(ln(2)*
*2-x)**5+(25*ln(2)**2-25*x)*ln(ln(2)**2-x)**4+(250*ln(2)**2-250*x)*ln(ln(2)**2-x)**3+(1250*ln(2)**2-1250*x)*ln
(ln(2)**2-x)**2+(3125*ln(2)**2-3125*x)*ln(ln(2)**2-x)+3125*ln(2)**2-3125*x),x)
[Out]
256*x**8 + (256*x**8*log(-x + log(2)**2)**3 + 3936*x**8*log(-x + log(2)**2)**2 + 20176*x**8*log(-x + log(2)**2
) + 34481*x**8)/(log(-x + log(2)**2)**4 + 20*log(-x + log(2)**2)**3 + 150*log(-x + log(2)**2)**2 + 500*log(-x
+ log(2)**2) + 625)
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