3.1.57 \(\int (e x)^m (2-2 a x)^2 (1+a x)^3 \, dx\)

Optimal. Leaf size=116 \[ \frac {4 a^5 (e x)^{m+6}}{e^6 (m+6)}+\frac {4 a^4 (e x)^{m+5}}{e^5 (m+5)}-\frac {8 a^3 (e x)^{m+4}}{e^4 (m+4)}-\frac {8 a^2 (e x)^{m+3}}{e^3 (m+3)}+\frac {4 a (e x)^{m+2}}{e^2 (m+2)}+\frac {4 (e x)^{m+1}}{e (m+1)} \]

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Rubi [A]  time = 0.04, antiderivative size = 116, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {88} \begin {gather*} -\frac {8 a^2 (e x)^{m+3}}{e^3 (m+3)}-\frac {8 a^3 (e x)^{m+4}}{e^4 (m+4)}+\frac {4 a^4 (e x)^{m+5}}{e^5 (m+5)}+\frac {4 a^5 (e x)^{m+6}}{e^6 (m+6)}+\frac {4 a (e x)^{m+2}}{e^2 (m+2)}+\frac {4 (e x)^{m+1}}{e (m+1)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(e*x)^m*(2 - 2*a*x)^2*(1 + a*x)^3,x]

[Out]

(4*(e*x)^(1 + m))/(e*(1 + m)) + (4*a*(e*x)^(2 + m))/(e^2*(2 + m)) - (8*a^2*(e*x)^(3 + m))/(e^3*(3 + m)) - (8*a
^3*(e*x)^(4 + m))/(e^4*(4 + m)) + (4*a^4*(e*x)^(5 + m))/(e^5*(5 + m)) + (4*a^5*(e*x)^(6 + m))/(e^6*(6 + m))

Rule 88

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandI
ntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] &&
(IntegerQ[p] || (GtQ[m, 0] && GeQ[n, -1]))

Rubi steps

\begin {align*} \int (e x)^m (2-2 a x)^2 (1+a x)^3 \, dx &=\int \left (4 (e x)^m+\frac {4 a (e x)^{1+m}}{e}-\frac {8 a^2 (e x)^{2+m}}{e^2}-\frac {8 a^3 (e x)^{3+m}}{e^3}+\frac {4 a^4 (e x)^{4+m}}{e^4}+\frac {4 a^5 (e x)^{5+m}}{e^5}\right ) \, dx\\ &=\frac {4 (e x)^{1+m}}{e (1+m)}+\frac {4 a (e x)^{2+m}}{e^2 (2+m)}-\frac {8 a^2 (e x)^{3+m}}{e^3 (3+m)}-\frac {8 a^3 (e x)^{4+m}}{e^4 (4+m)}+\frac {4 a^4 (e x)^{5+m}}{e^5 (5+m)}+\frac {4 a^5 (e x)^{6+m}}{e^6 (6+m)}\\ \end {align*}

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Mathematica [A]  time = 0.05, size = 72, normalized size = 0.62 \begin {gather*} 4 x \left (\frac {a^5 x^5}{m+6}+\frac {a^4 x^4}{m+5}-\frac {2 a^3 x^3}{m+4}-\frac {2 a^2 x^2}{m+3}+\frac {a x}{m+2}+\frac {1}{m+1}\right ) (e x)^m \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(e*x)^m*(2 - 2*a*x)^2*(1 + a*x)^3,x]

[Out]

4*x*(e*x)^m*((1 + m)^(-1) + (a*x)/(2 + m) - (2*a^2*x^2)/(3 + m) - (2*a^3*x^3)/(4 + m) + (a^4*x^4)/(5 + m) + (a
^5*x^5)/(6 + m))

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IntegrateAlgebraic [F]  time = 0.11, size = 0, normalized size = 0.00 \begin {gather*} \int (e x)^m (2-2 a x)^2 (1+a x)^3 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[(e*x)^m*(2 - 2*a*x)^2*(1 + a*x)^3,x]

[Out]

Defer[IntegrateAlgebraic][(e*x)^m*(2 - 2*a*x)^2*(1 + a*x)^3, x]

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fricas [B]  time = 2.00, size = 288, normalized size = 2.48 \begin {gather*} \frac {4 \, {\left ({\left (a^{5} m^{5} + 15 \, a^{5} m^{4} + 85 \, a^{5} m^{3} + 225 \, a^{5} m^{2} + 274 \, a^{5} m + 120 \, a^{5}\right )} x^{6} + {\left (a^{4} m^{5} + 16 \, a^{4} m^{4} + 95 \, a^{4} m^{3} + 260 \, a^{4} m^{2} + 324 \, a^{4} m + 144 \, a^{4}\right )} x^{5} - 2 \, {\left (a^{3} m^{5} + 17 \, a^{3} m^{4} + 107 \, a^{3} m^{3} + 307 \, a^{3} m^{2} + 396 \, a^{3} m + 180 \, a^{3}\right )} x^{4} - 2 \, {\left (a^{2} m^{5} + 18 \, a^{2} m^{4} + 121 \, a^{2} m^{3} + 372 \, a^{2} m^{2} + 508 \, a^{2} m + 240 \, a^{2}\right )} x^{3} + {\left (a m^{5} + 19 \, a m^{4} + 137 \, a m^{3} + 461 \, a m^{2} + 702 \, a m + 360 \, a\right )} x^{2} + {\left (m^{5} + 20 \, m^{4} + 155 \, m^{3} + 580 \, m^{2} + 1044 \, m + 720\right )} x\right )} \left (e x\right )^{m}}{m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x)^m*(-2*a*x+2)^2*(a*x+1)^3,x, algorithm="fricas")

[Out]

4*((a^5*m^5 + 15*a^5*m^4 + 85*a^5*m^3 + 225*a^5*m^2 + 274*a^5*m + 120*a^5)*x^6 + (a^4*m^5 + 16*a^4*m^4 + 95*a^
4*m^3 + 260*a^4*m^2 + 324*a^4*m + 144*a^4)*x^5 - 2*(a^3*m^5 + 17*a^3*m^4 + 107*a^3*m^3 + 307*a^3*m^2 + 396*a^3
*m + 180*a^3)*x^4 - 2*(a^2*m^5 + 18*a^2*m^4 + 121*a^2*m^3 + 372*a^2*m^2 + 508*a^2*m + 240*a^2)*x^3 + (a*m^5 +
19*a*m^4 + 137*a*m^3 + 461*a*m^2 + 702*a*m + 360*a)*x^2 + (m^5 + 20*m^4 + 155*m^3 + 580*m^2 + 1044*m + 720)*x)
*(e*x)^m/(m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)

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giac [B]  time = 1.25, size = 533, normalized size = 4.59 \begin {gather*} \frac {4 \, {\left (a^{5} m^{5} x^{6} x^{m} e^{m} + 15 \, a^{5} m^{4} x^{6} x^{m} e^{m} + a^{4} m^{5} x^{5} x^{m} e^{m} + 85 \, a^{5} m^{3} x^{6} x^{m} e^{m} + 16 \, a^{4} m^{4} x^{5} x^{m} e^{m} + 225 \, a^{5} m^{2} x^{6} x^{m} e^{m} - 2 \, a^{3} m^{5} x^{4} x^{m} e^{m} + 95 \, a^{4} m^{3} x^{5} x^{m} e^{m} + 274 \, a^{5} m x^{6} x^{m} e^{m} - 34 \, a^{3} m^{4} x^{4} x^{m} e^{m} + 260 \, a^{4} m^{2} x^{5} x^{m} e^{m} + 120 \, a^{5} x^{6} x^{m} e^{m} - 2 \, a^{2} m^{5} x^{3} x^{m} e^{m} - 214 \, a^{3} m^{3} x^{4} x^{m} e^{m} + 324 \, a^{4} m x^{5} x^{m} e^{m} - 36 \, a^{2} m^{4} x^{3} x^{m} e^{m} - 614 \, a^{3} m^{2} x^{4} x^{m} e^{m} + 144 \, a^{4} x^{5} x^{m} e^{m} + a m^{5} x^{2} x^{m} e^{m} - 242 \, a^{2} m^{3} x^{3} x^{m} e^{m} - 792 \, a^{3} m x^{4} x^{m} e^{m} + 19 \, a m^{4} x^{2} x^{m} e^{m} - 744 \, a^{2} m^{2} x^{3} x^{m} e^{m} - 360 \, a^{3} x^{4} x^{m} e^{m} + m^{5} x x^{m} e^{m} + 137 \, a m^{3} x^{2} x^{m} e^{m} - 1016 \, a^{2} m x^{3} x^{m} e^{m} + 20 \, m^{4} x x^{m} e^{m} + 461 \, a m^{2} x^{2} x^{m} e^{m} - 480 \, a^{2} x^{3} x^{m} e^{m} + 155 \, m^{3} x x^{m} e^{m} + 702 \, a m x^{2} x^{m} e^{m} + 580 \, m^{2} x x^{m} e^{m} + 360 \, a x^{2} x^{m} e^{m} + 1044 \, m x x^{m} e^{m} + 720 \, x x^{m} e^{m}\right )}}{m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x)^m*(-2*a*x+2)^2*(a*x+1)^3,x, algorithm="giac")

[Out]

4*(a^5*m^5*x^6*x^m*e^m + 15*a^5*m^4*x^6*x^m*e^m + a^4*m^5*x^5*x^m*e^m + 85*a^5*m^3*x^6*x^m*e^m + 16*a^4*m^4*x^
5*x^m*e^m + 225*a^5*m^2*x^6*x^m*e^m - 2*a^3*m^5*x^4*x^m*e^m + 95*a^4*m^3*x^5*x^m*e^m + 274*a^5*m*x^6*x^m*e^m -
34*a^3*m^4*x^4*x^m*e^m + 260*a^4*m^2*x^5*x^m*e^m + 120*a^5*x^6*x^m*e^m - 2*a^2*m^5*x^3*x^m*e^m - 214*a^3*m^3*
x^4*x^m*e^m + 324*a^4*m*x^5*x^m*e^m - 36*a^2*m^4*x^3*x^m*e^m - 614*a^3*m^2*x^4*x^m*e^m + 144*a^4*x^5*x^m*e^m +
a*m^5*x^2*x^m*e^m - 242*a^2*m^3*x^3*x^m*e^m - 792*a^3*m*x^4*x^m*e^m + 19*a*m^4*x^2*x^m*e^m - 744*a^2*m^2*x^3*
x^m*e^m - 360*a^3*x^4*x^m*e^m + m^5*x*x^m*e^m + 137*a*m^3*x^2*x^m*e^m - 1016*a^2*m*x^3*x^m*e^m + 20*m^4*x*x^m*
e^m + 461*a*m^2*x^2*x^m*e^m - 480*a^2*x^3*x^m*e^m + 155*m^3*x*x^m*e^m + 702*a*m*x^2*x^m*e^m + 580*m^2*x*x^m*e^
m + 360*a*x^2*x^m*e^m + 1044*m*x*x^m*e^m + 720*x*x^m*e^m)/(m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*
m + 720)

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maple [B]  time = 0.01, size = 340, normalized size = 2.93 \begin {gather*} \frac {4 \left (a^{5} m^{5} x^{5}+15 a^{5} m^{4} x^{5}+85 a^{5} m^{3} x^{5}+a^{4} m^{5} x^{4}+225 a^{5} m^{2} x^{5}+16 a^{4} m^{4} x^{4}+274 a^{5} m \,x^{5}+95 a^{4} m^{3} x^{4}-2 a^{3} m^{5} x^{3}+120 a^{5} x^{5}+260 a^{4} m^{2} x^{4}-34 a^{3} m^{4} x^{3}+324 a^{4} m \,x^{4}-214 a^{3} m^{3} x^{3}-2 a^{2} m^{5} x^{2}+144 a^{4} x^{4}-614 a^{3} m^{2} x^{3}-36 a^{2} m^{4} x^{2}-792 a^{3} m \,x^{3}-242 a^{2} m^{3} x^{2}+a \,m^{5} x -360 a^{3} x^{3}-744 a^{2} m^{2} x^{2}+19 a \,m^{4} x -1016 a^{2} m \,x^{2}+137 a \,m^{3} x +m^{5}-480 a^{2} x^{2}+461 a \,m^{2} x +20 m^{4}+702 a m x +155 m^{3}+360 a x +580 m^{2}+1044 m +720\right ) x \left (e x \right )^{m}}{\left (m +6\right ) \left (m +5\right ) \left (m +4\right ) \left (m +3\right ) \left (m +2\right ) \left (m +1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((e*x)^m*(-2*a*x+2)^2*(a*x+1)^3,x)

[Out]

4*(e*x)^m*(a^5*m^5*x^5+15*a^5*m^4*x^5+85*a^5*m^3*x^5+a^4*m^5*x^4+225*a^5*m^2*x^5+16*a^4*m^4*x^4+274*a^5*m*x^5+
95*a^4*m^3*x^4-2*a^3*m^5*x^3+120*a^5*x^5+260*a^4*m^2*x^4-34*a^3*m^4*x^3+324*a^4*m*x^4-214*a^3*m^3*x^3-2*a^2*m^
5*x^2+144*a^4*x^4-614*a^3*m^2*x^3-36*a^2*m^4*x^2-792*a^3*m*x^3-242*a^2*m^3*x^2+a*m^5*x-360*a^3*x^3-744*a^2*m^2
*x^2+19*a*m^4*x-1016*a^2*m*x^2+137*a*m^3*x+m^5-480*a^2*x^2+461*a*m^2*x+20*m^4+702*a*m*x+155*m^3+360*a*x+580*m^
2+1044*m+720)*x/(m+6)/(m+5)/(m+4)/(m+3)/(m+2)/(m+1)

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maxima [A]  time = 1.15, size = 111, normalized size = 0.96 \begin {gather*} \frac {4 \, a^{5} e^{m} x^{6} x^{m}}{m + 6} + \frac {4 \, a^{4} e^{m} x^{5} x^{m}}{m + 5} - \frac {8 \, a^{3} e^{m} x^{4} x^{m}}{m + 4} - \frac {8 \, a^{2} e^{m} x^{3} x^{m}}{m + 3} + \frac {4 \, a e^{m} x^{2} x^{m}}{m + 2} + \frac {4 \, \left (e x\right )^{m + 1}}{e {\left (m + 1\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x)^m*(-2*a*x+2)^2*(a*x+1)^3,x, algorithm="maxima")

[Out]

4*a^5*e^m*x^6*x^m/(m + 6) + 4*a^4*e^m*x^5*x^m/(m + 5) - 8*a^3*e^m*x^4*x^m/(m + 4) - 8*a^2*e^m*x^3*x^m/(m + 3)
+ 4*a*e^m*x^2*x^m/(m + 2) + 4*(e*x)^(m + 1)/(e*(m + 1))

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mupad [B]  time = 0.57, size = 367, normalized size = 3.16 \begin {gather*} {\left (e\,x\right )}^m\,\left (\frac {x\,\left (4\,m^5+80\,m^4+620\,m^3+2320\,m^2+4176\,m+2880\right )}{m^6+21\,m^5+175\,m^4+735\,m^3+1624\,m^2+1764\,m+720}+\frac {4\,a\,x^2\,\left (m^5+19\,m^4+137\,m^3+461\,m^2+702\,m+360\right )}{m^6+21\,m^5+175\,m^4+735\,m^3+1624\,m^2+1764\,m+720}+\frac {4\,a^5\,x^6\,\left (m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right )}{m^6+21\,m^5+175\,m^4+735\,m^3+1624\,m^2+1764\,m+720}+\frac {4\,a^4\,x^5\,\left (m^5+16\,m^4+95\,m^3+260\,m^2+324\,m+144\right )}{m^6+21\,m^5+175\,m^4+735\,m^3+1624\,m^2+1764\,m+720}-\frac {8\,a^3\,x^4\,\left (m^5+17\,m^4+107\,m^3+307\,m^2+396\,m+180\right )}{m^6+21\,m^5+175\,m^4+735\,m^3+1624\,m^2+1764\,m+720}-\frac {8\,a^2\,x^3\,\left (m^5+18\,m^4+121\,m^3+372\,m^2+508\,m+240\right )}{m^6+21\,m^5+175\,m^4+735\,m^3+1624\,m^2+1764\,m+720}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((e*x)^m*(a*x + 1)^3*(2*a*x - 2)^2,x)

[Out]

(e*x)^m*((x*(4176*m + 2320*m^2 + 620*m^3 + 80*m^4 + 4*m^5 + 2880))/(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21
*m^5 + m^6 + 720) + (4*a*x^2*(702*m + 461*m^2 + 137*m^3 + 19*m^4 + m^5 + 360))/(1764*m + 1624*m^2 + 735*m^3 +
175*m^4 + 21*m^5 + m^6 + 720) + (4*a^5*x^6*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120))/(1764*m + 1624*m^2
+ 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720) + (4*a^4*x^5*(324*m + 260*m^2 + 95*m^3 + 16*m^4 + m^5 + 144))/(1764
*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720) - (8*a^3*x^4*(396*m + 307*m^2 + 107*m^3 + 17*m^4 + m^5
+ 180))/(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720) - (8*a^2*x^3*(508*m + 372*m^2 + 121*m^3
+ 18*m^4 + m^5 + 240))/(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720))

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sympy [A]  time = 2.48, size = 1928, normalized size = 16.62

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x)**m*(-2*a*x+2)**2*(a*x+1)**3,x)

[Out]

Piecewise(((4*a**5*log(x) - 4*a**4/x + 4*a**3/x**2 + 8*a**2/(3*x**3) - a/x**4 - 4/(5*x**5))/e**6, Eq(m, -6)),
((4*a**5*x + 4*a**4*log(x) + 8*a**3/x + 4*a**2/x**2 - 4*a/(3*x**3) - 1/x**4)/e**5, Eq(m, -5)), ((2*a**5*x**2 +
4*a**4*x - 8*a**3*log(x) + 8*a**2/x - 2*a/x**2 - 4/(3*x**3))/e**4, Eq(m, -4)), ((4*a**5*x**3/3 + 2*a**4*x**2
- 8*a**3*x - 8*a**2*log(x) - 4*a/x - 2/x**2)/e**3, Eq(m, -3)), ((a**5*x**4 + 4*a**4*x**3/3 - 4*a**3*x**2 - 8*a
**2*x + 4*a*log(x) - 4/x)/e**2, Eq(m, -2)), ((4*a**5*x**5/5 + a**4*x**4 - 8*a**3*x**3/3 - 4*a**2*x**2 + 4*a*x
+ 4*log(x))/e, Eq(m, -1)), (4*a**5*e**m*m**5*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 176
4*m + 720) + 60*a**5*e**m*m**4*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 3
40*a**5*e**m*m**3*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 900*a**5*e**m*
m**2*x**6*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1096*a**5*e**m*m*x**6*x**m/
(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 480*a**5*e**m*x**6*x**m/(m**6 + 21*m**5 +
175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 4*a**4*e**m*m**5*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*
m**3 + 1624*m**2 + 1764*m + 720) + 64*a**4*e**m*m**4*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m*
*2 + 1764*m + 720) + 380*a**4*e**m*m**3*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m +
720) + 1040*a**4*e**m*m**2*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1296
*a**4*e**m*m*x**5*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 576*a**4*e**m*x**5*
x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) - 8*a**3*e**m*m**5*x**4*x**m/(m**6 + 21
*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) - 136*a**3*e**m*m**4*x**4*x**m/(m**6 + 21*m**5 + 175*m
**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) - 856*a**3*e**m*m**3*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**
3 + 1624*m**2 + 1764*m + 720) - 2456*a**3*e**m*m**2*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**
2 + 1764*m + 720) - 3168*a**3*e**m*m*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 72
0) - 1440*a**3*e**m*x**4*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) - 8*a**2*e**m*
m**5*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) - 144*a**2*e**m*m**4*x**3*x**
m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) - 968*a**2*e**m*m**3*x**3*x**m/(m**6 + 21*
m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) - 2976*a**2*e**m*m**2*x**3*x**m/(m**6 + 21*m**5 + 175*m
**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) - 4064*a**2*e**m*m*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3
+ 1624*m**2 + 1764*m + 720) - 1920*a**2*e**m*x**3*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 176
4*m + 720) + 4*a*e**m*m**5*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 76*a*
e**m*m**4*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 548*a*e**m*m**3*x**2*x
**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 1844*a*e**m*m**2*x**2*x**m/(m**6 + 21*
m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 2808*a*e**m*m*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 +
735*m**3 + 1624*m**2 + 1764*m + 720) + 1440*a*e**m*x**2*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2
+ 1764*m + 720) + 4*e**m*m**5*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 80*e
**m*m**4*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 620*e**m*m**3*x*x**m/(m**6
+ 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 2320*e**m*m**2*x*x**m/(m**6 + 21*m**5 + 175*m**
4 + 735*m**3 + 1624*m**2 + 1764*m + 720) + 4176*e**m*m*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**
2 + 1764*m + 720) + 2880*e**m*x*x**m/(m**6 + 21*m**5 + 175*m**4 + 735*m**3 + 1624*m**2 + 1764*m + 720), True))

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