3.91.81 \(\int \frac {-3+15 x-106 x^2+294 x^3-516 x^4+588 x^5-420 x^6+156 x^7+6 x^8-34 x^9+14 x^{10}-2 x^{11}+(-2+26 x-138 x^2+402 x^3-708 x^4+756 x^5-420 x^6-12 x^7+198 x^8-142 x^9+46 x^{10}-6 x^{11}) \log (x)}{-1+9 x-36 x^2+84 x^3-126 x^4+126 x^5-84 x^6+36 x^7-9 x^8+x^9} \, dx\)
Optimal. Leaf size=23 \[ \frac {x}{(-1+x)^8}-2 \left (-x+x^2 (2+x)\right ) \log (x) \]
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Rubi [B] time = 1.23, antiderivative size = 176, normalized size of antiderivative = 7.65,
number of steps used = 30, number of rules used = 8, integrand size = 159, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used
= {6688, 6742, 43, 45, 37, 2356, 2295, 2304} \begin {gather*} -\frac {39 x^8}{2 (1-x)^8}+\frac {15 x^7}{2 (1-x)^7}+\frac {105 x^7}{2 (1-x)^8}-\frac {7 x^6}{2 (1-x)^6}-\frac {21 x^6}{(1-x)^7}-\frac {147 x^6}{2 (1-x)^8}-2 x^3 \log (x)-4 x^2 \log (x)-\frac {156}{1-x}+\frac {336}{(1-x)^2}-\frac {448}{(1-x)^3}+\frac {525}{(1-x)^4}-\frac {588}{(1-x)^5}+\frac {476}{(1-x)^6}-\frac {217}{(1-x)^7}+\frac {83}{2 (1-x)^8}+2 x \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
Int[(-3 + 15*x - 106*x^2 + 294*x^3 - 516*x^4 + 588*x^5 - 420*x^6 + 156*x^7 + 6*x^8 - 34*x^9 + 14*x^10 - 2*x^11
+ (-2 + 26*x - 138*x^2 + 402*x^3 - 708*x^4 + 756*x^5 - 420*x^6 - 12*x^7 + 198*x^8 - 142*x^9 + 46*x^10 - 6*x^1
1)*Log[x])/(-1 + 9*x - 36*x^2 + 84*x^3 - 126*x^4 + 126*x^5 - 84*x^6 + 36*x^7 - 9*x^8 + x^9),x]
[Out]
83/(2*(1 - x)^8) - 217/(1 - x)^7 + 476/(1 - x)^6 - 588/(1 - x)^5 + 525/(1 - x)^4 - 448/(1 - x)^3 + 336/(1 - x)
^2 - 156/(1 - x) - (147*x^6)/(2*(1 - x)^8) - (21*x^6)/(1 - x)^7 - (7*x^6)/(2*(1 - x)^6) + (105*x^7)/(2*(1 - x)
^8) + (15*x^7)/(2*(1 - x)^7) - (39*x^8)/(2*(1 - x)^8) + 2*x*Log[x] - 4*x^2*Log[x] - 2*x^3*Log[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 45
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] - Dist[(d*Simplify[m + n + 2])/((b*c - a*d)*(m + 1)), Int[(a + b*x)^Simplify[m +
1]*(c + d*x)^n, x], x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[b*c - a*d, 0] && ILtQ[Simplify[m + n + 2], 0] &&
NeQ[m, -1] && !(LtQ[m, -1] && LtQ[n, -1] && (EqQ[a, 0] || (NeQ[c, 0] && LtQ[m - n, 0] && IntegerQ[n]))) && (
SumSimplerQ[m, 1] || !SumSimplerQ[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 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 2356
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*(Polyx_), x_Symbol] :> Int[ExpandIntegrand[Polyx*(a + b*Log[c*
x^n])^p, x], x] /; FreeQ[{a, b, c, n, p}, x] && PolynomialQ[Polyx, x]
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 {3-15 x+106 x^2-294 x^3+516 x^4-588 x^5+420 x^6-156 x^7-6 x^8+34 x^9-14 x^{10}+2 x^{11}+2 (-1+x)^9 \left (-1+4 x+3 x^2\right ) \log (x)}{(1-x)^9} \, dx\\ &=\int \left (-\frac {3}{(-1+x)^9}+\frac {15 x}{(-1+x)^9}-\frac {106 x^2}{(-1+x)^9}+\frac {294 x^3}{(-1+x)^9}-\frac {516 x^4}{(-1+x)^9}+\frac {588 x^5}{(-1+x)^9}-\frac {420 x^6}{(-1+x)^9}+\frac {156 x^7}{(-1+x)^9}+\frac {6 x^8}{(-1+x)^9}-\frac {34 x^9}{(-1+x)^9}+\frac {14 x^{10}}{(-1+x)^9}-\frac {2 x^{11}}{(-1+x)^9}-2 \left (-1+4 x+3 x^2\right ) \log (x)\right ) \, dx\\ &=\frac {3}{8 (1-x)^8}-2 \int \frac {x^{11}}{(-1+x)^9} \, dx-2 \int \left (-1+4 x+3 x^2\right ) \log (x) \, dx+6 \int \frac {x^8}{(-1+x)^9} \, dx+14 \int \frac {x^{10}}{(-1+x)^9} \, dx+15 \int \frac {x}{(-1+x)^9} \, dx-34 \int \frac {x^9}{(-1+x)^9} \, dx-106 \int \frac {x^2}{(-1+x)^9} \, dx+156 \int \frac {x^7}{(-1+x)^9} \, dx+294 \int \frac {x^3}{(-1+x)^9} \, dx-420 \int \frac {x^6}{(-1+x)^9} \, dx-516 \int \frac {x^4}{(-1+x)^9} \, dx+588 \int \frac {x^5}{(-1+x)^9} \, dx\\ &=\frac {3}{8 (1-x)^8}-\frac {147 x^6}{2 (1-x)^8}+\frac {105 x^7}{2 (1-x)^8}-\frac {39 x^8}{2 (1-x)^8}-2 \int \left (45+\frac {1}{(-1+x)^9}+\frac {11}{(-1+x)^8}+\frac {55}{(-1+x)^7}+\frac {165}{(-1+x)^6}+\frac {330}{(-1+x)^5}+\frac {462}{(-1+x)^4}+\frac {462}{(-1+x)^3}+\frac {330}{(-1+x)^2}+\frac {165}{-1+x}+9 x+x^2\right ) \, dx-2 \int \left (-\log (x)+4 x \log (x)+3 x^2 \log (x)\right ) \, dx+6 \int \left (\frac {1}{(-1+x)^9}+\frac {8}{(-1+x)^8}+\frac {28}{(-1+x)^7}+\frac {56}{(-1+x)^6}+\frac {70}{(-1+x)^5}+\frac {56}{(-1+x)^4}+\frac {28}{(-1+x)^3}+\frac {8}{(-1+x)^2}+\frac {1}{-1+x}\right ) \, dx+14 \int \left (9+\frac {1}{(-1+x)^9}+\frac {10}{(-1+x)^8}+\frac {45}{(-1+x)^7}+\frac {120}{(-1+x)^6}+\frac {210}{(-1+x)^5}+\frac {252}{(-1+x)^4}+\frac {210}{(-1+x)^3}+\frac {120}{(-1+x)^2}+\frac {45}{-1+x}+x\right ) \, dx+15 \int \left (\frac {1}{(-1+x)^9}+\frac {1}{(-1+x)^8}\right ) \, dx-34 \int \left (1+\frac {1}{(-1+x)^9}+\frac {9}{(-1+x)^8}+\frac {36}{(-1+x)^7}+\frac {84}{(-1+x)^6}+\frac {126}{(-1+x)^5}+\frac {126}{(-1+x)^4}+\frac {84}{(-1+x)^3}+\frac {36}{(-1+x)^2}+\frac {9}{-1+x}\right ) \, dx+\frac {105}{2} \int \frac {x^6}{(-1+x)^8} \, dx-106 \int \left (\frac {1}{(-1+x)^9}+\frac {2}{(-1+x)^8}+\frac {1}{(-1+x)^7}\right ) \, dx-147 \int \frac {x^5}{(-1+x)^8} \, dx+294 \int \left (\frac {1}{(-1+x)^9}+\frac {3}{(-1+x)^8}+\frac {3}{(-1+x)^7}+\frac {1}{(-1+x)^6}\right ) \, dx-516 \int \left (\frac {1}{(-1+x)^9}+\frac {4}{(-1+x)^8}+\frac {6}{(-1+x)^7}+\frac {4}{(-1+x)^6}+\frac {1}{(-1+x)^5}\right ) \, dx\\ &=\frac {83}{2 (1-x)^8}-\frac {217}{(1-x)^7}+\frac {476}{(1-x)^6}-\frac {588}{(1-x)^5}+\frac {525}{(1-x)^4}-\frac {448}{(1-x)^3}+\frac {336}{(1-x)^2}-\frac {156}{1-x}+2 x-2 x^2-\frac {2 x^3}{3}-\frac {147 x^6}{2 (1-x)^8}-\frac {21 x^6}{(1-x)^7}+\frac {105 x^7}{2 (1-x)^8}+\frac {15 x^7}{2 (1-x)^7}-\frac {39 x^8}{2 (1-x)^8}+2 \int \log (x) \, dx-6 \int x^2 \log (x) \, dx-8 \int x \log (x) \, dx+21 \int \frac {x^5}{(-1+x)^7} \, dx\\ &=\frac {83}{2 (1-x)^8}-\frac {217}{(1-x)^7}+\frac {476}{(1-x)^6}-\frac {588}{(1-x)^5}+\frac {525}{(1-x)^4}-\frac {448}{(1-x)^3}+\frac {336}{(1-x)^2}-\frac {156}{1-x}-\frac {147 x^6}{2 (1-x)^8}-\frac {21 x^6}{(1-x)^7}-\frac {7 x^6}{2 (1-x)^6}+\frac {105 x^7}{2 (1-x)^8}+\frac {15 x^7}{2 (1-x)^7}-\frac {39 x^8}{2 (1-x)^8}+2 x \log (x)-4 x^2 \log (x)-2 x^3 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 20, normalized size = 0.87 \begin {gather*} x \left (\frac {1}{(-1+x)^8}-2 \left (-1+2 x+x^2\right ) \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-3 + 15*x - 106*x^2 + 294*x^3 - 516*x^4 + 588*x^5 - 420*x^6 + 156*x^7 + 6*x^8 - 34*x^9 + 14*x^10 -
2*x^11 + (-2 + 26*x - 138*x^2 + 402*x^3 - 708*x^4 + 756*x^5 - 420*x^6 - 12*x^7 + 198*x^8 - 142*x^9 + 46*x^10 -
6*x^11)*Log[x])/(-1 + 9*x - 36*x^2 + 84*x^3 - 126*x^4 + 126*x^5 - 84*x^6 + 36*x^7 - 9*x^8 + x^9),x]
[Out]
x*((-1 + x)^(-8) - 2*(-1 + 2*x + x^2)*Log[x])
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fricas [B] time = 0.89, size = 102, normalized size = 4.43 \begin {gather*} -\frac {2 \, {\left (x^{11} - 6 \, x^{10} + 11 \, x^{9} + 8 \, x^{8} - 70 \, x^{7} + 140 \, x^{6} - 154 \, x^{5} + 104 \, x^{4} - 43 \, x^{3} + 10 \, x^{2} - x\right )} \log \relax (x) - x}{x^{8} - 8 \, x^{7} + 28 \, x^{6} - 56 \, x^{5} + 70 \, x^{4} - 56 \, x^{3} + 28 \, x^{2} - 8 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((-6*x^11+46*x^10-142*x^9+198*x^8-12*x^7-420*x^6+756*x^5-708*x^4+402*x^3-138*x^2+26*x-2)*log(x)-2*x^
11+14*x^10-34*x^9+6*x^8+156*x^7-420*x^6+588*x^5-516*x^4+294*x^3-106*x^2+15*x-3)/(x^9-9*x^8+36*x^7-84*x^6+126*x
^5-126*x^4+84*x^3-36*x^2+9*x-1),x, algorithm="fricas")
[Out]
-(2*(x^11 - 6*x^10 + 11*x^9 + 8*x^8 - 70*x^7 + 140*x^6 - 154*x^5 + 104*x^4 - 43*x^3 + 10*x^2 - x)*log(x) - x)/
(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1)
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giac [B] time = 0.17, size = 59, normalized size = 2.57 \begin {gather*} -2 \, {\left (x^{3} + 2 \, x^{2} - x\right )} \log \relax (x) + \frac {x}{x^{8} - 8 \, x^{7} + 28 \, x^{6} - 56 \, x^{5} + 70 \, x^{4} - 56 \, x^{3} + 28 \, x^{2} - 8 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((-6*x^11+46*x^10-142*x^9+198*x^8-12*x^7-420*x^6+756*x^5-708*x^4+402*x^3-138*x^2+26*x-2)*log(x)-2*x^
11+14*x^10-34*x^9+6*x^8+156*x^7-420*x^6+588*x^5-516*x^4+294*x^3-106*x^2+15*x-3)/(x^9-9*x^8+36*x^7-84*x^6+126*x
^5-126*x^4+84*x^3-36*x^2+9*x-1),x, algorithm="giac")
[Out]
-2*(x^3 + 2*x^2 - x)*log(x) + x/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1)
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maple [A] time = 0.08, size = 31, normalized size = 1.35
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| method |
result |
size |
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| default |
\(-2 x^{3} \ln \relax (x )-4 x^{2} \ln \relax (x )+2 x \ln \relax (x )+\frac {1}{\left (x -1\right )^{7}}+\frac {1}{\left (x -1\right )^{8}}\) |
\(31\) |
| risch |
\(\left (-2 x^{3}-4 x^{2}+2 x \right ) \ln \relax (x )+\frac {x}{x^{8}-8 x^{7}+28 x^{6}-56 x^{5}+70 x^{4}-56 x^{3}+28 x^{2}-8 x +1}\) |
\(61\) |
| norman |
\(\frac {x +2 x \ln \relax (x )-20 x^{2} \ln \relax (x )+86 x^{3} \ln \relax (x )-208 x^{4} \ln \relax (x )+308 x^{5} \ln \relax (x )-280 x^{6} \ln \relax (x )+140 x^{7} \ln \relax (x )-16 x^{8} \ln \relax (x )-22 x^{9} \ln \relax (x )+12 x^{10} \ln \relax (x )-2 x^{11} \ln \relax (x )}{\left (x -1\right )^{8}}\) |
\(84\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((-6*x^11+46*x^10-142*x^9+198*x^8-12*x^7-420*x^6+756*x^5-708*x^4+402*x^3-138*x^2+26*x-2)*ln(x)-2*x^11+14*x
^10-34*x^9+6*x^8+156*x^7-420*x^6+588*x^5-516*x^4+294*x^3-106*x^2+15*x-3)/(x^9-9*x^8+36*x^7-84*x^6+126*x^5-126*
x^4+84*x^3-36*x^2+9*x-1),x,method=_RETURNVERBOSE)
[Out]
-2*x^3*ln(x)-4*x^2*ln(x)+2*x*ln(x)+1/(x-1)^7+1/(x-1)^8
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maxima [B] time = 0.47, size = 1945, normalized size = 84.57 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((-6*x^11+46*x^10-142*x^9+198*x^8-12*x^7-420*x^6+756*x^5-708*x^4+402*x^3-138*x^2+26*x-2)*log(x)-2*x^
11+14*x^10-34*x^9+6*x^8+156*x^7-420*x^6+588*x^5-516*x^4+294*x^3-106*x^2+15*x-3)/(x^9-9*x^8+36*x^7-84*x^6+126*x
^5-126*x^4+84*x^3-36*x^2+9*x-1),x, algorithm="maxima")
[Out]
-2/3*x^3 - 2*x^2 + 2*x + 3/2*(8*x^7 - 28*x^6 + 56*x^5 - 70*x^4 + 56*x^3 - 28*x^2 + 8*x - 1)*log(x)/(x^8 - 8*x^
7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) + 15/2*(28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 -
8*x + 1)*log(x)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) - 9/2*(56*x^5 - 70*x^4 +
56*x^3 - 28*x^2 + 8*x - 1)*log(x)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) + 177/
70*(70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1)*log(x)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x
+ 1) - 201/140*(56*x^3 - 28*x^2 + 8*x - 1)*log(x)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 -
8*x + 1) + 23/28*(28*x^2 - 8*x + 1)*log(x)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x +
1) - 13/28*(8*x - 1)*log(x)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) + 2/105*(35*x
^11 - 175*x^10 + 35*x^9 + 1820*x^8 - 7840*x^7 + 15680*x^6 - 15680*x^5 + 4900*x^4 + 5488*x^3 - 6664*x^2 - 105*(
x^11 - 6*x^10 + 11*x^9)*log(x) + 2864*x - 463)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x
+ 1) + 1/84*(55440*x^7 - 349272*x^6 + 957264*x^5 - 1473780*x^4 + 1373064*x^3 - 772772*x^2 + 242968*x - 32891)
/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) + 17/140*(10080*x^7 - 58800*x^6 + 152880
*x^5 - 226380*x^4 + 204624*x^3 - 112392*x^2 + 34632*x - 4609)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3
+ 28*x^2 - 8*x + 1) - 1/140*(6720*x^7 - 35280*x^6 + 86240*x^5 - 122500*x^4 + 107408*x^3 - 57624*x^2 + 17424*x
- 2283)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) - 1/4*(6720*x^7 - 41160*x^6 + 11
0544*x^5 - 167580*x^4 + 154224*x^3 - 85932*x^2 + 26792*x - 3601)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*
x^3 + 28*x^2 - 8*x + 1) - 39/2*(8*x^7 - 28*x^6 + 56*x^5 - 70*x^4 + 56*x^3 - 28*x^2 + 8*x - 1)/(x^8 - 8*x^7 + 2
8*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) + 1/280*(2940*x^6 - 13230*x^5 + 26950*x^4 - 30625*x^3 + 2
0139*x^2 - 7203*x + 1089)/(x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1) + 1/1680*(420*x^6 - 2730
*x^5 + 7490*x^4 - 11165*x^3 + 9639*x^2 - 4683*x + 1089)/(x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x
- 1) + 1/8*(60*x^6 + 450*x^5 - 1450*x^4 + 1975*x^3 - 1437*x^2 + 549*x - 87)/(x^7 - 7*x^6 + 21*x^5 - 35*x^4 +
35*x^3 - 21*x^2 + 7*x - 1) + 23/1680*(60*x^6 - 390*x^5 + 1070*x^4 - 1595*x^3 + 1377*x^2 - 389*x + 47)/(x^7 - 7
*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1) + 13/1680*(60*x^6 - 390*x^5 + 1070*x^4 - 1595*x^3 + 1377*x
^2 - 669*x + 87)/(x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1) + 3/40*(60*x^6 - 390*x^5 - 50*x^4
+ 575*x^3 - 597*x^2 + 269*x - 47)/(x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1) + 15/2*(28*x^6
- 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x
+ 1) + 59/280*(12*x^6 - 78*x^5 + 214*x^4 - 109*x^3 + 15*x^2 + 9*x - 3)/(x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^
3 - 21*x^2 + 7*x - 1) + 67/560*(12*x^6 - 78*x^5 + 214*x^4 - 319*x^3 + 141*x^2 - 33*x + 3)/(x^7 - 7*x^6 + 21*x^
5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1) - 7/2*(56*x^5 - 70*x^4 + 56*x^3 - 28*x^2 + 8*x - 1)/(x^8 - 8*x^7 + 28*
x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) + 129/70*(70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1)/(x^8 - 8*x^7
+ 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) - 21/20*(56*x^3 - 28*x^2 + 8*x - 1)/(x^8 - 8*x^7 + 28*
x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) + 53/84*(28*x^2 - 8*x + 1)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 +
70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) - 15/56*(8*x - 1)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x
^2 - 8*x + 1) + 1/4*log(x)/(x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) + 3/8/(x^8 - 8
*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1) - 16*log(x)
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mupad [B] time = 7.03, size = 61, normalized size = 2.65 \begin {gather*} \frac {x}{x^8-8\,x^7+28\,x^6-56\,x^5+70\,x^4-56\,x^3+28\,x^2-8\,x+1}-\ln \relax (x)\,\left (2\,x^3+4\,x^2-2\,x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(log(x)*(138*x^2 - 26*x - 402*x^3 + 708*x^4 - 756*x^5 + 420*x^6 + 12*x^7 - 198*x^8 + 142*x^9 - 46*x^10 +
6*x^11 + 2) - 15*x + 106*x^2 - 294*x^3 + 516*x^4 - 588*x^5 + 420*x^6 - 156*x^7 - 6*x^8 + 34*x^9 - 14*x^10 + 2*
x^11 + 3)/(9*x - 36*x^2 + 84*x^3 - 126*x^4 + 126*x^5 - 84*x^6 + 36*x^7 - 9*x^8 + x^9 - 1),x)
[Out]
x/(28*x^2 - 8*x - 56*x^3 + 70*x^4 - 56*x^5 + 28*x^6 - 8*x^7 + x^8 + 1) - log(x)*(4*x^2 - 2*x + 2*x^3)
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sympy [B] time = 0.26, size = 56, normalized size = 2.43 \begin {gather*} \frac {x}{x^{8} - 8 x^{7} + 28 x^{6} - 56 x^{5} + 70 x^{4} - 56 x^{3} + 28 x^{2} - 8 x + 1} + \left (- 2 x^{3} - 4 x^{2} + 2 x\right ) \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((-6*x**11+46*x**10-142*x**9+198*x**8-12*x**7-420*x**6+756*x**5-708*x**4+402*x**3-138*x**2+26*x-2)*l
n(x)-2*x**11+14*x**10-34*x**9+6*x**8+156*x**7-420*x**6+588*x**5-516*x**4+294*x**3-106*x**2+15*x-3)/(x**9-9*x**
8+36*x**7-84*x**6+126*x**5-126*x**4+84*x**3-36*x**2+9*x-1),x)
[Out]
x/(x**8 - 8*x**7 + 28*x**6 - 56*x**5 + 70*x**4 - 56*x**3 + 28*x**2 - 8*x + 1) + (-2*x**3 - 4*x**2 + 2*x)*log(x
)
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