\(\int \frac {3840-8960 x+2560 x^2+(3840 x-1280 x^2) \log (-3+x)+(-7680 x+1280 x^2+(3840 x-1280 x^2) \log (-3+x)) \log (x)+(-480+640 x-160 x^2+(480 x-160 x^2) \log (x)) \log (\log (3))+(15-5 x) \log ^2(\log (3))}{-768 x+256 x^2} \, dx\) [2384]

Optimal result

Integrand size = 99, antiderivative size = 29 \[ \int \frac {3840-8960 x+2560 x^2+\left (3840 x-1280 x^2\right ) \log (-3+x)+\left (-7680 x+1280 x^2+\left (3840 x-1280 x^2\right ) \log (-3+x)\right ) \log (x)+\left (-480+640 x-160 x^2+\left (480 x-160 x^2\right ) \log (x)\right ) \log (\log (3))+(15-5 x) \log ^2(\log (3))}{-768 x+256 x^2} \, dx=5 \log (x) \left (x (x-\log (-3+x))-\left (-1+x+\frac {1}{16} \log (\log (3))\right )^2\right ) \]

[Out]

5*ln(x)*(x*(x-ln(-3+x))-(1/16*ln(ln(3))+x-1)^2)

Rubi [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(110\) vs. \(2(29)=58\).

Time = 0.27 (sec) , antiderivative size = 110, normalized size of antiderivative = 3.79, number of steps used = 18, number of rules used = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.131, Rules used = {1607, 6820, 2436, 2332, 2417, 2458, 45, 2393, 2354, 2438, 2404, 2353, 2352} \[ \int \frac {3840-8960 x+2560 x^2+\left (3840 x-1280 x^2\right ) \log (-3+x)+\left (-7680 x+1280 x^2+\left (3840 x-1280 x^2\right ) \log (-3+x)\right ) \log (x)+\left (-480+640 x-160 x^2+\left (480 x-160 x^2\right ) \log (x)\right ) \log (\log (3))+(15-5 x) \log ^2(\log (3))}{-768 x+256 x^2} \, dx=-10 x+5 x (\log (x)+1)+\frac {5}{8} x (16-\log (\log (3)))+\frac {5}{8} x (8-\log (\log (3))) \log (x)-\frac {5}{8} x (8-\log (\log (3)))-5 (3-x) \log (x-3)-15 \log (3) \log (x-3)-15 \log (x-3) \log \left (\frac {x}{3}\right )+5 (3-x) \log (x-3) (\log (x)+1)-\frac {5}{256} (16-\log (\log (3)))^2 \log (x) \]

[In]

Int[(3840 - 8960*x + 2560*x^2 + (3840*x - 1280*x^2)*Log[-3 + x] + (-7680*x + 1280*x^2 + (3840*x - 1280*x^2)*Lo
g[-3 + x])*Log[x] + (-480 + 640*x - 160*x^2 + (480*x - 160*x^2)*Log[x])*Log[Log[3]] + (15 - 5*x)*Log[Log[3]]^2
)/(-768*x + 256*x^2),x]

[Out]

-10*x - 5*(3 - x)*Log[-3 + x] - 15*Log[3]*Log[-3 + x] - 15*Log[-3 + x]*Log[x/3] + 5*x*(1 + Log[x]) + 5*(3 - x)
*Log[-3 + x]*(1 + Log[x]) - (5*x*(8 - Log[Log[3]]))/8 + (5*x*Log[x]*(8 - Log[Log[3]]))/8 + (5*x*(16 - Log[Log[
3]]))/8 - (5*Log[x]*(16 - Log[Log[3]])^2)/256

Rule 45

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 1607

Int[(u_.)*((a_.)*(x_)^(p_.) + (b_.)*(x_)^(q_.))^(n_.), x_Symbol] :> Int[u*x^(n*p)*(a + b*x^(q - p))^n, x] /; F
reeQ[{a, b, p, q}, x] && IntegerQ[n] && PosQ[q - p]

Rule 2332

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

Rule 2352

Int[Log[(c_.)*(x_)]/((d_) + (e_.)*(x_)), x_Symbol] :> Simp[(-e^(-1))*PolyLog[2, 1 - c*x], x] /; FreeQ[{c, d, e
}, x] && EqQ[e + c*d, 0]

Rule 2353

Int[((a_.) + Log[(c_.)*(x_)]*(b_.))/((d_) + (e_.)*(x_)), x_Symbol] :> Simp[(a + b*Log[(-c)*(d/e)])*(Log[d + e*
x]/e), x] + Dist[b, Int[Log[(-e)*(x/d)]/(d + e*x), x], x] /; FreeQ[{a, b, c, d, e}, x] && GtQ[(-c)*(d/e), 0]

Rule 2354

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)/((d_) + (e_.)*(x_)), x_Symbol] :> Simp[Log[1 + e*(x/d)]*((a +
b*Log[c*x^n])^p/e), x] - Dist[b*n*(p/e), Int[Log[1 + e*(x/d)]*((a + b*Log[c*x^n])^(p - 1)/x), x], x] /; FreeQ[
{a, b, c, d, e, n}, x] && IGtQ[p, 0]

Rule 2393

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((f_.)*(x_))^(m_.)*((d_) + (e_.)*(x_)^(r_.))^(q_.), x_Symbol] :> Wit
h[{u = ExpandIntegrand[a + b*Log[c*x^n], (f*x)^m*(d + e*x^r)^q, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[{a, b, c,
d, e, f, m, n, q, r}, x] && IntegerQ[q] && (GtQ[q, 0] || (IntegerQ[m] && IntegerQ[r]))

Rule 2404

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*(RFx_), x_Symbol] :> With[{u = ExpandIntegrand[(a + b*Log[c*x^
n])^p, RFx, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[{a, b, c, n}, x] && RationalFunctionQ[RFx, x] && IGtQ[p, 0]

Rule 2417

Int[Log[(d_.)*((e_) + (f_.)*(x_)^(m_.))^(r_.)]*((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.), x_Symbol] :> With[
{u = IntHide[Log[d*(e + f*x^m)^r], x]}, Dist[(a + b*Log[c*x^n])^p, u, x] - Dist[b*n*p, Int[Dist[(a + b*Log[c*x
^n])^(p - 1)/x, u, x], x], x]] /; FreeQ[{a, b, c, d, e, f, r, m, n}, x] && IGtQ[p, 0] && RationalQ[m] && (EqQ[
p, 1] || (FractionQ[m] && IntegerQ[1/m]) || (EqQ[r, 1] && EqQ[m, 1] && EqQ[d*e, 1]))

Rule 2436

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 2438

Int[Log[(c_.)*((d_) + (e_.)*(x_)^(n_.))]/(x_), x_Symbol] :> Simp[-PolyLog[2, (-c)*e*x^n]/n, x] /; FreeQ[{c, d,
e, n}, x] && EqQ[c*d, 1]

Rule 2458

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 6820

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

Rubi steps \begin{align*} \text {integral}& = \int \frac {3840-8960 x+2560 x^2+\left (3840 x-1280 x^2\right ) \log (-3+x)+\left (-7680 x+1280 x^2+\left (3840 x-1280 x^2\right ) \log (-3+x)\right ) \log (x)+\left (-480+640 x-160 x^2+\left (480 x-160 x^2\right ) \log (x)\right ) \log (\log (3))+(15-5 x) \log ^2(\log (3))}{x (-768+256 x)} \, dx \\ & = \int \left (-5 \log (-3+x) (1+\log (x))-\frac {5 \log (x) (48+x (-8+\log (\log (3)))-3 \log (\log (3)))}{8 (-3+x)}-\frac {5 (-16+\log (\log (3))) (-16+32 x+\log (\log (3)))}{256 x}\right ) \, dx \\ & = -\left (\frac {5}{8} \int \frac {\log (x) (48+x (-8+\log (\log (3)))-3 \log (\log (3)))}{-3+x} \, dx\right )-5 \int \log (-3+x) (1+\log (x)) \, dx+\frac {1}{256} (5 (16-\log (\log (3)))) \int \frac {-16+32 x+\log (\log (3))}{x} \, dx \\ & = 5 x (1+\log (x))+5 (3-x) \log (-3+x) (1+\log (x))-\frac {5}{8} \int \left (\frac {24 \log (x)}{-3+x}+\log (x) (-8+\log (\log (3)))\right ) \, dx+5 \int \left (-1-\frac {(3-x) \log (-3+x)}{x}\right ) \, dx+\frac {1}{256} (5 (16-\log (\log (3)))) \int \left (32+\frac {-16+\log (\log (3))}{x}\right ) \, dx \\ & = -5 x+5 x (1+\log (x))+5 (3-x) \log (-3+x) (1+\log (x))+\frac {5}{8} x (16-\log (\log (3)))-\frac {5}{256} \log (x) (16-\log (\log (3)))^2-5 \int \frac {(3-x) \log (-3+x)}{x} \, dx-15 \int \frac {\log (x)}{-3+x} \, dx+\frac {1}{8} (5 (8-\log (\log (3)))) \int \log (x) \, dx \\ & = -5 x-15 \log (3) \log (-3+x)+5 x (1+\log (x))+5 (3-x) \log (-3+x) (1+\log (x))-\frac {5}{8} x (8-\log (\log (3)))+\frac {5}{8} x \log (x) (8-\log (\log (3)))+\frac {5}{8} x (16-\log (\log (3)))-\frac {5}{256} \log (x) (16-\log (\log (3)))^2+5 \text {Subst}\left (\int \frac {x \log (x)}{3+x} \, dx,x,-3+x\right )-15 \int \frac {\log \left (\frac {x}{3}\right )}{-3+x} \, dx \\ & = -5 x-15 \log (3) \log (-3+x)+5 x (1+\log (x))+5 (3-x) \log (-3+x) (1+\log (x))-\frac {5}{8} x (8-\log (\log (3)))+\frac {5}{8} x \log (x) (8-\log (\log (3)))+\frac {5}{8} x (16-\log (\log (3)))-\frac {5}{256} \log (x) (16-\log (\log (3)))^2+15 \operatorname {PolyLog}\left (2,1-\frac {x}{3}\right )+5 \text {Subst}\left (\int \left (\log (x)-\frac {3 \log (x)}{3+x}\right ) \, dx,x,-3+x\right ) \\ & = -5 x-15 \log (3) \log (-3+x)+5 x (1+\log (x))+5 (3-x) \log (-3+x) (1+\log (x))-\frac {5}{8} x (8-\log (\log (3)))+\frac {5}{8} x \log (x) (8-\log (\log (3)))+\frac {5}{8} x (16-\log (\log (3)))-\frac {5}{256} \log (x) (16-\log (\log (3)))^2+15 \operatorname {PolyLog}\left (2,1-\frac {x}{3}\right )+5 \text {Subst}(\int \log (x) \, dx,x,-3+x)-15 \text {Subst}\left (\int \frac {\log (x)}{3+x} \, dx,x,-3+x\right ) \\ & = -10 x-5 (3-x) \log (-3+x)-15 \log (3) \log (-3+x)-15 \log (-3+x) \log \left (\frac {x}{3}\right )+5 x (1+\log (x))+5 (3-x) \log (-3+x) (1+\log (x))-\frac {5}{8} x (8-\log (\log (3)))+\frac {5}{8} x \log (x) (8-\log (\log (3)))+\frac {5}{8} x (16-\log (\log (3)))-\frac {5}{256} \log (x) (16-\log (\log (3)))^2+15 \operatorname {PolyLog}\left (2,1-\frac {x}{3}\right )+15 \text {Subst}\left (\int \frac {\log \left (1+\frac {x}{3}\right )}{x} \, dx,x,-3+x\right ) \\ & = -10 x-5 (3-x) \log (-3+x)-15 \log (3) \log (-3+x)-15 \log (-3+x) \log \left (\frac {x}{3}\right )+5 x (1+\log (x))+5 (3-x) \log (-3+x) (1+\log (x))-\frac {5}{8} x (8-\log (\log (3)))+\frac {5}{8} x \log (x) (8-\log (\log (3)))+\frac {5}{8} x (16-\log (\log (3)))-\frac {5}{256} \log (x) (16-\log (\log (3)))^2 \\ \end{align*}

Mathematica [C] (verified)

Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.

Time = 0.13 (sec) , antiderivative size = 89, normalized size of antiderivative = 3.07 \[ \int \frac {3840-8960 x+2560 x^2+\left (3840 x-1280 x^2\right ) \log (-3+x)+\left (-7680 x+1280 x^2+\left (3840 x-1280 x^2\right ) \log (-3+x)\right ) \log (x)+\left (-480+640 x-160 x^2+\left (480 x-160 x^2\right ) \log (x)\right ) \log (\log (3))+(15-5 x) \log ^2(\log (3))}{-768 x+256 x^2} \, dx=-15 \log (3) \log (-3+x)-5 \log (x)+10 x \log (x)+15 \log \left (1-\frac {x}{3}\right ) \log (x)-5 x \log (-3+x) \log (x)+\frac {5}{8} \log (x) \log (\log (3))-\frac {5}{8} x \log (x) \log (\log (3))-\frac {5}{256} \log (x) \log ^2(\log (3))+15 \operatorname {PolyLog}\left (2,1-\frac {x}{3}\right )+15 \operatorname {PolyLog}\left (2,\frac {x}{3}\right ) \]

[In]

Integrate[(3840 - 8960*x + 2560*x^2 + (3840*x - 1280*x^2)*Log[-3 + x] + (-7680*x + 1280*x^2 + (3840*x - 1280*x
^2)*Log[-3 + x])*Log[x] + (-480 + 640*x - 160*x^2 + (480*x - 160*x^2)*Log[x])*Log[Log[3]] + (15 - 5*x)*Log[Log
[3]]^2)/(-768*x + 256*x^2),x]

[Out]

-15*Log[3]*Log[-3 + x] - 5*Log[x] + 10*x*Log[x] + 15*Log[1 - x/3]*Log[x] - 5*x*Log[-3 + x]*Log[x] + (5*Log[x]*
Log[Log[3]])/8 - (5*x*Log[x]*Log[Log[3]])/8 - (5*Log[x]*Log[Log[3]]^2)/256 + 15*PolyLog[2, 1 - x/3] + 15*PolyL
og[2, x/3]

Maple [A] (verified)

Time = 0.82 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.34

method	result	size
norman	\(\left (-5-\frac {5 \ln \left (\ln \left (3\right )\right )^{2}}{256}+\frac {5 \ln \left (\ln \left (3\right )\right )}{8}\right ) \ln \left (x \right )+\left (10-\frac {5 \ln \left (\ln \left (3\right )\right )}{8}\right ) x \ln \left (x \right )-5 \ln \left (x \right ) \ln \left (-3+x \right ) x\)	\(39\)
risch	\(-5 \ln \left (x \right ) \ln \left (-3+x \right ) x -\frac {5 \ln \left (x \right ) \ln \left (\ln \left (3\right )\right ) x}{8}+10 x \ln \left (x \right )-\frac {5 \ln \left (\ln \left (3\right )\right )^{2} \ln \left (x \right )}{256}+\frac {5 \ln \left (\ln \left (3\right )\right ) \ln \left (x \right )}{8}-5 \ln \left (x \right )\)	\(44\)
parallelrisch	\(-5 \ln \left (x \right ) \ln \left (-3+x \right ) x -\frac {5 \ln \left (x \right ) \ln \left (\ln \left (3\right )\right ) x}{8}+10 x \ln \left (x \right )-\frac {5 \ln \left (\ln \left (3\right )\right )^{2} \ln \left (x \right )}{256}+\frac {5 \ln \left (\ln \left (3\right )\right ) \ln \left (x \right )}{8}-5 \ln \left (x \right )\)	\(44\)
parts	\(-15 \ln \left (-3+x \right )-10 x +\frac {5 \ln \left (\ln \left (3\right )\right ) x}{8}+\frac {5 \left (16-\ln \left (\ln \left (3\right )\right )\right ) \ln \left (x \right ) x}{8}+5 \ln \left (-3+x \right ) x -5 \ln \left (x \right ) \ln \left (-3+x \right ) x -\frac {5 \left (-16+\ln \left (\ln \left (3\right )\right )\right ) \left (32 x +\left (-16+\ln \left (\ln \left (3\right )\right )\right ) \ln \left (x \right )\right )}{256}-5 \left (-3+x \right ) \ln \left (-3+x \right )-15\)	\(74\)
default	\(-15 \ln \left (-3+x \right )+\frac {5 \ln \left (\ln \left (3\right )\right ) x}{8}+\frac {5 \left (16-\ln \left (\ln \left (3\right )\right )\right ) \ln \left (x \right ) x}{8}+5 \ln \left (-3+x \right ) x -5 \ln \left (x \right ) \ln \left (-3+x \right ) x -\frac {5 \ln \left (\ln \left (3\right )\right )^{2} \ln \left (x \right )}{256}-5 \ln \left (x \right )-\frac {5 \ln \left (\ln \left (3\right )\right ) \left (x -\ln \left (x \right )\right )}{8}-5 \left (-3+x \right ) \ln \left (-3+x \right )-15\)	\(76\)

[In]

int(((15-5*x)*ln(ln(3))^2+((-160*x^2+480*x)*ln(x)-160*x^2+640*x-480)*ln(ln(3))+((-1280*x^2+3840*x)*ln(-3+x)+12
80*x^2-7680*x)*ln(x)+(-1280*x^2+3840*x)*ln(-3+x)+2560*x^2-8960*x+3840)/(256*x^2-768*x),x,method=_RETURNVERBOSE
)

[Out]

(-5-5/256*ln(ln(3))^2+5/8*ln(ln(3)))*ln(x)+(10-5/8*ln(ln(3)))*x*ln(x)-5*ln(x)*ln(-3+x)*x

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.21 \[ \int \frac {3840-8960 x+2560 x^2+\left (3840 x-1280 x^2\right ) \log (-3+x)+\left (-7680 x+1280 x^2+\left (3840 x-1280 x^2\right ) \log (-3+x)\right ) \log (x)+\left (-480+640 x-160 x^2+\left (480 x-160 x^2\right ) \log (x)\right ) \log (\log (3))+(15-5 x) \log ^2(\log (3))}{-768 x+256 x^2} \, dx=-\frac {5}{8} \, {\left (x - 1\right )} \log \left (x\right ) \log \left (\log \left (3\right )\right ) - \frac {5}{256} \, \log \left (x\right ) \log \left (\log \left (3\right )\right )^{2} - 5 \, {\left (x \log \left (x - 3\right ) - 2 \, x + 1\right )} \log \left (x\right ) \]

[In]

integrate(((15-5*x)*log(log(3))^2+((-160*x^2+480*x)*log(x)-160*x^2+640*x-480)*log(log(3))+((-1280*x^2+3840*x)*
log(-3+x)+1280*x^2-7680*x)*log(x)+(-1280*x^2+3840*x)*log(-3+x)+2560*x^2-8960*x+3840)/(256*x^2-768*x),x, algori
thm="fricas")

[Out]

-5/8*(x - 1)*log(x)*log(log(3)) - 5/256*log(x)*log(log(3))^2 - 5*(x*log(x - 3) - 2*x + 1)*log(x)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 97 vs. \(2 (24) = 48\).

Time = 0.97 (sec) , antiderivative size = 97, normalized size of antiderivative = 3.34 \[ \int \frac {3840-8960 x+2560 x^2+\left (3840 x-1280 x^2\right ) \log (-3+x)+\left (-7680 x+1280 x^2+\left (3840 x-1280 x^2\right ) \log (-3+x)\right ) \log (x)+\left (-480+640 x-160 x^2+\left (480 x-160 x^2\right ) \log (x)\right ) \log (\log (3))+(15-5 x) \log ^2(\log (3))}{-768 x+256 x^2} \, dx=\left (- 5 x \log {\left (x \right )} - \frac {15}{4}\right ) \log {\left (x - 3 \right )} + \left (- \frac {5 x \log {\left (\log {\left (3 \right )} \right )}}{8} + 10 x\right ) \log {\left (x \right )} - \left (- \frac {5 \log {\left (\log {\left (3 \right )} \right )}}{8} + \frac {5 \log {\left (\log {\left (3 \right )} \right )}^{2}}{256} + 5\right ) \log {\left (x \right )} + \frac {15 \log {\left (x + \frac {-6720 - 15 \log {\left (\log {\left (3 \right )} \right )}^{2} + 480 \log {\left (\log {\left (3 \right )} \right )}}{- 160 \log {\left (\log {\left (3 \right )} \right )} + 5 \log {\left (\log {\left (3 \right )} \right )}^{2} + 2240} \right )}}{4} \]

[In]

integrate(((15-5*x)*ln(ln(3))**2+((-160*x**2+480*x)*ln(x)-160*x**2+640*x-480)*ln(ln(3))+((-1280*x**2+3840*x)*l
n(-3+x)+1280*x**2-7680*x)*ln(x)+(-1280*x**2+3840*x)*ln(-3+x)+2560*x**2-8960*x+3840)/(256*x**2-768*x),x)

[Out]

(-5*x*log(x) - 15/4)*log(x - 3) + (-5*x*log(log(3))/8 + 10*x)*log(x) - (-5*log(log(3))/8 + 5*log(log(3))**2/25
6 + 5)*log(x) + 15*log(x + (-6720 - 15*log(log(3))**2 + 480*log(log(3)))/(-160*log(log(3)) + 5*log(log(3))**2
+ 2240))/4

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 132 vs. \(2 (26) = 52\).

Time = 0.31 (sec) , antiderivative size = 132, normalized size of antiderivative = 4.55 \[ \int \frac {3840-8960 x+2560 x^2+\left (3840 x-1280 x^2\right ) \log (-3+x)+\left (-7680 x+1280 x^2+\left (3840 x-1280 x^2\right ) \log (-3+x)\right ) \log (x)+\left (-480+640 x-160 x^2+\left (480 x-160 x^2\right ) \log (x)\right ) \log (\log (3))+(15-5 x) \log ^2(\log (3))}{-768 x+256 x^2} \, dx=-\frac {5}{8} \, x {\left (\log \left (\log \left (3\right )\right ) - 16\right )} \log \left (x\right ) + \frac {5}{256} \, {\left (\log \left (x - 3\right ) - \log \left (x\right )\right )} \log \left (\log \left (3\right )\right )^{2} - \frac {5}{256} \, \log \left (x - 3\right ) \log \left (\log \left (3\right )\right )^{2} + \frac {5}{8} \, x {\left (\log \left (\log \left (3\right )\right ) - 24\right )} - 5 \, {\left (x \log \left (x\right ) - x + 3\right )} \log \left (x - 3\right ) - 5 \, {\left (x + 3 \, \log \left (x - 3\right )\right )} \log \left (x - 3\right ) + 15 \, \log \left (x - 3\right )^{2} - \frac {5}{8} \, {\left (x + 3 \, \log \left (x - 3\right )\right )} \log \left (\log \left (3\right )\right ) - \frac {5}{8} \, {\left (\log \left (x - 3\right ) - \log \left (x\right )\right )} \log \left (\log \left (3\right )\right ) + \frac {5}{2} \, \log \left (x - 3\right ) \log \left (\log \left (3\right )\right ) + 15 \, x + 15 \, \log \left (x - 3\right ) - 5 \, \log \left (x\right ) \]

[In]

integrate(((15-5*x)*log(log(3))^2+((-160*x^2+480*x)*log(x)-160*x^2+640*x-480)*log(log(3))+((-1280*x^2+3840*x)*
log(-3+x)+1280*x^2-7680*x)*log(x)+(-1280*x^2+3840*x)*log(-3+x)+2560*x^2-8960*x+3840)/(256*x^2-768*x),x, algori
thm="maxima")

[Out]

-5/8*x*(log(log(3)) - 16)*log(x) + 5/256*(log(x - 3) - log(x))*log(log(3))^2 - 5/256*log(x - 3)*log(log(3))^2
+ 5/8*x*(log(log(3)) - 24) - 5*(x*log(x) - x + 3)*log(x - 3) - 5*(x + 3*log(x - 3))*log(x - 3) + 15*log(x - 3)
^2 - 5/8*(x + 3*log(x - 3))*log(log(3)) - 5/8*(log(x - 3) - log(x))*log(log(3)) + 5/2*log(x - 3)*log(log(3)) +
15*x + 15*log(x - 3) - 5*log(x)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.24 \[ \int \frac {3840-8960 x+2560 x^2+\left (3840 x-1280 x^2\right ) \log (-3+x)+\left (-7680 x+1280 x^2+\left (3840 x-1280 x^2\right ) \log (-3+x)\right ) \log (x)+\left (-480+640 x-160 x^2+\left (480 x-160 x^2\right ) \log (x)\right ) \log (\log (3))+(15-5 x) \log ^2(\log (3))}{-768 x+256 x^2} \, dx=-\frac {5}{8} \, x {\left (\log \left (\log \left (3\right )\right ) - 16\right )} \log \left (x\right ) - 5 \, x \log \left (x - 3\right ) \log \left (x\right ) - \frac {5}{256} \, {\left (\log \left (\log \left (3\right )\right )^{2} - 32 \, \log \left (\log \left (3\right )\right ) + 256\right )} \log \left (x\right ) \]

[In]

integrate(((15-5*x)*log(log(3))^2+((-160*x^2+480*x)*log(x)-160*x^2+640*x-480)*log(log(3))+((-1280*x^2+3840*x)*
log(-3+x)+1280*x^2-7680*x)*log(x)+(-1280*x^2+3840*x)*log(-3+x)+2560*x^2-8960*x+3840)/(256*x^2-768*x),x, algori
thm="giac")

[Out]

-5/8*x*(log(log(3)) - 16)*log(x) - 5*x*log(x - 3)*log(x) - 5/256*(log(log(3))^2 - 32*log(log(3)) + 256)*log(x)

Mupad [B] (verification not implemented)

Time = 11.14 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.10 \[ \int \frac {3840-8960 x+2560 x^2+\left (3840 x-1280 x^2\right ) \log (-3+x)+\left (-7680 x+1280 x^2+\left (3840 x-1280 x^2\right ) \log (-3+x)\right ) \log (x)+\left (-480+640 x-160 x^2+\left (480 x-160 x^2\right ) \log (x)\right ) \log (\log (3))+(15-5 x) \log ^2(\log (3))}{-768 x+256 x^2} \, dx=-\frac {5\,\ln \left (x\right )\,\left (256\,x\,\ln \left (x-3\right )-32\,\ln \left (\ln \left (3\right )\right )-512\,x+{\ln \left (\ln \left (3\right )\right )}^2+32\,x\,\ln \left (\ln \left (3\right )\right )+256\right )}{256} \]

[In]

int(-(log(x - 3)*(3840*x - 1280*x^2) - 8960*x + log(log(3))*(640*x + log(x)*(480*x - 160*x^2) - 160*x^2 - 480)
+ log(x)*(log(x - 3)*(3840*x - 1280*x^2) - 7680*x + 1280*x^2) - log(log(3))^2*(5*x - 15) + 2560*x^2 + 3840)/(
768*x - 256*x^2),x)

[Out]

-(5*log(x)*(256*x*log(x - 3) - 32*log(log(3)) - 512*x + log(log(3))^2 + 32*x*log(log(3)) + 256))/256