Integrand size = 140, antiderivative size = 28 \[ \int \frac {-9 x^4-2 x^5+e^{15} \left (288 x-152 x^2-48 x^3\right )+e^{20} \left (-148+184 x-33 x^2-18 x^3\right )+e^{10} \left (-215 x^2+6 x^3+12 x^4\right )+e^5 \left (72 x^3+16 x^4\right )}{-8 e^5 x^3+x^4+e^{20} \left (16-24 x+9 x^2\right )+e^{15} \left (-32 x+24 x^2\right )+e^{10} \left (24 x^2-6 x^3\right )} \, dx=x-(5+x)^2+\frac {x}{3 x-\left (-2+\frac {x}{e^5}\right )^2} \]
Time = 0.06 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.21 \[ \int \frac {-9 x^4-2 x^5+e^{15} \left (288 x-152 x^2-48 x^3\right )+e^{20} \left (-148+184 x-33 x^2-18 x^3\right )+e^{10} \left (-215 x^2+6 x^3+12 x^4\right )+e^5 \left (72 x^3+16 x^4\right )}{-8 e^5 x^3+x^4+e^{20} \left (16-24 x+9 x^2\right )+e^{15} \left (-32 x+24 x^2\right )+e^{10} \left (24 x^2-6 x^3\right )} \, dx=x \left (-9-x+\frac {e^{10}}{4 e^5 x-x^2+e^{10} (-4+3 x)}\right ) \]
Integrate[(-9*x^4 - 2*x^5 + E^15*(288*x - 152*x^2 - 48*x^3) + E^20*(-148 + 184*x - 33*x^2 - 18*x^3) + E^10*(-215*x^2 + 6*x^3 + 12*x^4) + E^5*(72*x^3 + 16*x^4))/(-8*E^5*x^3 + x^4 + E^20*(16 - 24*x + 9*x^2) + E^15*(-32*x + 2 4*x^2) + E^10*(24*x^2 - 6*x^3)),x]
Leaf count is larger than twice the leaf count of optimal. \(131\) vs. \(2(28)=56\).
Time = 0.69 (sec) , antiderivative size = 131, normalized size of antiderivative = 4.68, number of steps used = 7, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {2459, 1380, 2345, 27, 2019, 17}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {-2 x^5-9 x^4+e^5 \left (16 x^4+72 x^3\right )+e^{15} \left (-48 x^3-152 x^2+288 x\right )+e^{20} \left (-18 x^3-33 x^2+184 x-148\right )+e^{10} \left (12 x^4+6 x^3-215 x^2\right )}{x^4-8 e^5 x^3+e^{20} \left (9 x^2-24 x+16\right )+e^{15} \left (24 x^2-32 x\right )+e^{10} \left (24 x^2-6 x^3\right )} \, dx\) |
| \(\Big \downarrow \) 2459 |
| \(\displaystyle \int \frac {-2 \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^5-\left (9+4 e^5+3 e^{10}\right ) \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^4+3 e^{15} \left (8+3 e^5\right ) \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^3+\frac {1}{2} e^{10} \left (2+216 e^5+177 e^{10}+108 e^{15}+27 e^{20}\right ) \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^2+\frac {1}{8} e^{15} \left (32+24 e^5-576 e^{15}-432 e^{20}-81 e^{25}\right ) \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )+\frac {3}{16} e^{25} \left (32-1716 e^5-2064 e^{10}-1395 e^{15}-540 e^{20}-81 e^{25}\right )}{\left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^4-\frac {3}{2} e^{15} \left (8+3 e^5\right ) \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^2+\frac {9}{16} e^{30} \left (8+3 e^5\right )^2}d\left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )\) |
| \(\Big \downarrow \) 1380 |
| \(\displaystyle \int \frac {-32 \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^5-16 \left (9+4 e^5+3 e^{10}\right ) \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^4+48 e^{15} \left (8+3 e^5\right ) \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^3+8 e^{10} \left (2+216 e^5+177 e^{10}+108 e^{15}+27 e^{20}\right ) \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^2+2 e^{15} \left (32+24 e^5-576 e^{15}-432 e^{20}-81 e^{25}\right ) \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )+3 e^{25} \left (32-1716 e^5-2064 e^{10}-1395 e^{15}-540 e^{20}-81 e^{25}\right )}{\left (3 e^{15} \left (8+3 e^5\right )-4 \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^2\right )^2}d\left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )\) |
| \(\Big \downarrow \) 2345 |
| \(\displaystyle \frac {2 e^{10} \left (2 \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )+e^5 \left (4+3 e^5\right )\right )}{3 e^{15} \left (8+3 e^5\right )-4 \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^2}-\frac {\int \frac {6 \left (-8 e^{15} \left (8+3 e^5\right ) \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^3-4 e^{15} \left (72+59 e^5+36 e^{10}+9 e^{15}\right ) \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^2+6 e^{30} \left (8+3 e^5\right )^2 \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )+3 e^{30} \left (8+3 e^5\right )^2 \left (9+4 e^5+3 e^{10}\right )\right )}{3 e^{15} \left (8+3 e^5\right )-4 \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^2}d\left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )}{6 e^{15} \left (8+3 e^5\right )}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2 e^{10} \left (2 \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )+e^5 \left (4+3 e^5\right )\right )}{3 e^{15} \left (8+3 e^5\right )-4 \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^2}-\frac {\int \frac {-8 e^{15} \left (8+3 e^5\right ) \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^3-4 e^{15} \left (72+59 e^5+36 e^{10}+9 e^{15}\right ) \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^2+6 e^{30} \left (8+3 e^5\right )^2 \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )+3 e^{30} \left (8+3 e^5\right )^2 \left (9+4 e^5+3 e^{10}\right )}{3 e^{15} \left (8+3 e^5\right )-4 \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^2}d\left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )}{e^{15} \left (8+3 e^5\right )}\) |
| \(\Big \downarrow \) 2019 |
| \(\displaystyle \frac {2 e^{10} \left (2 \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )+e^5 \left (4+3 e^5\right )\right )}{3 e^{15} \left (8+3 e^5\right )-4 \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^2}-\frac {\int \left (\left (16 e^{15}+6 e^{20}\right ) \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )+9 e^{30}+36 e^{25}+59 e^{20}+72 e^{15}\right )d\left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )}{e^{15} \left (8+3 e^5\right )}\) |
| \(\Big \downarrow \) 17 |
| \(\displaystyle \frac {2 e^{10} \left (2 \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )+e^5 \left (4+3 e^5\right )\right )}{3 e^{15} \left (8+3 e^5\right )-4 \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )^2}-\frac {\left (2 \left (8+3 e^5\right ) \left (x+\frac {1}{4} \left (-8 e^5-6 e^{10}\right )\right )+9 e^{15}+36 e^{10}+59 e^5+72\right )^2}{4 \left (8+3 e^5\right )^2}\) |
Int[(-9*x^4 - 2*x^5 + E^15*(288*x - 152*x^2 - 48*x^3) + E^20*(-148 + 184*x - 33*x^2 - 18*x^3) + E^10*(-215*x^2 + 6*x^3 + 12*x^4) + E^5*(72*x^3 + 16* x^4))/(-8*E^5*x^3 + x^4 + E^20*(16 - 24*x + 9*x^2) + E^15*(-32*x + 24*x^2) + E^10*(24*x^2 - 6*x^3)),x]
-1/4*(72 + 59*E^5 + 36*E^10 + 9*E^15 + 2*(8 + 3*E^5)*((-8*E^5 - 6*E^10)/4 + x))^2/(8 + 3*E^5)^2 + (2*E^10*(E^5*(4 + 3*E^5) + 2*((-8*E^5 - 6*E^10)/4 + x)))/(3*E^15*(8 + 3*E^5) - 4*((-8*E^5 - 6*E^10)/4 + x)^2)
3.24.96.3.1 Defintions of rubi rules used
Int[(c_.)*((a_.) + (b_.)*(x_))^(m_.), x_Symbol] :> Simp[c*((a + b*x)^(m + 1 )/(b*(m + 1))), x] /; FreeQ[{a, b, c, m}, x] && NeQ[m, -1]
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(u_)*((a_) + (c_.)*(x_)^(n2_.) + (b_.)*(x_)^(n_))^(p_.), x_Symbol] :> S imp[1/c^p Int[u*(b/2 + c*x^n)^(2*p), x], x] /; FreeQ[{a, b, c, n, p}, x] && EqQ[n2, 2*n] && EqQ[b^2 - 4*a*c, 0] && IntegerQ[p]
Int[(u_.)*(Px_)^(p_.)*(Qx_)^(q_.), x_Symbol] :> Int[u*PolynomialQuotient[Px , Qx, x]^p*Qx^(p + q), x] /; FreeQ[q, x] && PolyQ[Px, x] && PolyQ[Qx, x] && EqQ[PolynomialRemainder[Px, Qx, x], 0] && IntegerQ[p] && LtQ[p*q, 0]
Int[(Pq_)*((a_) + (b_.)*(x_)^2)^(p_), x_Symbol] :> With[{Q = PolynomialQuot ient[Pq, a + b*x^2, x], f = Coeff[PolynomialRemainder[Pq, a + b*x^2, x], x, 0], g = Coeff[PolynomialRemainder[Pq, a + b*x^2, x], x, 1]}, Simp[(a*g - b *f*x)*((a + b*x^2)^(p + 1)/(2*a*b*(p + 1))), x] + Simp[1/(2*a*(p + 1)) In t[(a + b*x^2)^(p + 1)*ExpandToSum[2*a*(p + 1)*Q + f*(2*p + 3), x], x], x]] /; FreeQ[{a, b}, x] && PolyQ[Pq, x] && LtQ[p, -1]
Int[(Pn_)^(p_.)*(Qx_), x_Symbol] :> With[{S = Coeff[Pn, x, Expon[Pn, x] - 1 ]/(Expon[Pn, x]*Coeff[Pn, x, Expon[Pn, x]])}, Subst[Int[ExpandToSum[Pn /. x -> x - S, x]^p*ExpandToSum[Qx /. x -> x - S, x], x], x, x + S] /; Binomial Q[Pn /. x -> x - S, x] || (IntegerQ[Expon[Pn, x]/2] && TrinomialQ[Pn /. x - > x - S, x])] /; FreeQ[p, x] && PolyQ[Pn, x] && GtQ[Expon[Pn, x], 2] && NeQ [Coeff[Pn, x, Expon[Pn, x] - 1], 0] && PolyQ[Qx, x] && !(MonomialQ[Qx, x] && IGtQ[p, 0])
Time = 0.42 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.29
| method | result | size |
| risch | \(-x^{2}-9 x +\frac {x \,{\mathrm e}^{10}}{4 x \,{\mathrm e}^{5}+3 x \,{\mathrm e}^{10}-x^{2}-4 \,{\mathrm e}^{10}}\) | \(36\) |
| norman | \(\frac {x^{4}+\left (9-3 \,{\mathrm e}^{10}-4 \,{\mathrm e}^{5}\right ) x^{3}+\left (-69 \,{\mathrm e}^{20}-200 \,{\mathrm e}^{15}-107 \,{\mathrm e}^{10}\right ) x +4 \,{\mathrm e}^{15} \left (23 \,{\mathrm e}^{5}+36\right )}{4 x \,{\mathrm e}^{5}+3 x \,{\mathrm e}^{10}-x^{2}-4 \,{\mathrm e}^{10}}\) | \(81\) |
| gosper | \(-\frac {69 x \,{\mathrm e}^{20}+3 x^{3} {\mathrm e}^{10}-92 \,{\mathrm e}^{20}+200 x \,{\mathrm e}^{15}+4 x^{3} {\mathrm e}^{5}-x^{4}-144 \,{\mathrm e}^{15}+107 x \,{\mathrm e}^{10}-9 x^{3}}{4 x \,{\mathrm e}^{5}+3 x \,{\mathrm e}^{10}-x^{2}-4 \,{\mathrm e}^{10}}\) | \(89\) |
| parallelrisch | \(-\frac {69 x \,{\mathrm e}^{20}+3 x^{3} {\mathrm e}^{10}-92 \,{\mathrm e}^{20}+200 x \,{\mathrm e}^{15}+4 x^{3} {\mathrm e}^{5}-x^{4}-144 \,{\mathrm e}^{15}+107 x \,{\mathrm e}^{10}-9 x^{3}}{4 x \,{\mathrm e}^{5}+3 x \,{\mathrm e}^{10}-x^{2}-4 \,{\mathrm e}^{10}}\) | \(89\) |
| default | \(-x^{2}-9 x -\frac {\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (\textit {\_Z}^{4}+\left (-8 \,{\mathrm e}^{5}-6 \,{\mathrm e}^{10}\right ) \textit {\_Z}^{3}+\left (24 \,{\mathrm e}^{10}+9 \,{\mathrm e}^{20}+24 \,{\mathrm e}^{15}\right ) \textit {\_Z}^{2}+\left (-24 \,{\mathrm e}^{20}-32 \,{\mathrm e}^{15}\right ) \textit {\_Z} +16 \,{\mathrm e}^{20}\right )}{\sum }\frac {\left (\textit {\_R}^{2} {\mathrm e}^{10}-4 \,{\mathrm e}^{20}\right ) \ln \left (x -\textit {\_R} \right )}{-9 \textit {\_R} \,{\mathrm e}^{20}+12 \,{\mathrm e}^{20}-24 \,{\mathrm e}^{15} \textit {\_R} +9 \textit {\_R}^{2} {\mathrm e}^{10}+16 \,{\mathrm e}^{15}-24 \textit {\_R} \,{\mathrm e}^{10}+12 \textit {\_R}^{2} {\mathrm e}^{5}-2 \textit {\_R}^{3}}\right )}{2}\) | \(128\) |
int(((-18*x^3-33*x^2+184*x-148)*exp(5)^4+(-48*x^3-152*x^2+288*x)*exp(5)^3+ (12*x^4+6*x^3-215*x^2)*exp(5)^2+(16*x^4+72*x^3)*exp(5)-2*x^5-9*x^4)/((9*x^ 2-24*x+16)*exp(5)^4+(24*x^2-32*x)*exp(5)^3+(-6*x^3+24*x^2)*exp(5)^2-8*x^3* exp(5)+x^4),x,method=_RETURNVERBOSE)
Leaf count of result is larger than twice the leaf count of optimal. 62 vs. \(2 (26) = 52\).
Time = 0.25 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.21 \[ \int \frac {-9 x^4-2 x^5+e^{15} \left (288 x-152 x^2-48 x^3\right )+e^{20} \left (-148+184 x-33 x^2-18 x^3\right )+e^{10} \left (-215 x^2+6 x^3+12 x^4\right )+e^5 \left (72 x^3+16 x^4\right )}{-8 e^5 x^3+x^4+e^{20} \left (16-24 x+9 x^2\right )+e^{15} \left (-32 x+24 x^2\right )+e^{10} \left (24 x^2-6 x^3\right )} \, dx=-\frac {x^{4} + 9 \, x^{3} - {\left (3 \, x^{3} + 23 \, x^{2} - 37 \, x\right )} e^{10} - 4 \, {\left (x^{3} + 9 \, x^{2}\right )} e^{5}}{x^{2} - {\left (3 \, x - 4\right )} e^{10} - 4 \, x e^{5}} \]
integrate(((-18*x^3-33*x^2+184*x-148)*exp(5)^4+(-48*x^3-152*x^2+288*x)*exp (5)^3+(12*x^4+6*x^3-215*x^2)*exp(5)^2+(16*x^4+72*x^3)*exp(5)-2*x^5-9*x^4)/ ((9*x^2-24*x+16)*exp(5)^4+(24*x^2-32*x)*exp(5)^3+(-6*x^3+24*x^2)*exp(5)^2- 8*x^3*exp(5)+x^4),x, algorithm=\
-(x^4 + 9*x^3 - (3*x^3 + 23*x^2 - 37*x)*e^10 - 4*(x^3 + 9*x^2)*e^5)/(x^2 - (3*x - 4)*e^10 - 4*x*e^5)
Time = 0.35 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.21 \[ \int \frac {-9 x^4-2 x^5+e^{15} \left (288 x-152 x^2-48 x^3\right )+e^{20} \left (-148+184 x-33 x^2-18 x^3\right )+e^{10} \left (-215 x^2+6 x^3+12 x^4\right )+e^5 \left (72 x^3+16 x^4\right )}{-8 e^5 x^3+x^4+e^{20} \left (16-24 x+9 x^2\right )+e^{15} \left (-32 x+24 x^2\right )+e^{10} \left (24 x^2-6 x^3\right )} \, dx=- x^{2} - 9 x - \frac {x e^{10}}{x^{2} + x \left (- 3 e^{10} - 4 e^{5}\right ) + 4 e^{10}} \]
integrate(((-18*x**3-33*x**2+184*x-148)*exp(5)**4+(-48*x**3-152*x**2+288*x )*exp(5)**3+(12*x**4+6*x**3-215*x**2)*exp(5)**2+(16*x**4+72*x**3)*exp(5)-2 *x**5-9*x**4)/((9*x**2-24*x+16)*exp(5)**4+(24*x**2-32*x)*exp(5)**3+(-6*x** 3+24*x**2)*exp(5)**2-8*x**3*exp(5)+x**4),x)
Time = 0.19 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.29 \[ \int \frac {-9 x^4-2 x^5+e^{15} \left (288 x-152 x^2-48 x^3\right )+e^{20} \left (-148+184 x-33 x^2-18 x^3\right )+e^{10} \left (-215 x^2+6 x^3+12 x^4\right )+e^5 \left (72 x^3+16 x^4\right )}{-8 e^5 x^3+x^4+e^{20} \left (16-24 x+9 x^2\right )+e^{15} \left (-32 x+24 x^2\right )+e^{10} \left (24 x^2-6 x^3\right )} \, dx=-x^{2} - 9 \, x - \frac {x e^{10}}{x^{2} - x {\left (3 \, e^{10} + 4 \, e^{5}\right )} + 4 \, e^{10}} \]
integrate(((-18*x^3-33*x^2+184*x-148)*exp(5)^4+(-48*x^3-152*x^2+288*x)*exp (5)^3+(12*x^4+6*x^3-215*x^2)*exp(5)^2+(16*x^4+72*x^3)*exp(5)-2*x^5-9*x^4)/ ((9*x^2-24*x+16)*exp(5)^4+(24*x^2-32*x)*exp(5)^3+(-6*x^3+24*x^2)*exp(5)^2- 8*x^3*exp(5)+x^4),x, algorithm=\
Time = 0.34 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.21 \[ \int \frac {-9 x^4-2 x^5+e^{15} \left (288 x-152 x^2-48 x^3\right )+e^{20} \left (-148+184 x-33 x^2-18 x^3\right )+e^{10} \left (-215 x^2+6 x^3+12 x^4\right )+e^5 \left (72 x^3+16 x^4\right )}{-8 e^5 x^3+x^4+e^{20} \left (16-24 x+9 x^2\right )+e^{15} \left (-32 x+24 x^2\right )+e^{10} \left (24 x^2-6 x^3\right )} \, dx=-x^{2} - 9 \, x - \frac {x e^{10}}{x^{2} - 3 \, x e^{10} - 4 \, x e^{5} + 4 \, e^{10}} \]
integrate(((-18*x^3-33*x^2+184*x-148)*exp(5)^4+(-48*x^3-152*x^2+288*x)*exp (5)^3+(12*x^4+6*x^3-215*x^2)*exp(5)^2+(16*x^4+72*x^3)*exp(5)-2*x^5-9*x^4)/ ((9*x^2-24*x+16)*exp(5)^4+(24*x^2-32*x)*exp(5)^3+(-6*x^3+24*x^2)*exp(5)^2- 8*x^3*exp(5)+x^4),x, algorithm=\
Time = 13.41 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.96 \[ \int \frac {-9 x^4-2 x^5+e^{15} \left (288 x-152 x^2-48 x^3\right )+e^{20} \left (-148+184 x-33 x^2-18 x^3\right )+e^{10} \left (-215 x^2+6 x^3+12 x^4\right )+e^5 \left (72 x^3+16 x^4\right )}{-8 e^5 x^3+x^4+e^{20} \left (16-24 x+9 x^2\right )+e^{15} \left (-32 x+24 x^2\right )+e^{10} \left (24 x^2-6 x^3\right )} \, dx=x\,\left (16\,{\mathrm {e}}^5+12\,{\mathrm {e}}^{10}-4\,{\mathrm {e}}^5\,\left (3\,{\mathrm {e}}^5+4\right )-9\right )-x^2-\frac {x\,{\mathrm {e}}^{10}}{x^2+\left (-4\,{\mathrm {e}}^5-3\,{\mathrm {e}}^{10}\right )\,x+4\,{\mathrm {e}}^{10}} \]
int(-(exp(20)*(33*x^2 - 184*x + 18*x^3 + 148) + exp(15)*(152*x^2 - 288*x + 48*x^3) - exp(5)*(72*x^3 + 16*x^4) - exp(10)*(6*x^3 - 215*x^2 + 12*x^4) + 9*x^4 + 2*x^5)/(exp(20)*(9*x^2 - 24*x + 16) - exp(15)*(32*x - 24*x^2) + e xp(10)*(24*x^2 - 6*x^3) - 8*x^3*exp(5) + x^4),x)