Integrand size = 44, antiderivative size = 358 \[ \int \frac {f+g x}{(d+e x)^3 \left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}} \, dx=\frac {32 c^2 (4 c e f+2 c d g-3 b e g) (b+2 c x)}{63 e (2 c d-b e)^5 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}-\frac {2 (e f-d g)}{9 e^2 (2 c d-b e) (d+e x)^3 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}-\frac {2 (4 c e f+2 c d g-3 b e g)}{21 e^2 (2 c d-b e)^2 (d+e x)^2 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}-\frac {4 c (4 c e f+2 c d g-3 b e g)}{21 e^2 (2 c d-b e)^3 (d+e x) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}+\frac {256 c^3 (4 c e f+2 c d g-3 b e g) (b+2 c x)}{63 e (2 c d-b e)^7 \sqrt {d (c d-b e)-b e^2 x-c e^2 x^2}} \]
32/63*c^2*(-3*b*e*g+2*c*d*g+4*c*e*f)*(2*c*x+b)/e/(-b*e+2*c*d)^5/(d*(-b*e+c *d)-b*e^2*x-c*e^2*x^2)^(3/2)-2/9*(-d*g+e*f)/e^2/(-b*e+2*c*d)/(e*x+d)^3/(d* (-b*e+c*d)-b*e^2*x-c*e^2*x^2)^(3/2)-2/21*(-3*b*e*g+2*c*d*g+4*c*e*f)/e^2/(- b*e+2*c*d)^2/(e*x+d)^2/(d*(-b*e+c*d)-b*e^2*x-c*e^2*x^2)^(3/2)-4/21*c*(-3*b *e*g+2*c*d*g+4*c*e*f)/e^2/(-b*e+2*c*d)^3/(e*x+d)/(d*(-b*e+c*d)-b*e^2*x-c*e ^2*x^2)^(3/2)+256/63*c^3*(-3*b*e*g+2*c*d*g+4*c*e*f)*(2*c*x+b)/e/(-b*e+2*c* d)^7/(d*(-b*e+c*d)-b*e^2*x-c*e^2*x^2)^(1/2)
Time = 0.72 (sec) , antiderivative size = 505, normalized size of antiderivative = 1.41 \[ \int \frac {f+g x}{(d+e x)^3 \left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}} \, dx=-\frac {2 \left (21 c^6 e f (d+e x)^6+21 c^6 d g (d+e x)^6-21 b c^5 e g (d+e x)^6-378 c^5 e f (d+e x)^5 (-c d+b e+c e x)+315 b c^4 e g (d+e x)^5 (-c d+b e+c e x)-945 c^4 e f (d+e x)^4 (-c d+b e+c e x)^2-315 c^4 d g (d+e x)^4 (-c d+b e+c e x)^2+630 b c^3 e g (d+e x)^4 (-c d+b e+c e x)^2+420 c^3 e f (d+e x)^3 (-c d+b e+c e x)^3-210 b c^2 e g (d+e x)^3 (-c d+b e+c e x)^3-189 c^2 e f (d+e x)^2 (-c d+b e+c e x)^4+63 c^2 d g (d+e x)^2 (-c d+b e+c e x)^4+63 b c e g (d+e x)^2 (-c d+b e+c e x)^4+54 c e f (d+e x) (-c d+b e+c e x)^5-9 b e g (d+e x) (-c d+b e+c e x)^5-7 e f (-c d+b e+c e x)^6+7 d g (-c d+b e+c e x)^6+252 c^5 d g (d+e x)^5 (-b e+c (d-e x))+36 c d g (d+e x) (-b e+c (d-e x))^5\right )}{63 e^2 (-2 c d+b e)^7 (d+e x)^3 ((d+e x) (-b e+c (d-e x)))^{3/2}} \]
(-2*(21*c^6*e*f*(d + e*x)^6 + 21*c^6*d*g*(d + e*x)^6 - 21*b*c^5*e*g*(d + e *x)^6 - 378*c^5*e*f*(d + e*x)^5*(-(c*d) + b*e + c*e*x) + 315*b*c^4*e*g*(d + e*x)^5*(-(c*d) + b*e + c*e*x) - 945*c^4*e*f*(d + e*x)^4*(-(c*d) + b*e + c*e*x)^2 - 315*c^4*d*g*(d + e*x)^4*(-(c*d) + b*e + c*e*x)^2 + 630*b*c^3*e* g*(d + e*x)^4*(-(c*d) + b*e + c*e*x)^2 + 420*c^3*e*f*(d + e*x)^3*(-(c*d) + b*e + c*e*x)^3 - 210*b*c^2*e*g*(d + e*x)^3*(-(c*d) + b*e + c*e*x)^3 - 189 *c^2*e*f*(d + e*x)^2*(-(c*d) + b*e + c*e*x)^4 + 63*c^2*d*g*(d + e*x)^2*(-( c*d) + b*e + c*e*x)^4 + 63*b*c*e*g*(d + e*x)^2*(-(c*d) + b*e + c*e*x)^4 + 54*c*e*f*(d + e*x)*(-(c*d) + b*e + c*e*x)^5 - 9*b*e*g*(d + e*x)*(-(c*d) + b*e + c*e*x)^5 - 7*e*f*(-(c*d) + b*e + c*e*x)^6 + 7*d*g*(-(c*d) + b*e + c* e*x)^6 + 252*c^5*d*g*(d + e*x)^5*(-(b*e) + c*(d - e*x)) + 36*c*d*g*(d + e* x)*(-(b*e) + c*(d - e*x))^5))/(63*e^2*(-2*c*d + b*e)^7*(d + e*x)^3*((d + e *x)*(-(b*e) + c*(d - e*x)))^(3/2))
Time = 0.53 (sec) , antiderivative size = 351, normalized size of antiderivative = 0.98, number of steps used = 5, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.114, Rules used = {1220, 1129, 1129, 1089, 1088}
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.
| \(\displaystyle \int \frac {f+g x}{(d+e x)^3 \left (-b d e-b e^2 x+c d^2-c e^2 x^2\right )^{5/2}} \, dx\) |
| \(\Big \downarrow \) 1220 |
| \(\displaystyle \frac {(-3 b e g+2 c d g+4 c e f) \int \frac {1}{(d+e x)^2 \left (-c x^2 e^2-b x e^2+d (c d-b e)\right )^{5/2}}dx}{3 e (2 c d-b e)}-\frac {2 (e f-d g)}{9 e^2 (d+e x)^3 (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}\) |
| \(\Big \downarrow \) 1129 |
| \(\displaystyle \frac {(-3 b e g+2 c d g+4 c e f) \left (\frac {10 c \int \frac {1}{(d+e x) \left (-c x^2 e^2-b x e^2+d (c d-b e)\right )^{5/2}}dx}{7 (2 c d-b e)}-\frac {2}{7 e (d+e x)^2 (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}\right )}{3 e (2 c d-b e)}-\frac {2 (e f-d g)}{9 e^2 (d+e x)^3 (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}\) |
| \(\Big \downarrow \) 1129 |
| \(\displaystyle \frac {(-3 b e g+2 c d g+4 c e f) \left (\frac {10 c \left (\frac {8 c \int \frac {1}{\left (-c x^2 e^2-b x e^2+d (c d-b e)\right )^{5/2}}dx}{5 (2 c d-b e)}-\frac {2}{5 e (d+e x) (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}\right )}{7 (2 c d-b e)}-\frac {2}{7 e (d+e x)^2 (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}\right )}{3 e (2 c d-b e)}-\frac {2 (e f-d g)}{9 e^2 (d+e x)^3 (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}\) |
| \(\Big \downarrow \) 1089 |
| \(\displaystyle \frac {(-3 b e g+2 c d g+4 c e f) \left (\frac {10 c \left (\frac {8 c \left (\frac {8 c \int \frac {1}{\left (-c x^2 e^2-b x e^2+d (c d-b e)\right )^{3/2}}dx}{3 (2 c d-b e)^2}+\frac {2 (b+2 c x)}{3 (2 c d-b e)^2 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}\right )}{5 (2 c d-b e)}-\frac {2}{5 e (d+e x) (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}\right )}{7 (2 c d-b e)}-\frac {2}{7 e (d+e x)^2 (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}\right )}{3 e (2 c d-b e)}-\frac {2 (e f-d g)}{9 e^2 (d+e x)^3 (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}\) |
| \(\Big \downarrow \) 1088 |
| \(\displaystyle \frac {\left (\frac {10 c \left (\frac {8 c \left (\frac {16 c (b+2 c x)}{3 (2 c d-b e)^4 \sqrt {d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac {2 (b+2 c x)}{3 (2 c d-b e)^2 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}\right )}{5 (2 c d-b e)}-\frac {2}{5 e (d+e x) (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}\right )}{7 (2 c d-b e)}-\frac {2}{7 e (d+e x)^2 (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}\right ) (-3 b e g+2 c d g+4 c e f)}{3 e (2 c d-b e)}-\frac {2 (e f-d g)}{9 e^2 (d+e x)^3 (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}\) |
(-2*(e*f - d*g))/(9*e^2*(2*c*d - b*e)*(d + e*x)^3*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) + ((4*c*e*f + 2*c*d*g - 3*b*e*g)*(-2/(7*e*(2*c*d - b* e)*(d + e*x)^2*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) + (10*c*(-2/(5 *e*(2*c*d - b*e)*(d + e*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) + (8*c*((2*(b + 2*c*x))/(3*(2*c*d - b*e)^2*(d*(c*d - b*e) - b*e^2*x - c*e^2* x^2)^(3/2)) + (16*c*(b + 2*c*x))/(3*(2*c*d - b*e)^4*Sqrt[d*(c*d - b*e) - b *e^2*x - c*e^2*x^2])))/(5*(2*c*d - b*e))))/(7*(2*c*d - b*e))))/(3*e*(2*c*d - b*e))
3.23.30.3.1 Defintions of rubi rules used
Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(-3/2), x_Symbol] :> Simp[-2*((b + 2*c*x)/((b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2])), x] /; FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0]
Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[(b + 2*c*x) *((a + b*x + c*x^2)^(p + 1)/((p + 1)*(b^2 - 4*a*c))), x] - Simp[2*c*((2*p + 3)/((p + 1)*(b^2 - 4*a*c))) Int[(a + b*x + c*x^2)^(p + 1), x], x] /; Fre eQ[{a, b, c}, x] && LtQ[p, -1] && (IntegerQ[4*p] || IntegerQ[3*p])
Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_S ymbol] :> Simp[(-e)*(d + e*x)^m*((a + b*x + c*x^2)^(p + 1)/((m + p + 1)*(2* c*d - b*e))), x] + Simp[c*(Simplify[m + 2*p + 2]/((m + p + 1)*(2*c*d - b*e) )) Int[(d + e*x)^(m + 1)*(a + b*x + c*x^2)^p, x], x] /; FreeQ[{a, b, c, d , e, m, p}, x] && EqQ[c*d^2 - b*d*e + a*e^2, 0] && ILtQ[Simplify[m + 2*p + 2], 0]
Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c _.)*(x_)^2)^(p_), x_Symbol] :> Simp[(d*g - e*f)*(d + e*x)^m*((a + b*x + c*x ^2)^(p + 1)/((2*c*d - b*e)*(m + p + 1))), x] + Simp[(m*(g*(c*d - b*e) + c*e *f) + e*(p + 1)*(2*c*f - b*g))/(e*(2*c*d - b*e)*(m + p + 1)) Int[(d + e*x )^(m + 1)*(a + b*x + c*x^2)^p, x], x] /; FreeQ[{a, b, c, d, e, f, g, m, p}, x] && EqQ[c*d^2 - b*d*e + a*e^2, 0] && ((LtQ[m, -1] && !IGtQ[m + p + 1, 0 ]) || (LtQ[m, 0] && LtQ[p, -1]) || EqQ[m + 2*p + 2, 0]) && NeQ[m + p + 1, 0 ]
Leaf count of result is larger than twice the leaf count of optimal. \(764\) vs. \(2(338)=676\).
Time = 0.84 (sec) , antiderivative size = 765, normalized size of antiderivative = 2.14
| method | result | size |
| default | \(\frac {g \left (-\frac {2}{7 \left (-b \,e^{2}+2 c d e \right ) \left (x +\frac {d}{e}\right )^{2} \left (-c \,e^{2} \left (x +\frac {d}{e}\right )^{2}+\left (-b \,e^{2}+2 c d e \right ) \left (x +\frac {d}{e}\right )\right )^{\frac {3}{2}}}+\frac {10 c \,e^{2} \left (-\frac {2}{5 \left (-b \,e^{2}+2 c d e \right ) \left (x +\frac {d}{e}\right ) \left (-c \,e^{2} \left (x +\frac {d}{e}\right )^{2}+\left (-b \,e^{2}+2 c d e \right ) \left (x +\frac {d}{e}\right )\right )^{\frac {3}{2}}}+\frac {8 c \,e^{2} \left (-\frac {2 \left (-2 c \,e^{2} \left (x +\frac {d}{e}\right )-b \,e^{2}+2 c d e \right )}{3 \left (-b \,e^{2}+2 c d e \right )^{2} \left (-c \,e^{2} \left (x +\frac {d}{e}\right )^{2}+\left (-b \,e^{2}+2 c d e \right ) \left (x +\frac {d}{e}\right )\right )^{\frac {3}{2}}}-\frac {16 c \,e^{2} \left (-2 c \,e^{2} \left (x +\frac {d}{e}\right )-b \,e^{2}+2 c d e \right )}{3 \left (-b \,e^{2}+2 c d e \right )^{4} \sqrt {-c \,e^{2} \left (x +\frac {d}{e}\right )^{2}+\left (-b \,e^{2}+2 c d e \right ) \left (x +\frac {d}{e}\right )}}\right )}{5 \left (-b \,e^{2}+2 c d e \right )}\right )}{7 \left (-b \,e^{2}+2 c d e \right )}\right )}{e^{3}}+\frac {\left (-d g +e f \right ) \left (-\frac {2}{9 \left (-b \,e^{2}+2 c d e \right ) \left (x +\frac {d}{e}\right )^{3} \left (-c \,e^{2} \left (x +\frac {d}{e}\right )^{2}+\left (-b \,e^{2}+2 c d e \right ) \left (x +\frac {d}{e}\right )\right )^{\frac {3}{2}}}+\frac {4 c \,e^{2} \left (-\frac {2}{7 \left (-b \,e^{2}+2 c d e \right ) \left (x +\frac {d}{e}\right )^{2} \left (-c \,e^{2} \left (x +\frac {d}{e}\right )^{2}+\left (-b \,e^{2}+2 c d e \right ) \left (x +\frac {d}{e}\right )\right )^{\frac {3}{2}}}+\frac {10 c \,e^{2} \left (-\frac {2}{5 \left (-b \,e^{2}+2 c d e \right ) \left (x +\frac {d}{e}\right ) \left (-c \,e^{2} \left (x +\frac {d}{e}\right )^{2}+\left (-b \,e^{2}+2 c d e \right ) \left (x +\frac {d}{e}\right )\right )^{\frac {3}{2}}}+\frac {8 c \,e^{2} \left (-\frac {2 \left (-2 c \,e^{2} \left (x +\frac {d}{e}\right )-b \,e^{2}+2 c d e \right )}{3 \left (-b \,e^{2}+2 c d e \right )^{2} \left (-c \,e^{2} \left (x +\frac {d}{e}\right )^{2}+\left (-b \,e^{2}+2 c d e \right ) \left (x +\frac {d}{e}\right )\right )^{\frac {3}{2}}}-\frac {16 c \,e^{2} \left (-2 c \,e^{2} \left (x +\frac {d}{e}\right )-b \,e^{2}+2 c d e \right )}{3 \left (-b \,e^{2}+2 c d e \right )^{4} \sqrt {-c \,e^{2} \left (x +\frac {d}{e}\right )^{2}+\left (-b \,e^{2}+2 c d e \right ) \left (x +\frac {d}{e}\right )}}\right )}{5 \left (-b \,e^{2}+2 c d e \right )}\right )}{7 \left (-b \,e^{2}+2 c d e \right )}\right )}{3 \left (-b \,e^{2}+2 c d e \right )}\right )}{e^{4}}\) | \(765\) |
| trager | \(\text {Expression too large to display}\) | \(1034\) |
| gosper | \(\text {Expression too large to display}\) | \(1036\) |
g/e^3*(-2/7/(-b*e^2+2*c*d*e)/(x+d/e)^2/(-c*e^2*(x+d/e)^2+(-b*e^2+2*c*d*e)* (x+d/e))^(3/2)+10/7*c*e^2/(-b*e^2+2*c*d*e)*(-2/5/(-b*e^2+2*c*d*e)/(x+d/e)/ (-c*e^2*(x+d/e)^2+(-b*e^2+2*c*d*e)*(x+d/e))^(3/2)+8/5*c*e^2/(-b*e^2+2*c*d* e)*(-2/3*(-2*c*e^2*(x+d/e)-b*e^2+2*c*d*e)/(-b*e^2+2*c*d*e)^2/(-c*e^2*(x+d/ e)^2+(-b*e^2+2*c*d*e)*(x+d/e))^(3/2)-16/3*c*e^2/(-b*e^2+2*c*d*e)^4*(-2*c*e ^2*(x+d/e)-b*e^2+2*c*d*e)/(-c*e^2*(x+d/e)^2+(-b*e^2+2*c*d*e)*(x+d/e))^(1/2 ))))+(-d*g+e*f)/e^4*(-2/9/(-b*e^2+2*c*d*e)/(x+d/e)^3/(-c*e^2*(x+d/e)^2+(-b *e^2+2*c*d*e)*(x+d/e))^(3/2)+4/3*c*e^2/(-b*e^2+2*c*d*e)*(-2/7/(-b*e^2+2*c* d*e)/(x+d/e)^2/(-c*e^2*(x+d/e)^2+(-b*e^2+2*c*d*e)*(x+d/e))^(3/2)+10/7*c*e^ 2/(-b*e^2+2*c*d*e)*(-2/5/(-b*e^2+2*c*d*e)/(x+d/e)/(-c*e^2*(x+d/e)^2+(-b*e^ 2+2*c*d*e)*(x+d/e))^(3/2)+8/5*c*e^2/(-b*e^2+2*c*d*e)*(-2/3*(-2*c*e^2*(x+d/ e)-b*e^2+2*c*d*e)/(-b*e^2+2*c*d*e)^2/(-c*e^2*(x+d/e)^2+(-b*e^2+2*c*d*e)*(x +d/e))^(3/2)-16/3*c*e^2/(-b*e^2+2*c*d*e)^4*(-2*c*e^2*(x+d/e)-b*e^2+2*c*d*e )/(-c*e^2*(x+d/e)^2+(-b*e^2+2*c*d*e)*(x+d/e))^(1/2)))))
Timed out. \[ \int \frac {f+g x}{(d+e x)^3 \left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}} \, dx=\text {Timed out} \]
Timed out. \[ \int \frac {f+g x}{(d+e x)^3 \left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}} \, dx=\text {Timed out} \]
Exception generated. \[ \int \frac {f+g x}{(d+e x)^3 \left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}} \, dx=\text {Exception raised: ValueError} \]
Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b*e-2*c*d>0)', see `assume?` for more deta
\[ \int \frac {f+g x}{(d+e x)^3 \left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}} \, dx=\int { \frac {g x + f}{{\left (-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e\right )}^{\frac {5}{2}} {\left (e x + d\right )}^{3}} \,d x } \]
Time = 32.41 (sec) , antiderivative size = 33819, normalized size of antiderivative = 94.47 \[ \int \frac {f+g x}{(d+e x)^3 \left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}} \, dx=\text {Too large to display} \]
((35968*c^9*d^6*g - 10062*b^5*c^4*e^6*f + 5714*b^6*c^3*e^6*g + 279680*c^9* d^5*e*f - 248960*b*c^8*d^5*e*g - 729600*b*c^8*d^4*e^2*f + 98950*b^4*c^5*d* e^5*f - 57260*b^5*c^4*d*e^5*g + 755040*b^2*c^7*d^3*e^3*f - 387748*b^3*c^6* d^2*e^4*f + 504032*b^2*c^7*d^4*e^2*g - 473132*b^3*c^6*d^3*e^3*g + 231104*b ^4*c^5*d^2*e^4*g)/(945*e^2*(b*e - 2*c*d)^11) - x*((b*((b*((b*((b*((32*c^8* e^3*(4*c*d*g - 7*b*e*g + 4*c*e*f))/(945*(b*e - 2*c*d)^11) + (32*b*c^8*e^4* g)/(945*(b*e - 2*c*d)^11)))/c - (16*c^7*e^2*(20*c^2*d^2*g - 43*b^2*e^2*g + 61*b*c*e^2*f - 82*c^2*d*e*f + 41*b*c*d*e*g))/(945*(b*e - 2*c*d)^11) + (32 *c^8*e^2*g*(c*d^2 - b*d*e))/(945*(b*e - 2*c*d)^11)))/c + (1608*b^2*c^7*e^6 *f - 912*b^3*c^6*e^6*g - 96*c^9*d^2*e^4*f + 224*c^9*d^3*e^3*g - 2528*b*c^8 *d*e^5*f + 352*b*c^8*d^2*e^4*g + 1112*b^2*c^7*d*e^5*g)/(945*e^2*(b*e - 2*c *d)^11) + (((32*c^8*e^3*(4*c*d*g - 7*b*e*g + 4*c*e*f))/(945*(b*e - 2*c*d)^ 11) + (32*b*c^8*e^4*g)/(945*(b*e - 2*c*d)^11))*(c*d^2 - b*d*e))/(c*e^2)))/ c - (326*b^4*c^5*e^6*g - 1372*b^3*c^6*e^6*f + 19840*c^9*d^3*e^3*f - 5248*c ^9*d^4*e^2*g - 29904*b*c^8*d^2*e^4*f + 13056*b^2*c^7*d*e^5*f + 912*b*c^8*d ^3*e^3*g - 3972*b^3*c^6*d*e^5*g + 7056*b^2*c^7*d^2*e^4*g)/(945*e^2*(b*e - 2*c*d)^11) + ((c*d^2 - b*d*e)*((b*((32*c^8*e^3*(4*c*d*g - 7*b*e*g + 4*c*e* f))/(945*(b*e - 2*c*d)^11) + (32*b*c^8*e^4*g)/(945*(b*e - 2*c*d)^11)))/c - (16*c^7*e^2*(20*c^2*d^2*g - 43*b^2*e^2*g + 61*b*c*e^2*f - 82*c^2*d*e*f + 41*b*c*d*e*g))/(945*(b*e - 2*c*d)^11) + (32*c^8*e^2*g*(c*d^2 - b*d*e))/...