3.99.49 \(\int \frac {2 x-7 x^2+3 x^3+e^3 (4 x^3-32 x^4+48 x^5-20 x^6)+e^6 (-28 x^6+84 x^7-84 x^8+28 x^9)+(-2+10 x-12 x^2+4 x^3+e^3 (16 x^3-48 x^4+48 x^5-16 x^6)) \log (x)+(-1+3 x-3 x^2+x^3) \log ^2(x)}{-1+3 x-3 x^2+x^3} \, dx\)

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

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Rubi [B]  time = 0.39, antiderivative size = 115, normalized size of antiderivative = 4.60, number of steps used = 17, number of rules used = 10, integrand size = 141, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {6742, 37, 43, 893, 2357, 2295, 2314, 31, 2304, 2296} \begin {gather*} 4 e^6 x^7-4 e^3 x^4-4 e^3 x^4 \log (x)-4 e^3 x^3-\frac {x^2}{(1-x)^2}-4 e^3 x^2-4 e^3 x+x+\frac {4 e^3}{1-x}-\frac {5}{1-x}+\frac {2}{(1-x)^2}+x \log ^2(x)-\frac {2 x \log (x)}{1-x}+2 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(2*x - 7*x^2 + 3*x^3 + E^3*(4*x^3 - 32*x^4 + 48*x^5 - 20*x^6) + E^6*(-28*x^6 + 84*x^7 - 84*x^8 + 28*x^9) +
(-2 + 10*x - 12*x^2 + 4*x^3 + E^3*(16*x^3 - 48*x^4 + 48*x^5 - 16*x^6))*Log[x] + (-1 + 3*x - 3*x^2 + x^3)*Log[
x]^2)/(-1 + 3*x - 3*x^2 + x^3),x]

[Out]

2/(1 - x)^2 - 5/(1 - x) + (4*E^3)/(1 - x) + x - 4*E^3*x - 4*E^3*x^2 - x^2/(1 - x)^2 - 4*E^3*x^3 - 4*E^3*x^4 +
4*E^6*x^7 + 2*x*Log[x] - (2*x*Log[x])/(1 - x) - 4*E^3*x^4*Log[x] + x*Log[x]^2

Rule 31

Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]

Rule 37

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[((a + b*x)^(m + 1)*(c + d*x)^(n +
1))/((b*c - a*d)*(m + 1)), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[b*c - a*d, 0] && EqQ[m + n + 2, 0] && 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 893

Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))^(n_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :
> Int[ExpandIntegrand[(d + e*x)^m*(f + g*x)^n*(a + b*x + c*x^2)^p, x], x] /; FreeQ[{a, b, c, d, e, f, g}, x] &
& NeQ[e*f - d*g, 0] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && IntegerQ[p] && ((EqQ[p, 1] && I
ntegersQ[m, n]) || (ILtQ[m, 0] && ILtQ[n, 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 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 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 2314

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

Rule 2357

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 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 {2 x}{(-1+x)^3}-\frac {7 x^2}{(-1+x)^3}+\frac {3 x^3}{(-1+x)^3}+28 e^6 x^6-\frac {4 e^3 x^3 \left (1-7 x+5 x^2\right )}{(-1+x)^2}-\frac {2 \left (-1+4 x-2 x^2+8 e^3 x^3-16 e^3 x^4+8 e^3 x^5\right ) \log (x)}{(-1+x)^2}+\log ^2(x)\right ) \, dx\\ &=4 e^6 x^7+2 \int \frac {x}{(-1+x)^3} \, dx-2 \int \frac {\left (-1+4 x-2 x^2+8 e^3 x^3-16 e^3 x^4+8 e^3 x^5\right ) \log (x)}{(-1+x)^2} \, dx+3 \int \frac {x^3}{(-1+x)^3} \, dx-7 \int \frac {x^2}{(-1+x)^3} \, dx-\left (4 e^3\right ) \int \frac {x^3 \left (1-7 x+5 x^2\right )}{(-1+x)^2} \, dx+\int \log ^2(x) \, dx\\ &=-\frac {x^2}{(1-x)^2}+4 e^6 x^7+x \log ^2(x)-2 \int \log (x) \, dx-2 \int \left (-2 \log (x)+\frac {\log (x)}{(-1+x)^2}+8 e^3 x^3 \log (x)\right ) \, dx+3 \int \left (1+\frac {1}{(-1+x)^3}+\frac {3}{(-1+x)^2}+\frac {3}{-1+x}\right ) \, dx-7 \int \left (\frac {1}{(-1+x)^3}+\frac {2}{(-1+x)^2}+\frac {1}{-1+x}\right ) \, dx-\left (4 e^3\right ) \int \left (1-\frac {1}{(-1+x)^2}+2 x+3 x^2+5 x^3\right ) \, dx\\ &=\frac {2}{(1-x)^2}-\frac {5}{1-x}+\frac {4 e^3}{1-x}+5 x-4 e^3 x-4 e^3 x^2-\frac {x^2}{(1-x)^2}-4 e^3 x^3-5 e^3 x^4+4 e^6 x^7+2 \log (1-x)-2 x \log (x)+x \log ^2(x)-2 \int \frac {\log (x)}{(-1+x)^2} \, dx+4 \int \log (x) \, dx-\left (16 e^3\right ) \int x^3 \log (x) \, dx\\ &=\frac {2}{(1-x)^2}-\frac {5}{1-x}+\frac {4 e^3}{1-x}+x-4 e^3 x-4 e^3 x^2-\frac {x^2}{(1-x)^2}-4 e^3 x^3-4 e^3 x^4+4 e^6 x^7+2 \log (1-x)+2 x \log (x)-\frac {2 x \log (x)}{1-x}-4 e^3 x^4 \log (x)+x \log ^2(x)-2 \int \frac {1}{-1+x} \, dx\\ &=\frac {2}{(1-x)^2}-\frac {5}{1-x}+\frac {4 e^3}{1-x}+x-4 e^3 x-4 e^3 x^2-\frac {x^2}{(1-x)^2}-4 e^3 x^3-4 e^3 x^4+4 e^6 x^7+2 x \log (x)-\frac {2 x \log (x)}{1-x}-4 e^3 x^4 \log (x)+x \log ^2(x)\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.10, size = 121, normalized size = 4.84 \begin {gather*} -3+17 e^3-4 e^6+\frac {1}{(-1+x)^2}+\frac {3}{-1+x}-\frac {4 e^3}{-1+x}+x-4 e^3 x-4 e^3 x^2-4 e^3 x^3-4 e^3 x^4+4 e^6 x^7-2 \log (1-x)+2 \log (-1+x)+2 \log (x)+\frac {2 \log (x)}{-1+x}+2 x \log (x)-4 e^3 x^4 \log (x)+x \log ^2(x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(2*x - 7*x^2 + 3*x^3 + E^3*(4*x^3 - 32*x^4 + 48*x^5 - 20*x^6) + E^6*(-28*x^6 + 84*x^7 - 84*x^8 + 28*
x^9) + (-2 + 10*x - 12*x^2 + 4*x^3 + E^3*(16*x^3 - 48*x^4 + 48*x^5 - 16*x^6))*Log[x] + (-1 + 3*x - 3*x^2 + x^3
)*Log[x]^2)/(-1 + 3*x - 3*x^2 + x^3),x]

[Out]

-3 + 17*E^3 - 4*E^6 + (-1 + x)^(-2) + 3/(-1 + x) - (4*E^3)/(-1 + x) + x - 4*E^3*x - 4*E^3*x^2 - 4*E^3*x^3 - 4*
E^3*x^4 + 4*E^6*x^7 - 2*Log[1 - x] + 2*Log[-1 + x] + 2*Log[x] + (2*Log[x])/(-1 + x) + 2*x*Log[x] - 4*E^3*x^4*L
og[x] + x*Log[x]^2

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fricas [B]  time = 0.57, size = 106, normalized size = 4.24 \begin {gather*} \frac {x^{3} + {\left (x^{3} - 2 \, x^{2} + x\right )} \log \relax (x)^{2} - 2 \, x^{2} + 4 \, {\left (x^{9} - 2 \, x^{8} + x^{7}\right )} e^{6} - 4 \, {\left (x^{6} - x^{5} - x^{2} + 2 \, x - 1\right )} e^{3} + 2 \, {\left (x^{3} - x^{2} - 2 \, {\left (x^{6} - 2 \, x^{5} + x^{4}\right )} e^{3}\right )} \log \relax (x) + 4 \, x - 2}{x^{2} - 2 \, x + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^3-3*x^2+3*x-1)*log(x)^2+((-16*x^6+48*x^5-48*x^4+16*x^3)*exp(3)+4*x^3-12*x^2+10*x-2)*log(x)+(28*x
^9-84*x^8+84*x^7-28*x^6)*exp(3)^2+(-20*x^6+48*x^5-32*x^4+4*x^3)*exp(3)+3*x^3-7*x^2+2*x)/(x^3-3*x^2+3*x-1),x, a
lgorithm="fricas")

[Out]

(x^3 + (x^3 - 2*x^2 + x)*log(x)^2 - 2*x^2 + 4*(x^9 - 2*x^8 + x^7)*e^6 - 4*(x^6 - x^5 - x^2 + 2*x - 1)*e^3 + 2*
(x^3 - x^2 - 2*(x^6 - 2*x^5 + x^4)*e^3)*log(x) + 4*x - 2)/(x^2 - 2*x + 1)

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giac [B]  time = 0.21, size = 139, normalized size = 5.56 \begin {gather*} \frac {4 \, x^{9} e^{6} - 8 \, x^{8} e^{6} + 4 \, x^{7} e^{6} - 4 \, x^{6} e^{3} \log \relax (x) - 4 \, x^{6} e^{3} + 8 \, x^{5} e^{3} \log \relax (x) + 4 \, x^{5} e^{3} - 4 \, x^{4} e^{3} \log \relax (x) + x^{3} \log \relax (x)^{2} + 2 \, x^{3} \log \relax (x) - 2 \, x^{2} \log \relax (x)^{2} + x^{3} + 4 \, x^{2} e^{3} - 2 \, x^{2} \log \relax (x) + x \log \relax (x)^{2} - 2 \, x^{2} - 8 \, x e^{3} + 4 \, x + 4 \, e^{3} - 2}{x^{2} - 2 \, x + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^3-3*x^2+3*x-1)*log(x)^2+((-16*x^6+48*x^5-48*x^4+16*x^3)*exp(3)+4*x^3-12*x^2+10*x-2)*log(x)+(28*x
^9-84*x^8+84*x^7-28*x^6)*exp(3)^2+(-20*x^6+48*x^5-32*x^4+4*x^3)*exp(3)+3*x^3-7*x^2+2*x)/(x^3-3*x^2+3*x-1),x, a
lgorithm="giac")

[Out]

(4*x^9*e^6 - 8*x^8*e^6 + 4*x^7*e^6 - 4*x^6*e^3*log(x) - 4*x^6*e^3 + 8*x^5*e^3*log(x) + 4*x^5*e^3 - 4*x^4*e^3*l
og(x) + x^3*log(x)^2 + 2*x^3*log(x) - 2*x^2*log(x)^2 + x^3 + 4*x^2*e^3 - 2*x^2*log(x) + x*log(x)^2 - 2*x^2 - 8
*x*e^3 + 4*x + 4*e^3 - 2)/(x^2 - 2*x + 1)

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maple [B]  time = 0.07, size = 87, normalized size = 3.48

method	result	size
default	\(x \ln \relax (x )^{2}+2 x \ln \relax (x )+x +4 x^{7} {\mathrm e}^{6}-4 x^{4} {\mathrm e}^{3}-4 x^{3} {\mathrm e}^{3}-4 x^{2} {\mathrm e}^{3}-4 x \,{\mathrm e}^{3}+\frac {1}{\left (x -1\right )^{2}}-\frac {4 \,{\mathrm e}^{3}}{x -1}+\frac {3}{x -1}-4 \ln \relax (x ) {\mathrm e}^{3} x^{4}+\frac {2 \ln \relax (x ) x}{x -1}\)	\(87\)
risch	\(x \ln \relax (x )^{2}-\frac {2 \left (2 x^{5} {\mathrm e}^{3}-2 x^{4} {\mathrm e}^{3}-x^{2}+x -1\right ) \ln \relax (x )}{x -1}+\frac {4 \,{\mathrm e}^{6} x^{9}-8 \,{\mathrm e}^{6} x^{8}+4 x^{7} {\mathrm e}^{6}-4 x^{6} {\mathrm e}^{3}+4 x^{5} {\mathrm e}^{3}+2 x^{2} \ln \relax (x )+4 x^{2} {\mathrm e}^{3}+x^{3}-4 x \ln \relax (x )-8 x \,{\mathrm e}^{3}-2 x^{2}+2 \ln \relax (x )+4 \,{\mathrm e}^{3}+4 x -2}{\left (x -1\right )^{2}}\)	\(125\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((x^3-3*x^2+3*x-1)*ln(x)^2+((-16*x^6+48*x^5-48*x^4+16*x^3)*exp(3)+4*x^3-12*x^2+10*x-2)*ln(x)+(28*x^9-84*x^
8+84*x^7-28*x^6)*exp(3)^2+(-20*x^6+48*x^5-32*x^4+4*x^3)*exp(3)+3*x^3-7*x^2+2*x)/(x^3-3*x^2+3*x-1),x,method=_RE
TURNVERBOSE)

[Out]

x*ln(x)^2+2*x*ln(x)+x+4*x^7*exp(6)-4*x^4*exp(3)-4*x^3*exp(3)-4*x^2*exp(3)-4*x*exp(3)+1/(x-1)^2-4/(x-1)*exp(3)+
3/(x-1)-4*ln(x)*exp(3)*x^4+2*ln(x)*x/(x-1)

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maxima [B]  time = 0.41, size = 557, normalized size = 22.28 \begin {gather*} \frac {2}{5} \, {\left (10 \, x^{7} + 35 \, x^{6} + 84 \, x^{5} + 175 \, x^{4} + 350 \, x^{3} + 735 \, x^{2} + 1960 \, x - \frac {35 \, {\left (18 \, x - 17\right )}}{x^{2} - 2 \, x + 1} + 2520 \, \log \left (x - 1\right )\right )} e^{6} - \frac {14}{5} \, {\left (5 \, x^{6} + 18 \, x^{5} + 45 \, x^{4} + 100 \, x^{3} + 225 \, x^{2} + 630 \, x - \frac {15 \, {\left (16 \, x - 15\right )}}{x^{2} - 2 \, x + 1} + 840 \, \log \left (x - 1\right )\right )} e^{6} + \frac {21}{5} \, {\left (4 \, x^{5} + 15 \, x^{4} + 40 \, x^{3} + 100 \, x^{2} + 300 \, x - \frac {10 \, {\left (14 \, x - 13\right )}}{x^{2} - 2 \, x + 1} + 420 \, \log \left (x - 1\right )\right )} e^{6} - 7 \, {\left (x^{4} + 4 \, x^{3} + 12 \, x^{2} + 40 \, x - \frac {2 \, {\left (12 \, x - 11\right )}}{x^{2} - 2 \, x + 1} + 60 \, \log \left (x - 1\right )\right )} e^{6} - 5 \, {\left (x^{4} + 4 \, x^{3} + 12 \, x^{2} + 40 \, x - \frac {2 \, {\left (12 \, x - 11\right )}}{x^{2} - 2 \, x + 1} + 60 \, \log \left (x - 1\right )\right )} e^{3} + 8 \, {\left (2 \, x^{3} + 9 \, x^{2} + 36 \, x - \frac {3 \, {\left (10 \, x - 9\right )}}{x^{2} - 2 \, x + 1} + 60 \, \log \left (x - 1\right )\right )} e^{3} - 16 \, {\left (x^{2} + 6 \, x - \frac {8 \, x - 7}{x^{2} - 2 \, x + 1} + 12 \, \log \left (x - 1\right )\right )} e^{3} + 2 \, {\left (2 \, x - \frac {6 \, x - 5}{x^{2} - 2 \, x + 1} + 6 \, \log \left (x - 1\right )\right )} e^{3} + 3 \, x - \frac {5 \, {\left (2 \, x - 1\right )} \log \relax (x)}{x^{2} - 2 \, x + 1} + \frac {x^{6} e^{3} - 2 \, x^{5} e^{3} + x^{4} e^{3} - 2 \, x^{3} + {\left (x^{3} - 2 \, x^{2} + x\right )} \log \relax (x)^{2} + 4 \, x^{2} - 2 \, {\left (2 \, x^{6} e^{3} - 4 \, x^{5} e^{3} + 2 \, x^{4} e^{3} - x^{3} - 2 \, x^{2} + x\right )} \log \relax (x) + 2 \, x - 4}{x^{2} - 2 \, x + 1} - \frac {3 \, {\left (6 \, x - 5\right )}}{2 \, {\left (x^{2} - 2 \, x + 1\right )}} + \frac {7 \, {\left (4 \, x - 3\right )}}{2 \, {\left (x^{2} - 2 \, x + 1\right )}} - \frac {2 \, x - 1}{x^{2} - 2 \, x + 1} + \frac {\log \relax (x)}{x^{2} - 2 \, x + 1} - \frac {4}{x - 1} - 6 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^3-3*x^2+3*x-1)*log(x)^2+((-16*x^6+48*x^5-48*x^4+16*x^3)*exp(3)+4*x^3-12*x^2+10*x-2)*log(x)+(28*x
^9-84*x^8+84*x^7-28*x^6)*exp(3)^2+(-20*x^6+48*x^5-32*x^4+4*x^3)*exp(3)+3*x^3-7*x^2+2*x)/(x^3-3*x^2+3*x-1),x, a
lgorithm="maxima")

[Out]

2/5*(10*x^7 + 35*x^6 + 84*x^5 + 175*x^4 + 350*x^3 + 735*x^2 + 1960*x - 35*(18*x - 17)/(x^2 - 2*x + 1) + 2520*l
og(x - 1))*e^6 - 14/5*(5*x^6 + 18*x^5 + 45*x^4 + 100*x^3 + 225*x^2 + 630*x - 15*(16*x - 15)/(x^2 - 2*x + 1) +
840*log(x - 1))*e^6 + 21/5*(4*x^5 + 15*x^4 + 40*x^3 + 100*x^2 + 300*x - 10*(14*x - 13)/(x^2 - 2*x + 1) + 420*l
og(x - 1))*e^6 - 7*(x^4 + 4*x^3 + 12*x^2 + 40*x - 2*(12*x - 11)/(x^2 - 2*x + 1) + 60*log(x - 1))*e^6 - 5*(x^4
+ 4*x^3 + 12*x^2 + 40*x - 2*(12*x - 11)/(x^2 - 2*x + 1) + 60*log(x - 1))*e^3 + 8*(2*x^3 + 9*x^2 + 36*x - 3*(10
*x - 9)/(x^2 - 2*x + 1) + 60*log(x - 1))*e^3 - 16*(x^2 + 6*x - (8*x - 7)/(x^2 - 2*x + 1) + 12*log(x - 1))*e^3
+ 2*(2*x - (6*x - 5)/(x^2 - 2*x + 1) + 6*log(x - 1))*e^3 + 3*x - 5*(2*x - 1)*log(x)/(x^2 - 2*x + 1) + (x^6*e^3
- 2*x^5*e^3 + x^4*e^3 - 2*x^3 + (x^3 - 2*x^2 + x)*log(x)^2 + 4*x^2 - 2*(2*x^6*e^3 - 4*x^5*e^3 + 2*x^4*e^3 - x
^3 - 2*x^2 + x)*log(x) + 2*x - 4)/(x^2 - 2*x + 1) - 3/2*(6*x - 5)/(x^2 - 2*x + 1) + 7/2*(4*x - 3)/(x^2 - 2*x +
1) - (2*x - 1)/(x^2 - 2*x + 1) + log(x)/(x^2 - 2*x + 1) - 4/(x - 1) - 6*log(x)

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mupad [B]  time = 5.85, size = 33, normalized size = 1.32 \begin {gather*} \frac {x\,{\left (x-\ln \relax (x)+2\,x^3\,{\mathrm {e}}^3-2\,x^4\,{\mathrm {e}}^3+x\,\ln \relax (x)\right )}^2}{{\left (x-1\right )}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x - 7*x^2 + 3*x^3 + log(x)*(10*x - 12*x^2 + 4*x^3 + exp(3)*(16*x^3 - 48*x^4 + 48*x^5 - 16*x^6) - 2) + l
og(x)^2*(3*x - 3*x^2 + x^3 - 1) + exp(3)*(4*x^3 - 32*x^4 + 48*x^5 - 20*x^6) - exp(6)*(28*x^6 - 84*x^7 + 84*x^8
- 28*x^9))/(3*x - 3*x^2 + x^3 - 1),x)

[Out]

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

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sympy [B]  time = 0.63, size = 110, normalized size = 4.40 \begin {gather*} 4 x^{7} e^{6} - 4 x^{4} e^{3} - 4 x^{3} e^{3} - 4 x^{2} e^{3} + x \log {\relax (x )}^{2} + x \left (1 - 4 e^{3}\right ) + 2 \log {\relax (x )} + \frac {x \left (3 - 4 e^{3}\right ) - 2 + 4 e^{3}}{x^{2} - 2 x + 1} + \frac {\left (- 4 x^{5} e^{3} + 4 x^{4} e^{3} + 2 x^{2} - 2 x + 2\right ) \log {\relax (x )}}{x - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x**3-3*x**2+3*x-1)*ln(x)**2+((-16*x**6+48*x**5-48*x**4+16*x**3)*exp(3)+4*x**3-12*x**2+10*x-2)*ln(x
)+(28*x**9-84*x**8+84*x**7-28*x**6)*exp(3)**2+(-20*x**6+48*x**5-32*x**4+4*x**3)*exp(3)+3*x**3-7*x**2+2*x)/(x**
3-3*x**2+3*x-1),x)

[Out]

4*x**7*exp(6) - 4*x**4*exp(3) - 4*x**3*exp(3) - 4*x**2*exp(3) + x*log(x)**2 + x*(1 - 4*exp(3)) + 2*log(x) + (x
*(3 - 4*exp(3)) - 2 + 4*exp(3))/(x**2 - 2*x + 1) + (-4*x**5*exp(3) + 4*x**4*exp(3) + 2*x**2 - 2*x + 2)*log(x)/
(x - 1)

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