3.20.64 \(\int \frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8+(-4660 x^2+240 x^3-2164 x^6+112 x^7) \log (79-4 x)+(-1580 x+80 x^2-2796 x^5+144 x^6) \log ^2(79-4 x)+(-1564 x^4+80 x^5) \log ^3(79-4 x)+(-316 x^3+16 x^4) \log ^4(79-4 x)}{-79+4 x} \, dx\)

Optimal. Leaf size=25 \[ -3-x+\left (5+x^2 (x+\log (67-4 (-3+x)))^2\right )^2 \]

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Rubi [B]  time = 3.73, antiderivative size = 850, normalized size of antiderivative = 34.00, number of steps used = 167, number of rules used = 20, integrand size = 129, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.155, Rules used = {6742, 1850, 2418, 2389, 2295, 2395, 43, 2390, 2301, 2296, 2401, 2305, 2304, 2398, 2411, 2334, 12, 14, 2302, 30} \begin {gather*} x^8+4 \log (79-4 x) x^7+6 \log ^2(79-4 x) x^6+2 \log (79-4 x) x^6-\frac {x^6}{3}+\frac {12}{5} \log ^2(79-4 x) x^5+\frac {237}{5} \log (79-4 x) x^5-\frac {869 x^5}{50}+\frac {237}{4} \log ^2(79-4 x) x^4+\frac {18723}{16} \log (79-4 x) x^4-\frac {227717 x^4}{320}+\frac {6241}{4} \log ^2(79-4 x) x^3+\frac {493359}{16} \log (79-4 x) x^3-\frac {9367741 x^3}{320}+\frac {116851523}{128} \log (79-4 x) x^2-\frac {3388669847 x^2}{2560}+\frac {655414019067 x}{5120}+\frac {(79-4 x)^6}{12288}-\frac {711 (79-4 x)^5}{12800}+\frac {280845 (79-4 x)^4}{16384}+\frac {1}{256} (79-4 x)^4 \log ^4(79-4 x)-\frac {79}{64} (79-4 x)^3 \log ^4(79-4 x)+\frac {18723}{128} (79-4 x)^2 \log ^4(79-4 x)-\frac {493039}{64} (79-4 x) \log ^4(79-4 x)+\frac {38950081}{256} \log ^4(79-4 x)-\frac {2465195}{768} (79-4 x)^3-\frac {1}{256} (79-4 x)^5 \log ^3(79-4 x)+\frac {395}{256} (79-4 x)^4 \log ^3(79-4 x)-\frac {31205}{128} (79-4 x)^3 \log ^3(79-4 x)+\frac {2465195}{128} (79-4 x)^2 \log ^3(79-4 x)-\frac {194750405}{256} (79-4 x) \log ^3(79-4 x)+\frac {3077056399}{256} \log ^3(79-4 x)+\frac {1752754925 (79-4 x)^2}{4096}+\frac {3 (79-4 x)^5 \log ^2(79-4 x)}{1280}-\frac {1185 (79-4 x)^4 \log ^2(79-4 x)}{1024}+\frac {31205}{128} (79-4 x)^3 \log ^2(79-4 x)-\frac {13311733}{512} (79-4 x)^2 \log ^2(79-4 x)+\frac {350525449}{256} (79-4 x) \log ^2(79-4 x)+\frac {236934590923}{320} \log ^2(79-4 x)-\frac {3 (79-4 x)^5 \log (79-4 x)}{3200}+\frac {1185 (79-4 x)^4 \log (79-4 x)}{2048}-\frac {31205}{192} (79-4 x)^3 \log (79-4 x)+\frac {13311733}{512} (79-4 x)^2 \log (79-4 x)-\frac {12035473909 (79-4 x) \log (79-4 x)}{1024}+\frac {\left (-10 (79-4 x)^6+5688 (79-4 x)^5-1404225 (79-4 x)^4+197215600 (79-4 x)^3-17527536450 (79-4 x)^2+1107740303640 (79-4 x)-14585247331260 \log (79-4 x)\right ) \log (79-4 x)}{20480}+\frac {\left (12 (79-4 x)^5-5925 (79-4 x)^4+1248200 (79-4 x)^3-147911700 (79-4 x)^2+11685024300 (79-4 x)-184623383940 \log (79-4 x)\right ) \log (79-4 x)}{12800}+\frac {79 \left (-3 (79-4 x)^4+1264 (79-4 x)^3-224676 (79-4 x)^2+23665872 (79-4 x)-467400972 \log (79-4 x)\right ) \log (79-4 x)}{2048}+\frac {6241}{768} \left (2 (79-4 x)^3-711 (79-4 x)^2+112338 (79-4 x)-2958234 \log (79-4 x)\right ) \log (79-4 x)-\frac {21148688515127 \log (79-4 x)}{20480} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(79 - 4*x - 3080*x^3 + 160*x^4 - 616*x^7 + 32*x^8 + (-4660*x^2 + 240*x^3 - 2164*x^6 + 112*x^7)*Log[79 - 4*
x] + (-1580*x + 80*x^2 - 2796*x^5 + 144*x^6)*Log[79 - 4*x]^2 + (-1564*x^4 + 80*x^5)*Log[79 - 4*x]^3 + (-316*x^
3 + 16*x^4)*Log[79 - 4*x]^4)/(-79 + 4*x),x]

[Out]

(1752754925*(79 - 4*x)^2)/4096 - (2465195*(79 - 4*x)^3)/768 + (280845*(79 - 4*x)^4)/16384 - (711*(79 - 4*x)^5)
/12800 + (79 - 4*x)^6/12288 + (655414019067*x)/5120 - (3388669847*x^2)/2560 - (9367741*x^3)/320 - (227717*x^4)
/320 - (869*x^5)/50 - x^6/3 + x^8 - (21148688515127*Log[79 - 4*x])/20480 - (12035473909*(79 - 4*x)*Log[79 - 4*
x])/1024 + (13311733*(79 - 4*x)^2*Log[79 - 4*x])/512 - (31205*(79 - 4*x)^3*Log[79 - 4*x])/192 + (1185*(79 - 4*
x)^4*Log[79 - 4*x])/2048 - (3*(79 - 4*x)^5*Log[79 - 4*x])/3200 + (116851523*x^2*Log[79 - 4*x])/128 + (493359*x
^3*Log[79 - 4*x])/16 + (18723*x^4*Log[79 - 4*x])/16 + (237*x^5*Log[79 - 4*x])/5 + 2*x^6*Log[79 - 4*x] + 4*x^7*
Log[79 - 4*x] + ((1107740303640*(79 - 4*x) - 17527536450*(79 - 4*x)^2 + 197215600*(79 - 4*x)^3 - 1404225*(79 -
4*x)^4 + 5688*(79 - 4*x)^5 - 10*(79 - 4*x)^6 - 14585247331260*Log[79 - 4*x])*Log[79 - 4*x])/20480 + ((1168502
4300*(79 - 4*x) - 147911700*(79 - 4*x)^2 + 1248200*(79 - 4*x)^3 - 5925*(79 - 4*x)^4 + 12*(79 - 4*x)^5 - 184623
383940*Log[79 - 4*x])*Log[79 - 4*x])/12800 + (79*(23665872*(79 - 4*x) - 224676*(79 - 4*x)^2 + 1264*(79 - 4*x)^
3 - 3*(79 - 4*x)^4 - 467400972*Log[79 - 4*x])*Log[79 - 4*x])/2048 + (6241*(112338*(79 - 4*x) - 711*(79 - 4*x)^
2 + 2*(79 - 4*x)^3 - 2958234*Log[79 - 4*x])*Log[79 - 4*x])/768 + (236934590923*Log[79 - 4*x]^2)/320 + (3505254
49*(79 - 4*x)*Log[79 - 4*x]^2)/256 - (13311733*(79 - 4*x)^2*Log[79 - 4*x]^2)/512 + (31205*(79 - 4*x)^3*Log[79
- 4*x]^2)/128 - (1185*(79 - 4*x)^4*Log[79 - 4*x]^2)/1024 + (3*(79 - 4*x)^5*Log[79 - 4*x]^2)/1280 + (6241*x^3*L
og[79 - 4*x]^2)/4 + (237*x^4*Log[79 - 4*x]^2)/4 + (12*x^5*Log[79 - 4*x]^2)/5 + 6*x^6*Log[79 - 4*x]^2 + (307705
6399*Log[79 - 4*x]^3)/256 - (194750405*(79 - 4*x)*Log[79 - 4*x]^3)/256 + (2465195*(79 - 4*x)^2*Log[79 - 4*x]^3
)/128 - (31205*(79 - 4*x)^3*Log[79 - 4*x]^3)/128 + (395*(79 - 4*x)^4*Log[79 - 4*x]^3)/256 - ((79 - 4*x)^5*Log[
79 - 4*x]^3)/256 + (38950081*Log[79 - 4*x]^4)/256 - (493039*(79 - 4*x)*Log[79 - 4*x]^4)/64 + (18723*(79 - 4*x)
^2*Log[79 - 4*x]^4)/128 - (79*(79 - 4*x)^3*Log[79 - 4*x]^4)/64 + ((79 - 4*x)^4*Log[79 - 4*x]^4)/256

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rule 43

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rule 1850

Int[(Pq_)*((a_) + (b_.)*(x_)^(n_.))^(p_.), x_Symbol] :> Int[ExpandIntegrand[Pq*(a + b*x^n)^p, x], x] /; FreeQ[
{a, b, n}, x] && PolyQ[Pq, x] && (IGtQ[p, 0] || EqQ[n, 1])

Rule 2295

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rule 2296

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.), x_Symbol] :> Simp[x*(a + b*Log[c*x^n])^p, x] - Dist[b*n*p, In
t[(a + b*Log[c*x^n])^(p - 1), x], x] /; FreeQ[{a, b, c, n}, x] && GtQ[p, 0] && IntegerQ[2*p]

Rule 2301

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))/(x_), x_Symbol] :> Simp[(a + b*Log[c*x^n])^2/(2*b*n), x] /; FreeQ[{a
, b, c, n}, x]

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 2304

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[((d*x)^(m + 1)*(a + b*Log[c*x^
n]))/(d*(m + 1)), x] - Simp[(b*n*(d*x)^(m + 1))/(d*(m + 1)^2), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1
]

Rule 2305

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[((d*x)^(m + 1)*(a + b*Lo
g[c*x^n])^p)/(d*(m + 1)), x] - Dist[(b*n*p)/(m + 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] && GtQ[p, 0]

Rule 2334

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*(x_)^(m_.)*((d_) + (e_.)*(x_)^(r_.))^(q_.), x_Symbol] :> With[{u = I
ntHide[x^m*(d + e*x^r)^q, x]}, Simp[u*(a + b*Log[c*x^n]), x] - Dist[b*n, Int[SimplifyIntegrand[u/x, x], x], x]
] /; FreeQ[{a, b, c, d, e, n, r}, x] && IGtQ[q, 0] && IntegerQ[m] &&  !(EqQ[q, 1] && EqQ[m, -1])

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 2395

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))*((f_.) + (g_.)*(x_))^(q_.), x_Symbol] :> Simp[((f + g
*x)^(q + 1)*(a + b*Log[c*(d + e*x)^n]))/(g*(q + 1)), x] - Dist[(b*e*n)/(g*(q + 1)), Int[(f + g*x)^(q + 1)/(d +
e*x), x], x] /; FreeQ[{a, b, c, d, e, f, g, n, q}, x] && NeQ[e*f - d*g, 0] && NeQ[q, -1]

Rule 2398

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_)*((f_.) + (g_.)*(x_))^(q_.), x_Symbol] :> Simp[((
f + g*x)^(q + 1)*(a + b*Log[c*(d + e*x)^n])^p)/(g*(q + 1)), x] - Dist[(b*e*n*p)/(g*(q + 1)), Int[((f + g*x)^(q
+ 1)*(a + b*Log[c*(d + e*x)^n])^(p - 1))/(d + e*x), x], x] /; FreeQ[{a, b, c, d, e, f, g, n, q}, x] && NeQ[e*
f - d*g, 0] && GtQ[p, 0] && NeQ[q, -1] && IntegersQ[2*p, 2*q] && ( !IGtQ[q, 0] || (EqQ[p, 2] && NeQ[q, 1]))

Rule 2401

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_)*((f_.) + (g_.)*(x_))^(q_.), x_Symbol] :> Int[Exp
andIntegrand[(f + g*x)^q*(a + b*Log[c*(d + e*x)^n])^p, x], x] /; FreeQ[{a, b, c, d, e, f, g, n, p}, x] && NeQ[
e*f - d*g, 0] && IGtQ[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 6742

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8}{-79+4 x}+\frac {4 x^2 \left (-1165+60 x-541 x^4+28 x^5\right ) \log (79-4 x)}{-79+4 x}+\frac {4 x \left (-395+20 x-699 x^4+36 x^5\right ) \log ^2(79-4 x)}{-79+4 x}+\frac {4 x^4 (-391+20 x) \log ^3(79-4 x)}{-79+4 x}+4 x^3 \log ^4(79-4 x)\right ) \, dx\\ &=4 \int \frac {x^2 \left (-1165+60 x-541 x^4+28 x^5\right ) \log (79-4 x)}{-79+4 x} \, dx+4 \int \frac {x \left (-395+20 x-699 x^4+36 x^5\right ) \log ^2(79-4 x)}{-79+4 x} \, dx+4 \int \frac {x^4 (-391+20 x) \log ^3(79-4 x)}{-79+4 x} \, dx+4 \int x^3 \log ^4(79-4 x) \, dx+\int \frac {79-4 x-3080 x^3+160 x^4-616 x^7+32 x^8}{-79+4 x} \, dx\\ &=4 \int \left (\frac {9231270317 \log (79-4 x)}{1024}+\frac {116851523}{256} x \log (79-4 x)+\frac {1480077}{64} x^2 \log (79-4 x)+\frac {18723}{16} x^3 \log (79-4 x)+\frac {237}{4} x^4 \log (79-4 x)+3 x^5 \log (79-4 x)+7 x^6 \log (79-4 x)+\frac {729270355043 \log (79-4 x)}{1024 (-79+4 x)}\right ) \, dx+4 \int \left (\frac {116850243}{256} \log ^2(79-4 x)+\frac {1479437}{64} x \log ^2(79-4 x)+\frac {18723}{16} x^2 \log ^2(79-4 x)+\frac {237}{4} x^3 \log ^2(79-4 x)+3 x^4 \log ^2(79-4 x)+9 x^5 \log ^2(79-4 x)+\frac {9231169197 \log ^2(79-4 x)}{256 (-79+4 x)}\right ) \, dx+4 \int \left (\frac {493039}{64} \log ^3(79-4 x)+\frac {6241}{16} x \log ^3(79-4 x)+\frac {79}{4} x^2 \log ^3(79-4 x)+x^3 \log ^3(79-4 x)+5 x^4 \log ^3(79-4 x)+\frac {38950081 \log ^3(79-4 x)}{64 (-79+4 x)}\right ) \, dx+4 \int \left (\frac {493039}{64} \log ^4(79-4 x)-\frac {18723}{64} (79-4 x) \log ^4(79-4 x)+\frac {237}{64} (79-4 x)^2 \log ^4(79-4 x)-\frac {1}{64} (79-4 x)^3 \log ^4(79-4 x)\right ) \, dx+\int \left (\frac {243095442977}{1024}+\frac {3077157519 x}{256}+\frac {38951361 x^2}{64}+\frac {493679 x^3}{16}+\frac {6241 x^4}{4}+79 x^5+4 x^6+8 x^7+\frac {19204540076079}{1024 (-79+4 x)}\right ) \, dx\\ &=\frac {243095442977 x}{1024}+\frac {3077157519 x^2}{512}+\frac {12983787 x^3}{64}+\frac {493679 x^4}{64}+\frac {6241 x^5}{20}+\frac {79 x^6}{6}+\frac {4 x^7}{7}+x^8+\frac {19204540076079 \log (79-4 x)}{4096}-\frac {1}{16} \int (79-4 x)^3 \log ^4(79-4 x) \, dx+4 \int x^3 \log ^3(79-4 x) \, dx+12 \int x^5 \log (79-4 x) \, dx+12 \int x^4 \log ^2(79-4 x) \, dx+\frac {237}{16} \int (79-4 x)^2 \log ^4(79-4 x) \, dx+20 \int x^4 \log ^3(79-4 x) \, dx+28 \int x^6 \log (79-4 x) \, dx+36 \int x^5 \log ^2(79-4 x) \, dx+79 \int x^2 \log ^3(79-4 x) \, dx+237 \int x^4 \log (79-4 x) \, dx+237 \int x^3 \log ^2(79-4 x) \, dx-\frac {18723}{16} \int (79-4 x) \log ^4(79-4 x) \, dx+\frac {6241}{4} \int x \log ^3(79-4 x) \, dx+\frac {18723}{4} \int x^3 \log (79-4 x) \, dx+\frac {18723}{4} \int x^2 \log ^2(79-4 x) \, dx+\frac {493039}{16} \int \log ^3(79-4 x) \, dx+\frac {493039}{16} \int \log ^4(79-4 x) \, dx+\frac {1479437}{16} \int x \log ^2(79-4 x) \, dx+\frac {1480077}{16} \int x^2 \log (79-4 x) \, dx+\frac {116850243}{64} \int \log ^2(79-4 x) \, dx+\frac {116851523}{64} \int x \log (79-4 x) \, dx+\frac {38950081}{16} \int \frac {\log ^3(79-4 x)}{-79+4 x} \, dx+\frac {9231270317}{256} \int \log (79-4 x) \, dx+\frac {9231169197}{64} \int \frac {\log ^2(79-4 x)}{-79+4 x} \, dx+\frac {729270355043}{256} \int \frac {\log (79-4 x)}{-79+4 x} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.05, size = 73, normalized size = 2.92 \begin {gather*} -x+10 x^4+x^8+4 x^3 \left (5+x^4\right ) \log (79-4 x)+2 x^2 \left (5+3 x^4\right ) \log ^2(79-4 x)+4 x^5 \log ^3(79-4 x)+x^4 \log ^4(79-4 x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(79 - 4*x - 3080*x^3 + 160*x^4 - 616*x^7 + 32*x^8 + (-4660*x^2 + 240*x^3 - 2164*x^6 + 112*x^7)*Log[7
9 - 4*x] + (-1580*x + 80*x^2 - 2796*x^5 + 144*x^6)*Log[79 - 4*x]^2 + (-1564*x^4 + 80*x^5)*Log[79 - 4*x]^3 + (-
316*x^3 + 16*x^4)*Log[79 - 4*x]^4)/(-79 + 4*x),x]

[Out]

-x + 10*x^4 + x^8 + 4*x^3*(5 + x^4)*Log[79 - 4*x] + 2*x^2*(5 + 3*x^4)*Log[79 - 4*x]^2 + 4*x^5*Log[79 - 4*x]^3
+ x^4*Log[79 - 4*x]^4

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fricas [B]  time = 0.63, size = 75, normalized size = 3.00 \begin {gather*} x^{8} + 4 \, x^{5} \log \left (-4 \, x + 79\right )^{3} + x^{4} \log \left (-4 \, x + 79\right )^{4} + 10 \, x^{4} + 2 \, {\left (3 \, x^{6} + 5 \, x^{2}\right )} \log \left (-4 \, x + 79\right )^{2} + 4 \, {\left (x^{7} + 5 \, x^{3}\right )} \log \left (-4 \, x + 79\right ) - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((16*x^4-316*x^3)*log(-4*x+79)^4+(80*x^5-1564*x^4)*log(-4*x+79)^3+(144*x^6-2796*x^5+80*x^2-1580*x)*l
og(-4*x+79)^2+(112*x^7-2164*x^6+240*x^3-4660*x^2)*log(-4*x+79)+32*x^8-616*x^7+160*x^4-3080*x^3-4*x+79)/(4*x-79
),x, algorithm="fricas")

[Out]

x^8 + 4*x^5*log(-4*x + 79)^3 + x^4*log(-4*x + 79)^4 + 10*x^4 + 2*(3*x^6 + 5*x^2)*log(-4*x + 79)^2 + 4*(x^7 + 5
*x^3)*log(-4*x + 79) - x

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giac [B]  time = 0.41, size = 75, normalized size = 3.00 \begin {gather*} x^{8} + 4 \, x^{5} \log \left (-4 \, x + 79\right )^{3} + x^{4} \log \left (-4 \, x + 79\right )^{4} + 10 \, x^{4} + 2 \, {\left (3 \, x^{6} + 5 \, x^{2}\right )} \log \left (-4 \, x + 79\right )^{2} + 4 \, {\left (x^{7} + 5 \, x^{3}\right )} \log \left (-4 \, x + 79\right ) - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((16*x^4-316*x^3)*log(-4*x+79)^4+(80*x^5-1564*x^4)*log(-4*x+79)^3+(144*x^6-2796*x^5+80*x^2-1580*x)*l
og(-4*x+79)^2+(112*x^7-2164*x^6+240*x^3-4660*x^2)*log(-4*x+79)+32*x^8-616*x^7+160*x^4-3080*x^3-4*x+79)/(4*x-79
),x, algorithm="giac")

[Out]

x^8 + 4*x^5*log(-4*x + 79)^3 + x^4*log(-4*x + 79)^4 + 10*x^4 + 2*(3*x^6 + 5*x^2)*log(-4*x + 79)^2 + 4*(x^7 + 5
*x^3)*log(-4*x + 79) - x

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maple [B]  time = 0.33, size = 76, normalized size = 3.04

method	result	size
risch	\(\ln \left (-4 x +79\right )^{4} x^{4}+4 \ln \left (-4 x +79\right )^{3} x^{5}+\left (6 x^{6}+10 x^{2}\right ) \ln \left (-4 x +79\right )^{2}+\left (4 x^{7}+20 x^{3}\right ) \ln \left (-4 x +79\right )+x^{8}+10 x^{4}-x\)	\(76\)
derivativedivides	\(\frac {19204540074031 x}{2048}+\frac {19204540076079 \ln \left (-4 x +79\right )}{4096}-\frac {7395585 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{3}}{512}+\frac {17256365 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{4}}{4096}-\frac {194750405 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )}{256}+\frac {1752754925 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{2}}{2048}-\frac {1363254115 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{3}}{4096}-\frac {27693608711 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )}{1024}+\frac {64618487739 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{2}}{4096}-\frac {1701636154087 \ln \left (-4 x +79\right ) \left (-4 x +79\right )}{4096}+\frac {\ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )^{4}}{256}-\frac {\ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{5}}{256}+\frac {3 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{6}}{2048}-\frac {\ln \left (-4 x +79\right ) \left (-4 x +79\right )^{7}}{4096}-\frac {79 \ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )^{3}}{64}+\frac {395 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{4}}{256}-\frac {711 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{5}}{1024}+\frac {553 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{6}}{4096}+\frac {18723 \ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )^{2}}{128}-\frac {31205 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{3}}{128}+\frac {280845 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{4}}{2048}-\frac {131061 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{5}}{4096}-\frac {493039 \ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )}{64}+\frac {2465195 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{2}}{128}+\frac {38950081 \ln \left (-4 x +79\right )^{4}}{256}+\frac {3077056399 \ln \left (-4 x +79\right )^{3}}{256}+\frac {729270355043 \ln \left (-4 x +79\right )^{2}}{2048}+\frac {1701636154087 \left (-4 x +79\right )^{2}}{16384}+\frac {43687 \left (-4 x +79\right )^{6}}{16384}-\frac {79 \left (-4 x +79\right )^{7}}{8192}+\frac {\left (-4 x +79\right )^{8}}{65536}-\frac {21539495913 \left (-4 x +79\right )^{3}}{8192}+\frac {1363254115 \left (-4 x +79\right )^{4}}{32768}-\frac {3451273 \left (-4 x +79\right )^{5}}{8192}-\frac {1517158665848449}{8192}\)	\(459\)
default	\(\frac {19204540074031 x}{2048}+\frac {19204540076079 \ln \left (-4 x +79\right )}{4096}-\frac {7395585 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{3}}{512}+\frac {17256365 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{4}}{4096}-\frac {194750405 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )}{256}+\frac {1752754925 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{2}}{2048}-\frac {1363254115 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{3}}{4096}-\frac {27693608711 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )}{1024}+\frac {64618487739 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{2}}{4096}-\frac {1701636154087 \ln \left (-4 x +79\right ) \left (-4 x +79\right )}{4096}+\frac {\ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )^{4}}{256}-\frac {\ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{5}}{256}+\frac {3 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{6}}{2048}-\frac {\ln \left (-4 x +79\right ) \left (-4 x +79\right )^{7}}{4096}-\frac {79 \ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )^{3}}{64}+\frac {395 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{4}}{256}-\frac {711 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{5}}{1024}+\frac {553 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{6}}{4096}+\frac {18723 \ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )^{2}}{128}-\frac {31205 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{3}}{128}+\frac {280845 \ln \left (-4 x +79\right )^{2} \left (-4 x +79\right )^{4}}{2048}-\frac {131061 \ln \left (-4 x +79\right ) \left (-4 x +79\right )^{5}}{4096}-\frac {493039 \ln \left (-4 x +79\right )^{4} \left (-4 x +79\right )}{64}+\frac {2465195 \ln \left (-4 x +79\right )^{3} \left (-4 x +79\right )^{2}}{128}+\frac {38950081 \ln \left (-4 x +79\right )^{4}}{256}+\frac {3077056399 \ln \left (-4 x +79\right )^{3}}{256}+\frac {729270355043 \ln \left (-4 x +79\right )^{2}}{2048}+\frac {1701636154087 \left (-4 x +79\right )^{2}}{16384}+\frac {43687 \left (-4 x +79\right )^{6}}{16384}-\frac {79 \left (-4 x +79\right )^{7}}{8192}+\frac {\left (-4 x +79\right )^{8}}{65536}-\frac {21539495913 \left (-4 x +79\right )^{3}}{8192}+\frac {1363254115 \left (-4 x +79\right )^{4}}{32768}-\frac {3451273 \left (-4 x +79\right )^{5}}{8192}-\frac {1517158665848449}{8192}\)	\(459\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((16*x^4-316*x^3)*ln(-4*x+79)^4+(80*x^5-1564*x^4)*ln(-4*x+79)^3+(144*x^6-2796*x^5+80*x^2-1580*x)*ln(-4*x+7
9)^2+(112*x^7-2164*x^6+240*x^3-4660*x^2)*ln(-4*x+79)+32*x^8-616*x^7+160*x^4-3080*x^3-4*x+79)/(4*x-79),x,method
=_RETURNVERBOSE)

[Out]

ln(-4*x+79)^4*x^4+4*ln(-4*x+79)^3*x^5+(6*x^6+10*x^2)*ln(-4*x+79)^2+(4*x^7+20*x^3)*ln(-4*x+79)+x^8+10*x^4-x

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maxima [B]  time = 0.56, size = 773, normalized size = 30.92 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((16*x^4-316*x^3)*log(-4*x+79)^4+(80*x^5-1564*x^4)*log(-4*x+79)^3+(144*x^6-2796*x^5+80*x^2-1580*x)*l
og(-4*x+79)^2+(112*x^7-2164*x^6+240*x^3-4660*x^2)*log(-4*x+79)+32*x^8-616*x^7+160*x^4-3080*x^3-4*x+79)/(4*x-79
),x, algorithm="maxima")

[Out]

x^8 + 1/12288*(18*log(-4*x + 79)^2 - 6*log(-4*x + 79) + 1)*(4*x - 79)^6 + 1/32000*(125*log(-4*x + 79)^3 - 75*l
og(-4*x + 79)^2 + 30*log(-4*x + 79) - 6)*(4*x - 79)^5 + 3567/128000*(25*log(-4*x + 79)^2 - 10*log(-4*x + 79) +
2)*(4*x - 79)^5 - 1/3*x^6 + 1/8192*(32*log(-4*x + 79)^4 - 32*log(-4*x + 79)^3 + 24*log(-4*x + 79)^2 - 12*log(
-4*x + 79) + 3)*(4*x - 79)^4 + 99/2048*(32*log(-4*x + 79)^3 - 24*log(-4*x + 79)^2 + 12*log(-4*x + 79) - 3)*(4*
x - 79)^4 + 283215/16384*(8*log(-4*x + 79)^2 - 4*log(-4*x + 79) + 1)*(4*x - 79)^4 - 869/50*x^5 + 79/1728*(27*l
og(-4*x + 79)^4 - 36*log(-4*x + 79)^3 + 36*log(-4*x + 79)^2 - 24*log(-4*x + 79) + 8)*(4*x - 79)^3 + 94247/3456
*(9*log(-4*x + 79)^3 - 9*log(-4*x + 79)^2 + 6*log(-4*x + 79) - 2)*(4*x - 79)^3 + 7520405/4608*(9*log(-4*x + 79
)^2 - 6*log(-4*x + 79) + 2)*(4*x - 79)^3 - 227717/320*x^4 + 38950081/256*log(-4*x + 79)^4 + 18723/256*(2*log(-
4*x + 79)^4 - 4*log(-4*x + 79)^3 + 6*log(-4*x + 79)^2 - 6*log(-4*x + 79) + 3)*(4*x - 79)^2 + 2502641/512*(4*lo
g(-4*x + 79)^3 - 6*log(-4*x + 79)^2 + 6*log(-4*x + 79) - 3)*(4*x - 79)^2 + 1811919605/4096*(2*log(-4*x + 79)^2
- 2*log(-4*x + 79) + 1)*(4*x - 79)^2 - 9367741/320*x^3 + 3077056399/256*log(-4*x + 79)^3 + 493039/64*(log(-4*
x + 79)^4 - 4*log(-4*x + 79)^3 + 12*log(-4*x + 79)^2 - 24*log(-4*x + 79) + 24)*(4*x - 79) + 202639029/256*(log
(-4*x + 79)^3 - 3*log(-4*x + 79)^2 + 6*log(-4*x + 79) - 6)*(4*x - 79) + 30030613571/1024*(log(-4*x + 79)^2 - 2
*log(-4*x + 79) + 2)*(4*x - 79) - 3388669847/2560*x^2 - 729270355043/2048*log(4*x - 79)^2 + 1/61440*(245760*x^
7 + 5662720*x^6 + 134206464*x^5 + 3313222080*x^4 + 87248181440*x^3 + 2584727375160*x^2 + 102096731318820*x + 2
016410443546695*log(4*x - 79))*log(-4*x + 79) - 541/61440*(10240*x^6 + 242688*x^5 + 5991360*x^4 + 157772480*x^
3 + 4674009720*x^2 + 184623383940*x + 3646311832815*log(4*x - 79))*log(-4*x + 79) + 5/16*(64*x^3 + 1896*x^2 +
74892*x + 1479117*log(4*x - 79))*log(-4*x + 79) - 1165/16*(8*x^2 + 316*x + 6241*log(4*x - 79))*log(-4*x + 79)
- 452330329373/5120*x - 35734095615987/20480*log(4*x - 79)

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mupad [B]  time = 1.26, size = 82, normalized size = 3.28 \begin {gather*} 10\,x^2\,{\ln \left (79-4\,x\right )}^2-x+4\,x^5\,{\ln \left (79-4\,x\right )}^3+6\,x^6\,{\ln \left (79-4\,x\right )}^2+x^4\,\left ({\ln \left (79-4\,x\right )}^4+10\right )+x^8+20\,x^3\,\ln \left (79-4\,x\right )+4\,x^7\,\ln \left (79-4\,x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(4*x + log(79 - 4*x)^4*(316*x^3 - 16*x^4) + log(79 - 4*x)^3*(1564*x^4 - 80*x^5) + log(79 - 4*x)^2*(1580*x
- 80*x^2 + 2796*x^5 - 144*x^6) + log(79 - 4*x)*(4660*x^2 - 240*x^3 + 2164*x^6 - 112*x^7) + 3080*x^3 - 160*x^4
+ 616*x^7 - 32*x^8 - 79)/(4*x - 79),x)

[Out]

10*x^2*log(79 - 4*x)^2 - x + 4*x^5*log(79 - 4*x)^3 + 6*x^6*log(79 - 4*x)^2 + x^4*(log(79 - 4*x)^4 + 10) + x^8
+ 20*x^3*log(79 - 4*x) + 4*x^7*log(79 - 4*x)

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sympy [B]  time = 0.23, size = 70, normalized size = 2.80 \begin {gather*} x^{8} + 4 x^{5} \log {\left (79 - 4 x \right )}^{3} + x^{4} \log {\left (79 - 4 x \right )}^{4} + 10 x^{4} - x + \left (6 x^{6} + 10 x^{2}\right ) \log {\left (79 - 4 x \right )}^{2} + \left (4 x^{7} + 20 x^{3}\right ) \log {\left (79 - 4 x \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((16*x**4-316*x**3)*ln(-4*x+79)**4+(80*x**5-1564*x**4)*ln(-4*x+79)**3+(144*x**6-2796*x**5+80*x**2-15
80*x)*ln(-4*x+79)**2+(112*x**7-2164*x**6+240*x**3-4660*x**2)*ln(-4*x+79)+32*x**8-616*x**7+160*x**4-3080*x**3-4
*x+79)/(4*x-79),x)

[Out]

x**8 + 4*x**5*log(79 - 4*x)**3 + x**4*log(79 - 4*x)**4 + 10*x**4 - x + (6*x**6 + 10*x**2)*log(79 - 4*x)**2 + (
4*x**7 + 20*x**3)*log(79 - 4*x)

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