3.26.52 \(\int (1-2 x) (2+3 x)^m (3+5 x)^3 \, dx\)
Optimal. Leaf size=91 \[ -\frac {7 (3 x+2)^{m+1}}{243 (m+1)}+\frac {107 (3 x+2)^{m+2}}{243 (m+2)}-\frac {185 (3 x+2)^{m+3}}{81 (m+3)}+\frac {1025 (3 x+2)^{m+4}}{243 (m+4)}-\frac {250 (3 x+2)^{m+5}}{243 (m+5)} \]
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Rubi [A] time = 0.02, antiderivative size = 91, normalized size of antiderivative = 1.00,
number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used =
{77} \begin {gather*} -\frac {7 (3 x+2)^{m+1}}{243 (m+1)}+\frac {107 (3 x+2)^{m+2}}{243 (m+2)}-\frac {185 (3 x+2)^{m+3}}{81 (m+3)}+\frac {1025 (3 x+2)^{m+4}}{243 (m+4)}-\frac {250 (3 x+2)^{m+5}}{243 (m+5)} \end {gather*}
Antiderivative was successfully verified.
[In]
Int[(1 - 2*x)*(2 + 3*x)^m*(3 + 5*x)^3,x]
[Out]
(-7*(2 + 3*x)^(1 + m))/(243*(1 + m)) + (107*(2 + 3*x)^(2 + m))/(243*(2 + m)) - (185*(2 + 3*x)^(3 + m))/(81*(3
+ m)) + (1025*(2 + 3*x)^(4 + m))/(243*(4 + m)) - (250*(2 + 3*x)^(5 + m))/(243*(5 + m))
Rule 77
Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))
Rubi steps
\begin {align*} \int (1-2 x) (2+3 x)^m (3+5 x)^3 \, dx &=\int \left (-\frac {7}{81} (2+3 x)^m+\frac {107}{81} (2+3 x)^{1+m}-\frac {185}{27} (2+3 x)^{2+m}+\frac {1025}{81} (2+3 x)^{3+m}-\frac {250}{81} (2+3 x)^{4+m}\right ) \, dx\\ &=-\frac {7 (2+3 x)^{1+m}}{243 (1+m)}+\frac {107 (2+3 x)^{2+m}}{243 (2+m)}-\frac {185 (2+3 x)^{3+m}}{81 (3+m)}+\frac {1025 (2+3 x)^{4+m}}{243 (4+m)}-\frac {250 (2+3 x)^{5+m}}{243 (5+m)}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 75, normalized size = 0.82 \begin {gather*} \frac {1}{243} (3 x+2)^{m+1} \left (-\frac {250 (3 x+2)^4}{m+5}+\frac {1025 (3 x+2)^3}{m+4}-\frac {555 (3 x+2)^2}{m+3}+\frac {107 (3 x+2)}{m+2}-\frac {7}{m+1}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(1 - 2*x)*(2 + 3*x)^m*(3 + 5*x)^3,x]
[Out]
((2 + 3*x)^(1 + m)*(-7/(1 + m) + (107*(2 + 3*x))/(2 + m) - (555*(2 + 3*x)^2)/(3 + m) + (1025*(2 + 3*x)^3)/(4 +
m) - (250*(2 + 3*x)^4)/(5 + m)))/243
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IntegrateAlgebraic [F] time = 0.05, size = 0, normalized size = 0.00 \begin {gather*} \int (1-2 x) (2+3 x)^m (3+5 x)^3 \, dx \end {gather*}
Verification is not applicable to the result.
[In]
IntegrateAlgebraic[(1 - 2*x)*(2 + 3*x)^m*(3 + 5*x)^3,x]
[Out]
Defer[IntegrateAlgebraic][(1 - 2*x)*(2 + 3*x)^m*(3 + 5*x)^3, x]
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fricas [B] time = 1.25, size = 175, normalized size = 1.92 \begin {gather*} -\frac {{\left (20250 \, {\left (m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right )} x^{5} + 675 \, {\left (59 \, m^{4} + 549 \, m^{3} + 1819 \, m^{2} + 2499 \, m + 1170\right )} x^{4} - 1458 \, m^{4} + 45 \, {\left (471 \, m^{4} + 3292 \, m^{3} + 8199 \, m^{2} + 8618 \, m + 3240\right )} x^{3} - 17496 \, m^{3} - 9 \, {\left (459 \, m^{4} + 10677 \, m^{3} + 50581 \, m^{2} + 84103 \, m + 43740\right )} x^{2} - 66366 \, m^{2} - 3 \, {\left (2187 \, m^{4} + 28782 \, m^{3} + 114405 \, m^{2} + 175346 \, m + 87480\right )} x - 99240 \, m - 48800\right )} {\left (3 \, x + 2\right )}^{m}}{81 \, {\left (m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((1-2*x)*(2+3*x)^m*(3+5*x)^3,x, algorithm="fricas")
[Out]
-1/81*(20250*(m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*x^5 + 675*(59*m^4 + 549*m^3 + 1819*m^2 + 2499*m + 1170)*x^4 -
1458*m^4 + 45*(471*m^4 + 3292*m^3 + 8199*m^2 + 8618*m + 3240)*x^3 - 17496*m^3 - 9*(459*m^4 + 10677*m^3 + 5058
1*m^2 + 84103*m + 43740)*x^2 - 66366*m^2 - 3*(2187*m^4 + 28782*m^3 + 114405*m^2 + 175346*m + 87480)*x - 99240*
m - 48800)*(3*x + 2)^m/(m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)
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giac [B] time = 1.15, size = 423, normalized size = 4.65 \begin {gather*} -\frac {20250 \, m^{4} {\left (3 \, x + 2\right )}^{m} x^{5} + 39825 \, m^{4} {\left (3 \, x + 2\right )}^{m} x^{4} + 202500 \, m^{3} {\left (3 \, x + 2\right )}^{m} x^{5} + 21195 \, m^{4} {\left (3 \, x + 2\right )}^{m} x^{3} + 370575 \, m^{3} {\left (3 \, x + 2\right )}^{m} x^{4} + 708750 \, m^{2} {\left (3 \, x + 2\right )}^{m} x^{5} - 4131 \, m^{4} {\left (3 \, x + 2\right )}^{m} x^{2} + 148140 \, m^{3} {\left (3 \, x + 2\right )}^{m} x^{3} + 1227825 \, m^{2} {\left (3 \, x + 2\right )}^{m} x^{4} + 1012500 \, m {\left (3 \, x + 2\right )}^{m} x^{5} - 6561 \, m^{4} {\left (3 \, x + 2\right )}^{m} x - 96093 \, m^{3} {\left (3 \, x + 2\right )}^{m} x^{2} + 368955 \, m^{2} {\left (3 \, x + 2\right )}^{m} x^{3} + 1686825 \, m {\left (3 \, x + 2\right )}^{m} x^{4} + 486000 \, {\left (3 \, x + 2\right )}^{m} x^{5} - 1458 \, m^{4} {\left (3 \, x + 2\right )}^{m} - 86346 \, m^{3} {\left (3 \, x + 2\right )}^{m} x - 455229 \, m^{2} {\left (3 \, x + 2\right )}^{m} x^{2} + 387810 \, m {\left (3 \, x + 2\right )}^{m} x^{3} + 789750 \, {\left (3 \, x + 2\right )}^{m} x^{4} - 17496 \, m^{3} {\left (3 \, x + 2\right )}^{m} - 343215 \, m^{2} {\left (3 \, x + 2\right )}^{m} x - 756927 \, m {\left (3 \, x + 2\right )}^{m} x^{2} + 145800 \, {\left (3 \, x + 2\right )}^{m} x^{3} - 66366 \, m^{2} {\left (3 \, x + 2\right )}^{m} - 526038 \, m {\left (3 \, x + 2\right )}^{m} x - 393660 \, {\left (3 \, x + 2\right )}^{m} x^{2} - 99240 \, m {\left (3 \, x + 2\right )}^{m} - 262440 \, {\left (3 \, x + 2\right )}^{m} x - 48800 \, {\left (3 \, x + 2\right )}^{m}}{81 \, {\left (m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((1-2*x)*(2+3*x)^m*(3+5*x)^3,x, algorithm="giac")
[Out]
-1/81*(20250*m^4*(3*x + 2)^m*x^5 + 39825*m^4*(3*x + 2)^m*x^4 + 202500*m^3*(3*x + 2)^m*x^5 + 21195*m^4*(3*x + 2
)^m*x^3 + 370575*m^3*(3*x + 2)^m*x^4 + 708750*m^2*(3*x + 2)^m*x^5 - 4131*m^4*(3*x + 2)^m*x^2 + 148140*m^3*(3*x
+ 2)^m*x^3 + 1227825*m^2*(3*x + 2)^m*x^4 + 1012500*m*(3*x + 2)^m*x^5 - 6561*m^4*(3*x + 2)^m*x - 96093*m^3*(3*
x + 2)^m*x^2 + 368955*m^2*(3*x + 2)^m*x^3 + 1686825*m*(3*x + 2)^m*x^4 + 486000*(3*x + 2)^m*x^5 - 1458*m^4*(3*x
+ 2)^m - 86346*m^3*(3*x + 2)^m*x - 455229*m^2*(3*x + 2)^m*x^2 + 387810*m*(3*x + 2)^m*x^3 + 789750*(3*x + 2)^m
*x^4 - 17496*m^3*(3*x + 2)^m - 343215*m^2*(3*x + 2)^m*x - 756927*m*(3*x + 2)^m*x^2 + 145800*(3*x + 2)^m*x^3 -
66366*m^2*(3*x + 2)^m - 526038*m*(3*x + 2)^m*x - 393660*(3*x + 2)^m*x^2 - 99240*m*(3*x + 2)^m - 262440*(3*x +
2)^m*x - 48800*(3*x + 2)^m)/(m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)
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maple [B] time = 0.01, size = 187, normalized size = 2.05 \begin {gather*} -\frac {\left (6750 m^{4} x^{4}+8775 m^{4} x^{3}+67500 m^{3} x^{4}+1215 m^{4} x^{2}+78525 m^{3} x^{3}+236250 m^{2} x^{4}-2187 m^{4} x -2970 m^{3} x^{2}+251775 m^{2} x^{3}+337500 m \,x^{4}-729 m^{4}-30051 m^{3} x -44865 m^{2} x^{2}+337275 m \,x^{3}+162000 x^{4}-8748 m^{3}-121833 m^{2} x -95580 m \,x^{2}+155250 x^{3}-33183 m^{2}-188589 m x -54900 x^{2}-49620 m -94620 x -24400\right ) \left (3 x +2\right )^{m +1}}{81 \left (m^{5}+15 m^{4}+85 m^{3}+225 m^{2}+274 m +120\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((-2*x+1)*(3*x+2)^m*(5*x+3)^3,x)
[Out]
-1/81*(3*x+2)^(m+1)*(6750*m^4*x^4+8775*m^4*x^3+67500*m^3*x^4+1215*m^4*x^2+78525*m^3*x^3+236250*m^2*x^4-2187*m^
4*x-2970*m^3*x^2+251775*m^2*x^3+337500*m*x^4-729*m^4-30051*m^3*x-44865*m^2*x^2+337275*m*x^3+162000*x^4-8748*m^
3-121833*m^2*x-95580*m*x^2+155250*x^3-33183*m^2-188589*m*x-54900*x^2-49620*m-94620*x-24400)/(m^5+15*m^4+85*m^3
+225*m^2+274*m+120)
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maxima [B] time = 0.48, size = 295, normalized size = 3.24 \begin {gather*} -\frac {250 \, {\left (81 \, {\left (m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right )} x^{5} + 54 \, {\left (m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right )} x^{4} - 144 \, {\left (m^{3} + 3 \, m^{2} + 2 \, m\right )} x^{3} + 288 \, {\left (m^{2} + m\right )} x^{2} - 384 \, m x + 256\right )} {\left (3 \, x + 2\right )}^{m}}{81 \, {\left (m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120\right )}} - \frac {325 \, {\left (27 \, {\left (m^{3} + 6 \, m^{2} + 11 \, m + 6\right )} x^{4} + 18 \, {\left (m^{3} + 3 \, m^{2} + 2 \, m\right )} x^{3} - 36 \, {\left (m^{2} + m\right )} x^{2} + 48 \, m x - 32\right )} {\left (3 \, x + 2\right )}^{m}}{27 \, {\left (m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right )}} - \frac {5 \, {\left (27 \, {\left (m^{2} + 3 \, m + 2\right )} x^{3} + 18 \, {\left (m^{2} + m\right )} x^{2} - 24 \, m x + 16\right )} {\left (3 \, x + 2\right )}^{m}}{3 \, {\left (m^{3} + 6 \, m^{2} + 11 \, m + 6\right )}} + \frac {9 \, {\left (9 \, {\left (m + 1\right )} x^{2} + 6 \, m x - 4\right )} {\left (3 \, x + 2\right )}^{m}}{m^{2} + 3 \, m + 2} + \frac {9 \, {\left (3 \, x + 2\right )}^{m + 1}}{m + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((1-2*x)*(2+3*x)^m*(3+5*x)^3,x, algorithm="maxima")
[Out]
-250/81*(81*(m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*x^5 + 54*(m^4 + 6*m^3 + 11*m^2 + 6*m)*x^4 - 144*(m^3 + 3*m^2 +
2*m)*x^3 + 288*(m^2 + m)*x^2 - 384*m*x + 256)*(3*x + 2)^m/(m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120) - 3
25/27*(27*(m^3 + 6*m^2 + 11*m + 6)*x^4 + 18*(m^3 + 3*m^2 + 2*m)*x^3 - 36*(m^2 + m)*x^2 + 48*m*x - 32)*(3*x + 2
)^m/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24) - 5/3*(27*(m^2 + 3*m + 2)*x^3 + 18*(m^2 + m)*x^2 - 24*m*x + 16)*(3*x +
2)^m/(m^3 + 6*m^2 + 11*m + 6) + 9*(9*(m + 1)*x^2 + 6*m*x - 4)*(3*x + 2)^m/(m^2 + 3*m + 2) + 9*(3*x + 2)^(m +
1)/(m + 1)
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mupad [B] time = 0.26, size = 313, normalized size = 3.44 \begin {gather*} {\left (3\,x+2\right )}^m\,\left (\frac {1458\,m^4+17496\,m^3+66366\,m^2+99240\,m+48800}{81\,m^5+1215\,m^4+6885\,m^3+18225\,m^2+22194\,m+9720}-\frac {x^3\,\left (21195\,m^4+148140\,m^3+368955\,m^2+387810\,m+145800\right )}{81\,m^5+1215\,m^4+6885\,m^3+18225\,m^2+22194\,m+9720}+\frac {x^2\,\left (4131\,m^4+96093\,m^3+455229\,m^2+756927\,m+393660\right )}{81\,m^5+1215\,m^4+6885\,m^3+18225\,m^2+22194\,m+9720}-\frac {x^5\,\left (20250\,m^4+202500\,m^3+708750\,m^2+1012500\,m+486000\right )}{81\,m^5+1215\,m^4+6885\,m^3+18225\,m^2+22194\,m+9720}-\frac {x^4\,\left (39825\,m^4+370575\,m^3+1227825\,m^2+1686825\,m+789750\right )}{81\,m^5+1215\,m^4+6885\,m^3+18225\,m^2+22194\,m+9720}+\frac {x\,\left (6561\,m^4+86346\,m^3+343215\,m^2+526038\,m+262440\right )}{81\,m^5+1215\,m^4+6885\,m^3+18225\,m^2+22194\,m+9720}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(2*x - 1)*(3*x + 2)^m*(5*x + 3)^3,x)
[Out]
(3*x + 2)^m*((99240*m + 66366*m^2 + 17496*m^3 + 1458*m^4 + 48800)/(22194*m + 18225*m^2 + 6885*m^3 + 1215*m^4 +
81*m^5 + 9720) - (x^3*(387810*m + 368955*m^2 + 148140*m^3 + 21195*m^4 + 145800))/(22194*m + 18225*m^2 + 6885*
m^3 + 1215*m^4 + 81*m^5 + 9720) + (x^2*(756927*m + 455229*m^2 + 96093*m^3 + 4131*m^4 + 393660))/(22194*m + 182
25*m^2 + 6885*m^3 + 1215*m^4 + 81*m^5 + 9720) - (x^5*(1012500*m + 708750*m^2 + 202500*m^3 + 20250*m^4 + 486000
))/(22194*m + 18225*m^2 + 6885*m^3 + 1215*m^4 + 81*m^5 + 9720) - (x^4*(1686825*m + 1227825*m^2 + 370575*m^3 +
39825*m^4 + 789750))/(22194*m + 18225*m^2 + 6885*m^3 + 1215*m^4 + 81*m^5 + 9720) + (x*(526038*m + 343215*m^2 +
86346*m^3 + 6561*m^4 + 262440))/(22194*m + 18225*m^2 + 6885*m^3 + 1215*m^4 + 81*m^5 + 9720))
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sympy [A] time = 2.81, size = 1822, normalized size = 20.02
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((1-2*x)*(2+3*x)**m*(3+5*x)**3,x)
[Out]
Piecewise((-243000*x**4*log(x + 2/3)/(236196*x**4 + 629856*x**3 + 629856*x**2 + 279936*x + 46656) - 648000*x**
3*log(x + 2/3)/(236196*x**4 + 629856*x**3 + 629856*x**2 + 279936*x + 46656) - 332100*x**3/(236196*x**4 + 62985
6*x**3 + 629856*x**2 + 279936*x + 46656) - 648000*x**2*log(x + 2/3)/(236196*x**4 + 629856*x**3 + 629856*x**2 +
279936*x + 46656) - 634230*x**2/(236196*x**4 + 629856*x**3 + 629856*x**2 + 279936*x + 46656) - 288000*x*log(x
+ 2/3)/(236196*x**4 + 629856*x**3 + 629856*x**2 + 279936*x + 46656) - 404124*x/(236196*x**4 + 629856*x**3 + 6
29856*x**2 + 279936*x + 46656) - 48000*log(x + 2/3)/(236196*x**4 + 629856*x**3 + 629856*x**2 + 279936*x + 4665
6) - 85915/(236196*x**4 + 629856*x**3 + 629856*x**2 + 279936*x + 46656), Eq(m, -5)), (-121500*x**4/(39366*x**3
+ 78732*x**2 + 52488*x + 11664) + 166050*x**3*log(x + 2/3)/(39366*x**3 + 78732*x**2 + 52488*x + 11664) + 3321
00*x**2*log(x + 2/3)/(39366*x**3 + 78732*x**2 + 52488*x + 11664) + 353970*x**2/(39366*x**3 + 78732*x**2 + 5248
8*x + 11664) + 221400*x*log(x + 2/3)/(39366*x**3 + 78732*x**2 + 52488*x + 11664) + 326997*x/(39366*x**3 + 7873
2*x**2 + 52488*x + 11664) + 49200*log(x + 2/3)/(39366*x**3 + 78732*x**2 + 52488*x + 11664) + 84692/(39366*x**3
+ 78732*x**2 + 52488*x + 11664), Eq(m, -4)), (-6750*x**4/(1458*x**2 + 1944*x + 648) + 450*x**3/(1458*x**2 + 1
944*x + 648) - 3330*x**2*log(x + 2/3)/(1458*x**2 + 1944*x + 648) - 4440*x*log(x + 2/3)/(1458*x**2 + 1944*x + 6
48) - 8814*x/(1458*x**2 + 1944*x + 648) - 1480*log(x + 2/3)/(1458*x**2 + 1944*x + 648) - 4407/(1458*x**2 + 194
4*x + 648), Eq(m, -3)), (-13500*x**4/(1458*x + 972) - 8325*x**3/(1458*x + 972) + 9360*x**2/(1458*x + 972) + 64
2*x*log(x + 2/3)/(1458*x + 972) + 428*log(x + 2/3)/(1458*x + 972) - 3946/(1458*x + 972), Eq(m, -2)), (-125*x**
4/6 - 475*x**3/27 + 545*x**2/54 + 1097*x/81 - 7*log(x + 2/3)/243, Eq(m, -1)), (-20250*m**4*x**5*(3*x + 2)**m/(
81*m**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) - 39825*m**4*x**4*(3*x + 2)**m/(81*m**5 + 1215*
m**4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) - 21195*m**4*x**3*(3*x + 2)**m/(81*m**5 + 1215*m**4 + 6885*m**
3 + 18225*m**2 + 22194*m + 9720) + 4131*m**4*x**2*(3*x + 2)**m/(81*m**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 +
22194*m + 9720) + 6561*m**4*x*(3*x + 2)**m/(81*m**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) +
1458*m**4*(3*x + 2)**m/(81*m**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) - 202500*m**3*x**5*(3*x
+ 2)**m/(81*m**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) - 370575*m**3*x**4*(3*x + 2)**m/(81*m
**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) - 148140*m**3*x**3*(3*x + 2)**m/(81*m**5 + 1215*m**
4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) + 96093*m**3*x**2*(3*x + 2)**m/(81*m**5 + 1215*m**4 + 6885*m**3 +
18225*m**2 + 22194*m + 9720) + 86346*m**3*x*(3*x + 2)**m/(81*m**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 + 2219
4*m + 9720) + 17496*m**3*(3*x + 2)**m/(81*m**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) - 708750
*m**2*x**5*(3*x + 2)**m/(81*m**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) - 1227825*m**2*x**4*(3
*x + 2)**m/(81*m**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) - 368955*m**2*x**3*(3*x + 2)**m/(81
*m**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) + 455229*m**2*x**2*(3*x + 2)**m/(81*m**5 + 1215*m
**4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) + 343215*m**2*x*(3*x + 2)**m/(81*m**5 + 1215*m**4 + 6885*m**3 +
18225*m**2 + 22194*m + 9720) + 66366*m**2*(3*x + 2)**m/(81*m**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 + 22194*
m + 9720) - 1012500*m*x**5*(3*x + 2)**m/(81*m**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) - 1686
825*m*x**4*(3*x + 2)**m/(81*m**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) - 387810*m*x**3*(3*x +
2)**m/(81*m**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) + 756927*m*x**2*(3*x + 2)**m/(81*m**5 +
1215*m**4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) + 526038*m*x*(3*x + 2)**m/(81*m**5 + 1215*m**4 + 6885*m*
*3 + 18225*m**2 + 22194*m + 9720) + 99240*m*(3*x + 2)**m/(81*m**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 + 22194
*m + 9720) - 486000*x**5*(3*x + 2)**m/(81*m**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) - 789750
*x**4*(3*x + 2)**m/(81*m**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) - 145800*x**3*(3*x + 2)**m/
(81*m**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) + 393660*x**2*(3*x + 2)**m/(81*m**5 + 1215*m**
4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720) + 262440*x*(3*x + 2)**m/(81*m**5 + 1215*m**4 + 6885*m**3 + 18225*
m**2 + 22194*m + 9720) + 48800*(3*x + 2)**m/(81*m**5 + 1215*m**4 + 6885*m**3 + 18225*m**2 + 22194*m + 9720), T
rue))
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