Integrand size = 28, antiderivative size = 129 \[ \int \frac {\sqrt {1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{5/2}} \, dx=-\frac {214 \sqrt {1-2 x} \sqrt {3+5 x}}{189 \sqrt {2+3 x}}-\frac {2 \sqrt {1-2 x} (3+5 x)^{3/2}}{9 (2+3 x)^{3/2}}+\frac {494}{81} \sqrt {\frac {5}{7}} E\left (\arcsin \left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right )|\frac {33}{35}\right )-\frac {230}{81} \sqrt {\frac {5}{7}} \operatorname {EllipticF}\left (\arcsin \left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right ),\frac {33}{35}\right ) \] Output:
-214/189*(1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x)^(1/2)-2/9*(1-2*x)^(1/2)*(3+5* x)^(3/2)/(2+3*x)^(3/2)+494/567*EllipticE(1/11*55^(1/2)*(1-2*x)^(1/2),1/35* 1155^(1/2))*35^(1/2)-230/567*EllipticF(1/11*55^(1/2)*(1-2*x)^(1/2),1/35*11 55^(1/2))*35^(1/2)
Result contains complex when optimal does not.
Time = 6.36 (sec) , antiderivative size = 93, normalized size of antiderivative = 0.72 \[ \int \frac {\sqrt {1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{5/2}} \, dx=\frac {2}{567} \left (-\frac {3 \sqrt {1-2 x} \sqrt {3+5 x} (277+426 x)}{(2+3 x)^{3/2}}-247 i \sqrt {33} E\left (i \text {arcsinh}\left (\sqrt {9+15 x}\right )|-\frac {2}{33}\right )+140 i \sqrt {33} \operatorname {EllipticF}\left (i \text {arcsinh}\left (\sqrt {9+15 x}\right ),-\frac {2}{33}\right )\right ) \] Input:
Integrate[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^(5/2),x]
Output:
(2*((-3*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(277 + 426*x))/(2 + 3*x)^(3/2) - (247* I)*Sqrt[33]*EllipticE[I*ArcSinh[Sqrt[9 + 15*x]], -2/33] + (140*I)*Sqrt[33] *EllipticF[I*ArcSinh[Sqrt[9 + 15*x]], -2/33]))/567
Time = 0.24 (sec) , antiderivative size = 139, normalized size of antiderivative = 1.08, number of steps used = 7, number of rules used = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {108, 27, 167, 27, 176, 123, 129}
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.
| \(\displaystyle \int \frac {\sqrt {1-2 x} (5 x+3)^{3/2}}{(3 x+2)^{5/2}} \, dx\) |
| \(\Big \downarrow \) 108 |
| \(\displaystyle \frac {2}{9} \int \frac {(9-40 x) \sqrt {5 x+3}}{2 \sqrt {1-2 x} (3 x+2)^{3/2}}dx-\frac {2 \sqrt {1-2 x} (5 x+3)^{3/2}}{9 (3 x+2)^{3/2}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{9} \int \frac {(9-40 x) \sqrt {5 x+3}}{\sqrt {1-2 x} (3 x+2)^{3/2}}dx-\frac {2 \sqrt {1-2 x} (5 x+3)^{3/2}}{9 (3 x+2)^{3/2}}\) |
| \(\Big \downarrow \) 167 |
| \(\displaystyle \frac {1}{9} \left (\frac {2}{21} \int -\frac {5 (494 x+61)}{2 \sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3}}dx-\frac {214 \sqrt {1-2 x} \sqrt {5 x+3}}{21 \sqrt {3 x+2}}\right )-\frac {2 \sqrt {1-2 x} (5 x+3)^{3/2}}{9 (3 x+2)^{3/2}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{9} \left (-\frac {5}{21} \int \frac {494 x+61}{\sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3}}dx-\frac {214 \sqrt {1-2 x} \sqrt {5 x+3}}{21 \sqrt {3 x+2}}\right )-\frac {2 \sqrt {1-2 x} (5 x+3)^{3/2}}{9 (3 x+2)^{3/2}}\) |
| \(\Big \downarrow \) 176 |
| \(\displaystyle \frac {1}{9} \left (-\frac {5}{21} \left (\frac {494}{5} \int \frac {\sqrt {5 x+3}}{\sqrt {1-2 x} \sqrt {3 x+2}}dx-\frac {1177}{5} \int \frac {1}{\sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3}}dx\right )-\frac {214 \sqrt {1-2 x} \sqrt {5 x+3}}{21 \sqrt {3 x+2}}\right )-\frac {2 \sqrt {1-2 x} (5 x+3)^{3/2}}{9 (3 x+2)^{3/2}}\) |
| \(\Big \downarrow \) 123 |
| \(\displaystyle \frac {1}{9} \left (-\frac {5}{21} \left (-\frac {1177}{5} \int \frac {1}{\sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3}}dx-\frac {494}{5} \sqrt {\frac {11}{3}} E\left (\arcsin \left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )\right )-\frac {214 \sqrt {1-2 x} \sqrt {5 x+3}}{21 \sqrt {3 x+2}}\right )-\frac {2 \sqrt {1-2 x} (5 x+3)^{3/2}}{9 (3 x+2)^{3/2}}\) |
| \(\Big \downarrow \) 129 |
| \(\displaystyle \frac {1}{9} \left (-\frac {5}{21} \left (\frac {214}{5} \sqrt {\frac {11}{3}} \operatorname {EllipticF}\left (\arcsin \left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right ),\frac {35}{33}\right )-\frac {494}{5} \sqrt {\frac {11}{3}} E\left (\arcsin \left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )\right )-\frac {214 \sqrt {1-2 x} \sqrt {5 x+3}}{21 \sqrt {3 x+2}}\right )-\frac {2 \sqrt {1-2 x} (5 x+3)^{3/2}}{9 (3 x+2)^{3/2}}\) |
Input:
Int[(Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(2 + 3*x)^(5/2),x]
Output:
(-2*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(9*(2 + 3*x)^(3/2)) + ((-214*Sqrt[1 - 2 *x]*Sqrt[3 + 5*x])/(21*Sqrt[2 + 3*x]) - (5*((-494*Sqrt[11/3]*EllipticE[Arc Sin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/5 + (214*Sqrt[11/3]*EllipticF[ArcSin [Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/5))/21)/9
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_) )^(p_), x_] :> Simp[(a + b*x)^(m + 1)*(c + d*x)^n*((e + f*x)^p/(b*(m + 1))) , x] - Simp[1/(b*(m + 1)) Int[(a + b*x)^(m + 1)*(c + d*x)^(n - 1)*(e + f* x)^(p - 1)*Simp[d*e*n + c*f*p + d*f*(n + p)*x, x], x], x] /; FreeQ[{a, b, c , d, e, f}, x] && LtQ[m, -1] && GtQ[n, 0] && GtQ[p, 0] && (IntegersQ[2*m, 2 *n, 2*p] || IntegersQ[m, n + p] || IntegersQ[p, m + n])
Int[Sqrt[(e_.) + (f_.)*(x_)]/(Sqrt[(a_) + (b_.)*(x_)]*Sqrt[(c_) + (d_.)*(x_ )]), x_] :> Simp[(2/b)*Rt[-(b*e - a*f)/d, 2]*EllipticE[ArcSin[Sqrt[a + b*x] /Rt[-(b*c - a*d)/d, 2]], f*((b*c - a*d)/(d*(b*e - a*f)))], x] /; FreeQ[{a, b, c, d, e, f}, x] && GtQ[b/(b*c - a*d), 0] && GtQ[b/(b*e - a*f), 0] && !L tQ[-(b*c - a*d)/d, 0] && !(SimplerQ[c + d*x, a + b*x] && GtQ[-d/(b*c - a*d ), 0] && GtQ[d/(d*e - c*f), 0] && !LtQ[(b*c - a*d)/b, 0])
Int[1/(Sqrt[(a_) + (b_.)*(x_)]*Sqrt[(c_) + (d_.)*(x_)]*Sqrt[(e_) + (f_.)*(x _)]), x_] :> Simp[2*(Rt[-b/d, 2]/(b*Sqrt[(b*e - a*f)/b]))*EllipticF[ArcSin[ Sqrt[a + b*x]/(Rt[-b/d, 2]*Sqrt[(b*c - a*d)/b])], f*((b*c - a*d)/(d*(b*e - a*f)))], x] /; FreeQ[{a, b, c, d, e, f}, x] && GtQ[(b*c - a*d)/b, 0] && GtQ [(b*e - a*f)/b, 0] && PosQ[-b/d] && !(SimplerQ[c + d*x, a + b*x] && GtQ[(d *e - c*f)/d, 0] && GtQ[-d/b, 0]) && !(SimplerQ[c + d*x, a + b*x] && GtQ[(( -b)*e + a*f)/f, 0] && GtQ[-f/b, 0]) && !(SimplerQ[e + f*x, a + b*x] && GtQ [((-d)*e + c*f)/f, 0] && GtQ[((-b)*e + a*f)/f, 0] && (PosQ[-f/d] || PosQ[-f /b]))
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_) )^(p_)*((g_.) + (h_.)*(x_)), x_] :> Simp[(b*g - a*h)*(a + b*x)^(m + 1)*(c + d*x)^n*((e + f*x)^(p + 1)/(b*(b*e - a*f)*(m + 1))), x] - Simp[1/(b*(b*e - a*f)*(m + 1)) Int[(a + b*x)^(m + 1)*(c + d*x)^(n - 1)*(e + f*x)^p*Simp[b* c*(f*g - e*h)*(m + 1) + (b*g - a*h)*(d*e*n + c*f*(p + 1)) + d*(b*(f*g - e*h )*(m + 1) + f*(b*g - a*h)*(n + p + 1))*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, g, h, p}, x] && LtQ[m, -1] && GtQ[n, 0] && IntegersQ[2*m, 2*n, 2*p]
Int[((g_.) + (h_.)*(x_))/(Sqrt[(a_.) + (b_.)*(x_)]*Sqrt[(c_) + (d_.)*(x_)]* Sqrt[(e_) + (f_.)*(x_)]), x_] :> Simp[h/f Int[Sqrt[e + f*x]/(Sqrt[a + b*x ]*Sqrt[c + d*x]), x], x] + Simp[(f*g - e*h)/f Int[1/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]), x], x] /; FreeQ[{a, b, c, d, e, f, g, h}, x] && Sim plerQ[a + b*x, e + f*x] && SimplerQ[c + d*x, e + f*x]
Leaf count of result is larger than twice the leaf count of optimal. \(214\) vs. \(2(93)=186\).
Time = 0.30 (sec) , antiderivative size = 215, normalized size of antiderivative = 1.67
| method | result | size |
| default | \(-\frac {\left (10593 \sqrt {2}\, \operatorname {EllipticF}\left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}+1482 \sqrt {2}\, \operatorname {EllipticE}\left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}+7062 \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \operatorname {EllipticF}\left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )+988 \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \operatorname {EllipticE}\left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )+25560 x^{3}+19176 x^{2}-6006 x -4986\right ) \sqrt {1-2 x}\, \sqrt {3+5 x}}{567 \left (10 x^{2}+x -3\right ) \left (2+3 x \right )^{\frac {3}{2}}}\) | \(215\) |
| elliptic | \(\frac {\sqrt {-\left (3+5 x \right ) \left (-1+2 x \right ) \left (2+3 x \right )}\, \left (\frac {2 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{243 \left (\frac {2}{3}+x \right )^{2}}-\frac {284 \left (-30 x^{2}-3 x +9\right )}{567 \sqrt {\left (\frac {2}{3}+x \right ) \left (-30 x^{2}-3 x +9\right )}}-\frac {305 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \operatorname {EllipticF}\left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{3969 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}-\frac {2470 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \left (-\frac {\operatorname {EllipticE}\left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{15}-\frac {3 \operatorname {EllipticF}\left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{5}\right )}{3969 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}\right )}{\sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}\) | \(225\) |
Input:
int((1-2*x)^(1/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2),x,method=_RETURNVERBOSE)
Output:
-1/567*(10593*2^(1/2)*EllipticF(1/7*(28+42*x)^(1/2),1/2*70^(1/2))*x*(2+3*x )^(1/2)*(-3-5*x)^(1/2)*(1-2*x)^(1/2)+1482*2^(1/2)*EllipticE(1/7*(28+42*x)^ (1/2),1/2*70^(1/2))*x*(2+3*x)^(1/2)*(-3-5*x)^(1/2)*(1-2*x)^(1/2)+7062*2^(1 /2)*(2+3*x)^(1/2)*(-3-5*x)^(1/2)*(1-2*x)^(1/2)*EllipticF(1/7*(28+42*x)^(1/ 2),1/2*70^(1/2))+988*2^(1/2)*(2+3*x)^(1/2)*(-3-5*x)^(1/2)*(1-2*x)^(1/2)*El lipticE(1/7*(28+42*x)^(1/2),1/2*70^(1/2))+25560*x^3+19176*x^2-6006*x-4986) *(1-2*x)^(1/2)*(3+5*x)^(1/2)/(10*x^2+x-3)/(2+3*x)^(3/2)
Time = 0.10 (sec) , antiderivative size = 88, normalized size of antiderivative = 0.68 \[ \int \frac {\sqrt {1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{5/2}} \, dx=-\frac {2 \, {\left (135 \, {\left (426 \, x + 277\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1} + 1468 \, \sqrt {-30} {\left (9 \, x^{2} + 12 \, x + 4\right )} {\rm weierstrassPInverse}\left (\frac {1159}{675}, \frac {38998}{91125}, x + \frac {23}{90}\right ) + 11115 \, \sqrt {-30} {\left (9 \, x^{2} + 12 \, x + 4\right )} {\rm weierstrassZeta}\left (\frac {1159}{675}, \frac {38998}{91125}, {\rm weierstrassPInverse}\left (\frac {1159}{675}, \frac {38998}{91125}, x + \frac {23}{90}\right )\right )\right )}}{25515 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \] Input:
integrate((1-2*x)^(1/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2),x, algorithm="fricas")
Output:
-2/25515*(135*(426*x + 277)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1) + 1 468*sqrt(-30)*(9*x^2 + 12*x + 4)*weierstrassPInverse(1159/675, 38998/91125 , x + 23/90) + 11115*sqrt(-30)*(9*x^2 + 12*x + 4)*weierstrassZeta(1159/675 , 38998/91125, weierstrassPInverse(1159/675, 38998/91125, x + 23/90)))/(9* x^2 + 12*x + 4)
\[ \int \frac {\sqrt {1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{5/2}} \, dx=\int \frac {\sqrt {1 - 2 x} \left (5 x + 3\right )^{\frac {3}{2}}}{\left (3 x + 2\right )^{\frac {5}{2}}}\, dx \] Input:
integrate((1-2*x)**(1/2)*(3+5*x)**(3/2)/(2+3*x)**(5/2),x)
Output:
Integral(sqrt(1 - 2*x)*(5*x + 3)**(3/2)/(3*x + 2)**(5/2), x)
\[ \int \frac {\sqrt {1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{5/2}} \, dx=\int { \frac {{\left (5 \, x + 3\right )}^{\frac {3}{2}} \sqrt {-2 \, x + 1}}{{\left (3 \, x + 2\right )}^{\frac {5}{2}}} \,d x } \] Input:
integrate((1-2*x)^(1/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2),x, algorithm="maxima")
Output:
integrate((5*x + 3)^(3/2)*sqrt(-2*x + 1)/(3*x + 2)^(5/2), x)
\[ \int \frac {\sqrt {1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{5/2}} \, dx=\int { \frac {{\left (5 \, x + 3\right )}^{\frac {3}{2}} \sqrt {-2 \, x + 1}}{{\left (3 \, x + 2\right )}^{\frac {5}{2}}} \,d x } \] Input:
integrate((1-2*x)^(1/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2),x, algorithm="giac")
Output:
integrate((5*x + 3)^(3/2)*sqrt(-2*x + 1)/(3*x + 2)^(5/2), x)
Timed out. \[ \int \frac {\sqrt {1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{5/2}} \, dx=\int \frac {\sqrt {1-2\,x}\,{\left (5\,x+3\right )}^{3/2}}{{\left (3\,x+2\right )}^{5/2}} \,d x \] Input:
int(((1 - 2*x)^(1/2)*(5*x + 3)^(3/2))/(3*x + 2)^(5/2),x)
Output:
int(((1 - 2*x)^(1/2)*(5*x + 3)^(3/2))/(3*x + 2)^(5/2), x)
\[ \int \frac {\sqrt {1-2 x} (3+5 x)^{3/2}}{(2+3 x)^{5/2}} \, dx=\frac {340 \sqrt {3 x +2}\, \sqrt {5 x +3}\, \sqrt {-2 x +1}\, x -222 \sqrt {3 x +2}\, \sqrt {5 x +3}\, \sqrt {-2 x +1}-120240 \left (\int \frac {\sqrt {3 x +2}\, \sqrt {5 x +3}\, \sqrt {-2 x +1}\, x^{2}}{270 x^{5}+567 x^{4}+333 x^{3}-46 x^{2}-100 x -24}d x \right ) x^{2}-160320 \left (\int \frac {\sqrt {3 x +2}\, \sqrt {5 x +3}\, \sqrt {-2 x +1}\, x^{2}}{270 x^{5}+567 x^{4}+333 x^{3}-46 x^{2}-100 x -24}d x \right ) x -53440 \left (\int \frac {\sqrt {3 x +2}\, \sqrt {5 x +3}\, \sqrt {-2 x +1}\, x^{2}}{270 x^{5}+567 x^{4}+333 x^{3}-46 x^{2}-100 x -24}d x \right )+39069 \left (\int \frac {\sqrt {3 x +2}\, \sqrt {5 x +3}\, \sqrt {-2 x +1}}{270 x^{5}+567 x^{4}+333 x^{3}-46 x^{2}-100 x -24}d x \right ) x^{2}+52092 \left (\int \frac {\sqrt {3 x +2}\, \sqrt {5 x +3}\, \sqrt {-2 x +1}}{270 x^{5}+567 x^{4}+333 x^{3}-46 x^{2}-100 x -24}d x \right ) x +17364 \left (\int \frac {\sqrt {3 x +2}\, \sqrt {5 x +3}\, \sqrt {-2 x +1}}{270 x^{5}+567 x^{4}+333 x^{3}-46 x^{2}-100 x -24}d x \right )}{918 x^{2}+1224 x +408} \] Input:
int((1-2*x)^(1/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2),x)
Output:
(340*sqrt(3*x + 2)*sqrt(5*x + 3)*sqrt( - 2*x + 1)*x - 222*sqrt(3*x + 2)*sq rt(5*x + 3)*sqrt( - 2*x + 1) - 120240*int((sqrt(3*x + 2)*sqrt(5*x + 3)*sqr t( - 2*x + 1)*x**2)/(270*x**5 + 567*x**4 + 333*x**3 - 46*x**2 - 100*x - 24 ),x)*x**2 - 160320*int((sqrt(3*x + 2)*sqrt(5*x + 3)*sqrt( - 2*x + 1)*x**2) /(270*x**5 + 567*x**4 + 333*x**3 - 46*x**2 - 100*x - 24),x)*x - 53440*int( (sqrt(3*x + 2)*sqrt(5*x + 3)*sqrt( - 2*x + 1)*x**2)/(270*x**5 + 567*x**4 + 333*x**3 - 46*x**2 - 100*x - 24),x) + 39069*int((sqrt(3*x + 2)*sqrt(5*x + 3)*sqrt( - 2*x + 1))/(270*x**5 + 567*x**4 + 333*x**3 - 46*x**2 - 100*x - 24),x)*x**2 + 52092*int((sqrt(3*x + 2)*sqrt(5*x + 3)*sqrt( - 2*x + 1))/(27 0*x**5 + 567*x**4 + 333*x**3 - 46*x**2 - 100*x - 24),x)*x + 17364*int((sqr t(3*x + 2)*sqrt(5*x + 3)*sqrt( - 2*x + 1))/(270*x**5 + 567*x**4 + 333*x**3 - 46*x**2 - 100*x - 24),x))/(102*(9*x**2 + 12*x + 4))