3.79.91 \(\int \frac {6-9 x^2+12 x^3-15 x^4+15 x^5+(-6+6 x-9 x^2+9 x^3) \log (-1+x)+(-12 x+6 x^2+24 x^3-24 x^4+(12 x-12 x^2) \log (-1+x)) \log ^2(\log (5))+(3-9 x^2+9 x^3+(-3+3 x) \log (-1+x)) \log ^4(\log (5))}{-1+x} \, dx\)

Optimal. Leaf size=25 \[ 3 x \left (-1+x^2+\log (-1+x)\right ) \left (2+\left (-x+\log ^2(\log (5))\right )^2\right ) \]

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Rubi [B]  time = 0.48, antiderivative size = 358, normalized size of antiderivative = 14.32, number of steps used = 22, number of rules used = 6, integrand size = 115, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.052, Rules used = {6742, 43, 2417, 2395, 2389, 2295} \begin {gather*} 3 x^5+\frac {15 x^4}{4}-\frac {3}{4} x^4 \left (5+8 \log ^2(\log (5))\right )+4 x^3-x^3 \left (5+8 \log ^2(\log (5))\right )+x^3 \left (4+3 \log ^4(\log (5))+8 \log ^2(\log (5))\right )+3 x^3 \log (x-1)+6 x^2-\frac {3}{2} x^2 \left (5+8 \log ^2(\log (5))\right )-6 x^2 \log ^2(\log (5)) \log (x-1)+3 x^2 \log ^2(\log (5))+\frac {3}{2} x^2 \left (4+3 \log ^4(\log (5))+8 \log ^2(\log (5))\right )-\frac {3}{2} x^2 \left (3+3 \log ^4(\log (5))-2 \log ^2(\log (5))\right )+12 x-3 x \left (2+\log ^4(\log (5))\right )+3 \left (2+\log ^4(\log (5))\right ) \log (1-x)-3 (1-x) \left (2+\log ^4(\log (5))\right ) \log (x-1)-3 x \left (5+8 \log ^2(\log (5))\right )-6 x \log ^2(\log (5))-3 \left (5+8 \log ^2(\log (5))\right ) \log (1-x)-6 \log ^2(\log (5)) \log (1-x)+3 x \left (4+3 \log ^4(\log (5))+8 \log ^2(\log (5))\right )-3 x \left (3+3 \log ^4(\log (5))-2 \log ^2(\log (5))\right )+3 \left (4+3 \log ^4(\log (5))+8 \log ^2(\log (5))\right ) \log (1-x)-3 \left (3+3 \log ^4(\log (5))-2 \log ^2(\log (5))\right ) \log (1-x)+12 \log (1-x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(6 - 9*x^2 + 12*x^3 - 15*x^4 + 15*x^5 + (-6 + 6*x - 9*x^2 + 9*x^3)*Log[-1 + x] + (-12*x + 6*x^2 + 24*x^3 -
24*x^4 + (12*x - 12*x^2)*Log[-1 + x])*Log[Log[5]]^2 + (3 - 9*x^2 + 9*x^3 + (-3 + 3*x)*Log[-1 + x])*Log[Log[5]
]^4)/(-1 + x),x]

[Out]

12*x + 6*x^2 + 4*x^3 + (15*x^4)/4 + 3*x^5 + 12*Log[1 - x] + 3*x^3*Log[-1 + x] - 6*x*Log[Log[5]]^2 + 3*x^2*Log[
Log[5]]^2 - 6*Log[1 - x]*Log[Log[5]]^2 - 6*x^2*Log[-1 + x]*Log[Log[5]]^2 - 3*x*(5 + 8*Log[Log[5]]^2) - (3*x^2*
(5 + 8*Log[Log[5]]^2))/2 - x^3*(5 + 8*Log[Log[5]]^2) - (3*x^4*(5 + 8*Log[Log[5]]^2))/4 - 3*Log[1 - x]*(5 + 8*L
og[Log[5]]^2) - 3*x*(2 + Log[Log[5]]^4) + 3*Log[1 - x]*(2 + Log[Log[5]]^4) - 3*(1 - x)*Log[-1 + x]*(2 + Log[Lo
g[5]]^4) - 3*x*(3 - 2*Log[Log[5]]^2 + 3*Log[Log[5]]^4) - (3*x^2*(3 - 2*Log[Log[5]]^2 + 3*Log[Log[5]]^4))/2 - 3
*Log[1 - x]*(3 - 2*Log[Log[5]]^2 + 3*Log[Log[5]]^4) + 3*x*(4 + 8*Log[Log[5]]^2 + 3*Log[Log[5]]^4) + (3*x^2*(4
+ 8*Log[Log[5]]^2 + 3*Log[Log[5]]^4))/2 + x^3*(4 + 8*Log[Log[5]]^2 + 3*Log[Log[5]]^4) + 3*Log[1 - x]*(4 + 8*Lo
g[Log[5]]^2 + 3*Log[Log[5]]^4)

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 2295

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

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 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 2417

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.)*(Polyx_), x_Symbol] :> Int[ExpandIntegrand[Poly
x*(a + b*Log[c*(d + e*x)^n])^p, x], x] /; FreeQ[{a, b, c, d, e, n, p}, x] && PolynomialQ[Polyx, 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 \left (\frac {15 x^5}{-1+x}-\frac {12 x \log ^2(\log (5))}{-1+x}-\frac {15 x^4 \left (1+\frac {8}{5} \log ^2(\log (5))\right )}{-1+x}+\frac {6 \left (1+\frac {1}{2} \log ^4(\log (5))\right )}{-1+x}+\frac {12 x^3 \left (1+2 \log ^2(\log (5))+\frac {3}{4} \log ^4(\log (5))\right )}{-1+x}-\frac {9 x^2 \left (1-\frac {2}{3} \log ^2(\log (5))+\log ^4(\log (5))\right )}{-1+x}+3 \log (-1+x) \left (2+3 x^2-4 x \log ^2(\log (5))+\log ^4(\log (5))\right )\right ) \, dx\\ &=3 \log (1-x) \left (2+\log ^4(\log (5))\right )+3 \int \log (-1+x) \left (2+3 x^2-4 x \log ^2(\log (5))+\log ^4(\log (5))\right ) \, dx+15 \int \frac {x^5}{-1+x} \, dx-\left (12 \log ^2(\log (5))\right ) \int \frac {x}{-1+x} \, dx-\left (3 \left (5+8 \log ^2(\log (5))\right )\right ) \int \frac {x^4}{-1+x} \, dx-\left (3 \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )\right ) \int \frac {x^2}{-1+x} \, dx+\left (3 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )\right ) \int \frac {x^3}{-1+x} \, dx\\ &=3 \log (1-x) \left (2+\log ^4(\log (5))\right )+3 \int \left (3 x^2 \log (-1+x)-4 x \log (-1+x) \log ^2(\log (5))+2 \log (-1+x) \left (1+\frac {1}{2} \log ^4(\log (5))\right )\right ) \, dx+15 \int \left (1+\frac {1}{-1+x}+x+x^2+x^3+x^4\right ) \, dx-\left (12 \log ^2(\log (5))\right ) \int \left (1+\frac {1}{-1+x}\right ) \, dx-\left (3 \left (5+8 \log ^2(\log (5))\right )\right ) \int \left (1+\frac {1}{-1+x}+x+x^2+x^3\right ) \, dx-\left (3 \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )\right ) \int \left (1+\frac {1}{-1+x}+x\right ) \, dx+\left (3 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )\right ) \int \left (1+\frac {1}{-1+x}+x+x^2\right ) \, dx\\ &=15 x+\frac {15 x^2}{2}+5 x^3+\frac {15 x^4}{4}+3 x^5+15 \log (1-x)-12 x \log ^2(\log (5))-12 \log (1-x) \log ^2(\log (5))-3 x \left (5+8 \log ^2(\log (5))\right )-\frac {3}{2} x^2 \left (5+8 \log ^2(\log (5))\right )-x^3 \left (5+8 \log ^2(\log (5))\right )-\frac {3}{4} x^4 \left (5+8 \log ^2(\log (5))\right )-3 \log (1-x) \left (5+8 \log ^2(\log (5))\right )+3 \log (1-x) \left (2+\log ^4(\log (5))\right )-3 x \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-\frac {3}{2} x^2 \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-3 \log (1-x) \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+3 x \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+\frac {3}{2} x^2 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+x^3 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+3 \log (1-x) \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+9 \int x^2 \log (-1+x) \, dx-\left (12 \log ^2(\log (5))\right ) \int x \log (-1+x) \, dx+\left (3 \left (2+\log ^4(\log (5))\right )\right ) \int \log (-1+x) \, dx\\ &=15 x+\frac {15 x^2}{2}+5 x^3+\frac {15 x^4}{4}+3 x^5+15 \log (1-x)+3 x^3 \log (-1+x)-12 x \log ^2(\log (5))-12 \log (1-x) \log ^2(\log (5))-6 x^2 \log (-1+x) \log ^2(\log (5))-3 x \left (5+8 \log ^2(\log (5))\right )-\frac {3}{2} x^2 \left (5+8 \log ^2(\log (5))\right )-x^3 \left (5+8 \log ^2(\log (5))\right )-\frac {3}{4} x^4 \left (5+8 \log ^2(\log (5))\right )-3 \log (1-x) \left (5+8 \log ^2(\log (5))\right )+3 \log (1-x) \left (2+\log ^4(\log (5))\right )-3 x \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-\frac {3}{2} x^2 \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-3 \log (1-x) \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+3 x \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+\frac {3}{2} x^2 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+x^3 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+3 \log (1-x) \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-3 \int \frac {x^3}{-1+x} \, dx+\left (6 \log ^2(\log (5))\right ) \int \frac {x^2}{-1+x} \, dx+\left (3 \left (2+\log ^4(\log (5))\right )\right ) \operatorname {Subst}(\int \log (x) \, dx,x,-1+x)\\ &=15 x+\frac {15 x^2}{2}+5 x^3+\frac {15 x^4}{4}+3 x^5+15 \log (1-x)+3 x^3 \log (-1+x)-12 x \log ^2(\log (5))-12 \log (1-x) \log ^2(\log (5))-6 x^2 \log (-1+x) \log ^2(\log (5))-3 x \left (5+8 \log ^2(\log (5))\right )-\frac {3}{2} x^2 \left (5+8 \log ^2(\log (5))\right )-x^3 \left (5+8 \log ^2(\log (5))\right )-\frac {3}{4} x^4 \left (5+8 \log ^2(\log (5))\right )-3 \log (1-x) \left (5+8 \log ^2(\log (5))\right )-3 x \left (2+\log ^4(\log (5))\right )+3 \log (1-x) \left (2+\log ^4(\log (5))\right )-3 (1-x) \log (-1+x) \left (2+\log ^4(\log (5))\right )-3 x \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-\frac {3}{2} x^2 \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-3 \log (1-x) \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+3 x \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+\frac {3}{2} x^2 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+x^3 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+3 \log (1-x) \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-3 \int \left (1+\frac {1}{-1+x}+x+x^2\right ) \, dx+\left (6 \log ^2(\log (5))\right ) \int \left (1+\frac {1}{-1+x}+x\right ) \, dx\\ &=12 x+6 x^2+4 x^3+\frac {15 x^4}{4}+3 x^5+12 \log (1-x)+3 x^3 \log (-1+x)-6 x \log ^2(\log (5))+3 x^2 \log ^2(\log (5))-6 \log (1-x) \log ^2(\log (5))-6 x^2 \log (-1+x) \log ^2(\log (5))-3 x \left (5+8 \log ^2(\log (5))\right )-\frac {3}{2} x^2 \left (5+8 \log ^2(\log (5))\right )-x^3 \left (5+8 \log ^2(\log (5))\right )-\frac {3}{4} x^4 \left (5+8 \log ^2(\log (5))\right )-3 \log (1-x) \left (5+8 \log ^2(\log (5))\right )-3 x \left (2+\log ^4(\log (5))\right )+3 \log (1-x) \left (2+\log ^4(\log (5))\right )-3 (1-x) \log (-1+x) \left (2+\log ^4(\log (5))\right )-3 x \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-\frac {3}{2} x^2 \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )-3 \log (1-x) \left (3-2 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+3 x \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+\frac {3}{2} x^2 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+x^3 \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )+3 \log (1-x) \left (4+8 \log ^2(\log (5))+3 \log ^4(\log (5))\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.05, size = 30, normalized size = 1.20 \begin {gather*} 3 x \left (-1+x^2+\log (-1+x)\right ) \left (2+x^2-2 x \log ^2(\log (5))+\log ^4(\log (5))\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(6 - 9*x^2 + 12*x^3 - 15*x^4 + 15*x^5 + (-6 + 6*x - 9*x^2 + 9*x^3)*Log[-1 + x] + (-12*x + 6*x^2 + 24
*x^3 - 24*x^4 + (12*x - 12*x^2)*Log[-1 + x])*Log[Log[5]]^2 + (3 - 9*x^2 + 9*x^3 + (-3 + 3*x)*Log[-1 + x])*Log[
Log[5]]^4)/(-1 + x),x]

[Out]

3*x*(-1 + x^2 + Log[-1 + x])*(2 + x^2 - 2*x*Log[Log[5]]^2 + Log[Log[5]]^4)

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fricas [B]  time = 0.61, size = 71, normalized size = 2.84 \begin {gather*} 3 \, x^{5} + 3 \, {\left (x^{3} + x \log \left (x - 1\right ) - x\right )} \log \left (\log \relax (5)\right )^{4} + 3 \, x^{3} - 6 \, {\left (x^{4} + x^{2} \log \left (x - 1\right ) - x^{2}\right )} \log \left (\log \relax (5)\right )^{2} + 3 \, {\left (x^{3} + 2 \, x\right )} \log \left (x - 1\right ) - 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3*x-3)*log(x-1)+9*x^3-9*x^2+3)*log(log(5))^4+((-12*x^2+12*x)*log(x-1)-24*x^4+24*x^3+6*x^2-12*x)*l
og(log(5))^2+(9*x^3-9*x^2+6*x-6)*log(x-1)+15*x^5-15*x^4+12*x^3-9*x^2+6)/(x-1),x, algorithm="fricas")

[Out]

3*x^5 + 3*(x^3 + x*log(x - 1) - x)*log(log(5))^4 + 3*x^3 - 6*(x^4 + x^2*log(x - 1) - x^2)*log(log(5))^2 + 3*(x
^3 + 2*x)*log(x - 1) - 6*x

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giac [B]  time = 0.14, size = 80, normalized size = 3.20 \begin {gather*} -6 \, x^{4} \log \left (\log \relax (5)\right )^{2} + 3 \, x^{5} + 3 \, {\left (\log \left (\log \relax (5)\right )^{4} + 1\right )} x^{3} + 6 \, x^{2} \log \left (\log \relax (5)\right )^{2} - 3 \, {\left (\log \left (\log \relax (5)\right )^{4} + 2\right )} x - 3 \, {\left (2 \, x^{2} \log \left (\log \relax (5)\right )^{2} - x^{3} - {\left (\log \left (\log \relax (5)\right )^{4} + 2\right )} x\right )} \log \left (x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3*x-3)*log(x-1)+9*x^3-9*x^2+3)*log(log(5))^4+((-12*x^2+12*x)*log(x-1)-24*x^4+24*x^3+6*x^2-12*x)*l
og(log(5))^2+(9*x^3-9*x^2+6*x-6)*log(x-1)+15*x^5-15*x^4+12*x^3-9*x^2+6)/(x-1),x, algorithm="giac")

[Out]

-6*x^4*log(log(5))^2 + 3*x^5 + 3*(log(log(5))^4 + 1)*x^3 + 6*x^2*log(log(5))^2 - 3*(log(log(5))^4 + 2)*x - 3*(
2*x^2*log(log(5))^2 - x^3 - (log(log(5))^4 + 2)*x)*log(x - 1)

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maple [B]  time = 0.23, size = 85, normalized size = 3.40

method	result	size
risch	\(\left (3 \ln \left (\ln \relax (5)\right )^{4} x -6 x^{2} \ln \left (\ln \relax (5)\right )^{2}+3 x^{3}+6 x \right ) \ln \left (x -1\right )+3 \ln \left (\ln \relax (5)\right )^{4} x^{3}-6 \ln \left (\ln \relax (5)\right )^{2} x^{4}-3 \ln \left (\ln \relax (5)\right )^{4} x +3 x^{5}+6 x^{2} \ln \left (\ln \relax (5)\right )^{2}+3 x^{3}-6 x\)	\(85\)
norman	\(\left (-6-3 \ln \left (\ln \relax (5)\right )^{4}\right ) x +\left (3+3 \ln \left (\ln \relax (5)\right )^{4}\right ) x^{3}+\left (3 \ln \left (\ln \relax (5)\right )^{4}+6\right ) x \ln \left (x -1\right )+3 x^{5}+6 x^{2} \ln \left (\ln \relax (5)\right )^{2}+3 \ln \left (x -1\right ) x^{3}-6 \ln \left (\ln \relax (5)\right )^{2} x^{4}-6 \ln \left (x -1\right ) \ln \left (\ln \relax (5)\right )^{2} x^{2}\)	\(89\)
derivativedivides	\(3 \ln \left (\ln \relax (5)\right )^{4} \left (x -1\right )^{3}+3 \ln \left (\ln \relax (5)\right )^{4} \left (\left (x -1\right ) \ln \left (x -1\right )-x +1\right )+9 \ln \left (\ln \relax (5)\right )^{4} \left (x -1\right )^{2}-6 \ln \left (\ln \relax (5)\right )^{2} \left (x -1\right )^{4}-12 \ln \left (\ln \relax (5)\right )^{2} \left (\frac {\ln \left (x -1\right ) \left (x -1\right )^{2}}{2}-\frac {\left (x -1\right )^{2}}{4}\right )+9 \ln \left (\ln \relax (5)\right )^{4} \left (x -1\right )-24 \ln \left (\ln \relax (5)\right )^{2} \left (x -1\right )^{3}+3 \left (x -1\right )^{5}-12 \ln \left (\ln \relax (5)\right )^{2} \left (\left (x -1\right ) \ln \left (x -1\right )-x +1\right )+3 \ln \left (x -1\right ) \left (x -1\right )^{3}+33 \left (x -1\right )^{3}+3 \ln \left (x -1\right ) \ln \left (\ln \relax (5)\right )^{4}-33 \ln \left (\ln \relax (5)\right )^{2} \left (x -1\right )^{2}+15 \left (x -1\right )^{4}+9 \ln \left (x -1\right ) \left (x -1\right )^{2}+39 \left (x -1\right )^{2}-24 \ln \left (\ln \relax (5)\right )^{2} \left (x -1\right )+15 \left (x -1\right ) \ln \left (x -1\right )+18 x -18-6 \ln \left (x -1\right ) \ln \left (\ln \relax (5)\right )^{2}+9 \ln \left (x -1\right )\)	\(239\)
default	\(3 \ln \left (\ln \relax (5)\right )^{4} \left (x -1\right )^{3}+3 \ln \left (\ln \relax (5)\right )^{4} \left (\left (x -1\right ) \ln \left (x -1\right )-x +1\right )+9 \ln \left (\ln \relax (5)\right )^{4} \left (x -1\right )^{2}-6 \ln \left (\ln \relax (5)\right )^{2} \left (x -1\right )^{4}-12 \ln \left (\ln \relax (5)\right )^{2} \left (\frac {\ln \left (x -1\right ) \left (x -1\right )^{2}}{2}-\frac {\left (x -1\right )^{2}}{4}\right )+9 \ln \left (\ln \relax (5)\right )^{4} \left (x -1\right )-24 \ln \left (\ln \relax (5)\right )^{2} \left (x -1\right )^{3}+3 \left (x -1\right )^{5}-12 \ln \left (\ln \relax (5)\right )^{2} \left (\left (x -1\right ) \ln \left (x -1\right )-x +1\right )+3 \ln \left (x -1\right ) \left (x -1\right )^{3}+33 \left (x -1\right )^{3}+3 \ln \left (x -1\right ) \ln \left (\ln \relax (5)\right )^{4}-33 \ln \left (\ln \relax (5)\right )^{2} \left (x -1\right )^{2}+15 \left (x -1\right )^{4}+9 \ln \left (x -1\right ) \left (x -1\right )^{2}+39 \left (x -1\right )^{2}-24 \ln \left (\ln \relax (5)\right )^{2} \left (x -1\right )+15 \left (x -1\right ) \ln \left (x -1\right )+18 x -18-6 \ln \left (x -1\right ) \ln \left (\ln \relax (5)\right )^{2}+9 \ln \left (x -1\right )\)	\(239\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((3*x-3)*ln(x-1)+9*x^3-9*x^2+3)*ln(ln(5))^4+((-12*x^2+12*x)*ln(x-1)-24*x^4+24*x^3+6*x^2-12*x)*ln(ln(5))^2
+(9*x^3-9*x^2+6*x-6)*ln(x-1)+15*x^5-15*x^4+12*x^3-9*x^2+6)/(x-1),x,method=_RETURNVERBOSE)

[Out]

(3*ln(ln(5))^4*x-6*x^2*ln(ln(5))^2+3*x^3+6*x)*ln(x-1)+3*ln(ln(5))^4*x^3-6*ln(ln(5))^2*x^4-3*ln(ln(5))^4*x+3*x^
5+6*x^2*ln(ln(5))^2+3*x^3-6*x

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maxima [B]  time = 0.38, size = 374, normalized size = 14.96 \begin {gather*} 3 \, {\left (x + \log \left (x - 1\right )\right )} \log \left (x - 1\right ) \log \left (\log \relax (5)\right )^{4} - \frac {3}{2} \, \log \left (x - 1\right )^{2} \log \left (\log \relax (5)\right )^{4} + 3 \, x^{5} + \frac {3}{2} \, {\left (2 \, x^{3} + 3 \, x^{2} + 6 \, x + 6 \, \log \left (x - 1\right )\right )} \log \left (\log \relax (5)\right )^{4} - \frac {9}{2} \, {\left (x^{2} + 2 \, x + 2 \, \log \left (x - 1\right )\right )} \log \left (\log \relax (5)\right )^{4} - \frac {3}{2} \, {\left (\log \left (x - 1\right )^{2} + 2 \, x + 2 \, \log \left (x - 1\right )\right )} \log \left (\log \relax (5)\right )^{4} + 3 \, \log \left (x - 1\right ) \log \left (\log \relax (5)\right )^{4} - 6 \, {\left (x^{2} + 2 \, x + 2 \, \log \left (x - 1\right )\right )} \log \left (x - 1\right ) \log \left (\log \relax (5)\right )^{2} + 12 \, {\left (x + \log \left (x - 1\right )\right )} \log \left (x - 1\right ) \log \left (\log \relax (5)\right )^{2} + 3 \, x^{3} - 2 \, {\left (3 \, x^{4} + 4 \, x^{3} + 6 \, x^{2} + 12 \, x + 12 \, \log \left (x - 1\right )\right )} \log \left (\log \relax (5)\right )^{2} + 4 \, {\left (2 \, x^{3} + 3 \, x^{2} + 6 \, x + 6 \, \log \left (x - 1\right )\right )} \log \left (\log \relax (5)\right )^{2} + 3 \, {\left (x^{2} + 2 \, \log \left (x - 1\right )^{2} + 6 \, x + 6 \, \log \left (x - 1\right )\right )} \log \left (\log \relax (5)\right )^{2} + 3 \, {\left (x^{2} + 2 \, x + 2 \, \log \left (x - 1\right )\right )} \log \left (\log \relax (5)\right )^{2} - 6 \, {\left (\log \left (x - 1\right )^{2} + 2 \, x + 2 \, \log \left (x - 1\right )\right )} \log \left (\log \relax (5)\right )^{2} - 12 \, {\left (x + \log \left (x - 1\right )\right )} \log \left (\log \relax (5)\right )^{2} + \frac {3}{2} \, {\left (2 \, x^{3} + 3 \, x^{2} + 6 \, x + 6 \, \log \left (x - 1\right )\right )} \log \left (x - 1\right ) - \frac {9}{2} \, {\left (x^{2} + 2 \, x + 2 \, \log \left (x - 1\right )\right )} \log \left (x - 1\right ) + 6 \, {\left (x + \log \left (x - 1\right )\right )} \log \left (x - 1\right ) - 6 \, \log \left (x - 1\right )^{2} - 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3*x-3)*log(x-1)+9*x^3-9*x^2+3)*log(log(5))^4+((-12*x^2+12*x)*log(x-1)-24*x^4+24*x^3+6*x^2-12*x)*l
og(log(5))^2+(9*x^3-9*x^2+6*x-6)*log(x-1)+15*x^5-15*x^4+12*x^3-9*x^2+6)/(x-1),x, algorithm="maxima")

[Out]

3*(x + log(x - 1))*log(x - 1)*log(log(5))^4 - 3/2*log(x - 1)^2*log(log(5))^4 + 3*x^5 + 3/2*(2*x^3 + 3*x^2 + 6*
x + 6*log(x - 1))*log(log(5))^4 - 9/2*(x^2 + 2*x + 2*log(x - 1))*log(log(5))^4 - 3/2*(log(x - 1)^2 + 2*x + 2*l
og(x - 1))*log(log(5))^4 + 3*log(x - 1)*log(log(5))^4 - 6*(x^2 + 2*x + 2*log(x - 1))*log(x - 1)*log(log(5))^2
+ 12*(x + log(x - 1))*log(x - 1)*log(log(5))^2 + 3*x^3 - 2*(3*x^4 + 4*x^3 + 6*x^2 + 12*x + 12*log(x - 1))*log(
log(5))^2 + 4*(2*x^3 + 3*x^2 + 6*x + 6*log(x - 1))*log(log(5))^2 + 3*(x^2 + 2*log(x - 1)^2 + 6*x + 6*log(x - 1
))*log(log(5))^2 + 3*(x^2 + 2*x + 2*log(x - 1))*log(log(5))^2 - 6*(log(x - 1)^2 + 2*x + 2*log(x - 1))*log(log(
5))^2 - 12*(x + log(x - 1))*log(log(5))^2 + 3/2*(2*x^3 + 3*x^2 + 6*x + 6*log(x - 1))*log(x - 1) - 9/2*(x^2 + 2
*x + 2*log(x - 1))*log(x - 1) + 6*(x + log(x - 1))*log(x - 1) - 6*log(x - 1)^2 - 6*x

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mupad [B]  time = 5.96, size = 30, normalized size = 1.20 \begin {gather*} 3\,x\,\left (\ln \left (x-1\right )+x^2-1\right )\,\left (x^2-2\,{\ln \left (\ln \relax (5)\right )}^2\,x+{\ln \left (\ln \relax (5)\right )}^4+2\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(log(5))^4*(9*x^3 - 9*x^2 + log(x - 1)*(3*x - 3) + 3) + log(x - 1)*(6*x - 9*x^2 + 9*x^3 - 6) + log(log
(5))^2*(log(x - 1)*(12*x - 12*x^2) - 12*x + 6*x^2 + 24*x^3 - 24*x^4) - 9*x^2 + 12*x^3 - 15*x^4 + 15*x^5 + 6)/(
x - 1),x)

[Out]

3*x*(log(x - 1) + x^2 - 1)*(log(log(5))^4 - 2*x*log(log(5))^2 + x^2 + 2)

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sympy [B]  time = 0.22, size = 90, normalized size = 3.60 \begin {gather*} 3 x^{5} - 6 x^{4} \log {\left (\log {\relax (5 )} \right )}^{2} + x^{3} \left (3 \log {\left (\log {\relax (5 )} \right )}^{4} + 3\right ) + 6 x^{2} \log {\left (\log {\relax (5 )} \right )}^{2} + x \left (-6 - 3 \log {\left (\log {\relax (5 )} \right )}^{4}\right ) + \left (3 x^{3} - 6 x^{2} \log {\left (\log {\relax (5 )} \right )}^{2} + 3 x \log {\left (\log {\relax (5 )} \right )}^{4} + 6 x\right ) \log {\left (x - 1 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3*x-3)*ln(x-1)+9*x**3-9*x**2+3)*ln(ln(5))**4+((-12*x**2+12*x)*ln(x-1)-24*x**4+24*x**3+6*x**2-12*x
)*ln(ln(5))**2+(9*x**3-9*x**2+6*x-6)*ln(x-1)+15*x**5-15*x**4+12*x**3-9*x**2+6)/(x-1),x)

[Out]

3*x**5 - 6*x**4*log(log(5))**2 + x**3*(3*log(log(5))**4 + 3) + 6*x**2*log(log(5))**2 + x*(-6 - 3*log(log(5))**
4) + (3*x**3 - 6*x**2*log(log(5))**2 + 3*x*log(log(5))**4 + 6*x)*log(x - 1)

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