\(\int \frac {(2-5 x) (2+5 x+3 x^2)^{3/2}}{x^{7/2}} \, dx\) [195]

Optimal result

Integrand size = 25, antiderivative size = 181 \[ \int \frac {(2-5 x) \left (2+5 x+3 x^2\right )^{3/2}}{x^{7/2}} \, dx=-\frac {1418 \sqrt {x} (2+3 x)}{15 \sqrt {2+5 x+3 x^2}}+\frac {2 (89-35 x) \sqrt {2+5 x+3 x^2}}{5 \sqrt {x}}-\frac {4 (3-5 x) \left (2+5 x+3 x^2\right )^{3/2}}{15 x^{5/2}}+\frac {1418 \sqrt {2} \sqrt {2+5 x+3 x^2} E\left (\arctan \left (\sqrt {x}\right )|-\frac {1}{2}\right )}{15 \sqrt {1+x} \sqrt {2+3 x}}-\frac {117 \sqrt {2} \sqrt {1+x} \sqrt {2+3 x} \operatorname {EllipticF}\left (\arctan \left (\sqrt {x}\right ),-\frac {1}{2}\right )}{\sqrt {2+5 x+3 x^2}} \] Output:

-1418/15*x^(1/2)*(2+3*x)/(3*x^2+5*x+2)^(1/2)+2/5*(89-35*x)*(3*x^2+5*x+2)^( 
1/2)/x^(1/2)-4/15*(3-5*x)*(3*x^2+5*x+2)^(3/2)/x^(5/2)+1418/15*2^(1/2)*(3*x 
^2+5*x+2)^(1/2)*EllipticE(x^(1/2)/(1+x)^(1/2),1/2*I*2^(1/2))/(1+x)^(1/2)/( 
2+3*x)^(1/2)-117*2^(1/2)*(1+x)^(1/2)*(2+3*x)^(1/2)*InverseJacobiAM(arctan( 
x^(1/2)),1/2*I*2^(1/2))/(3*x^2+5*x+2)^(1/2)
 

Mathematica [C] (verified)

Result contains complex when optimal does not.

Time = 21.22 (sec) , antiderivative size = 163, normalized size of antiderivative = 0.90 \[ \int \frac {(2-5 x) \left (2+5 x+3 x^2\right )^{3/2}}{x^{7/2}} \, dx=\frac {-2 \left (24+80 x+906 x^2+2230 x^3+1605 x^4+225 x^5\right )-1418 i \sqrt {2} \sqrt {1+\frac {1}{x}} \sqrt {3+\frac {2}{x}} x^{7/2} E\left (i \text {arcsinh}\left (\frac {\sqrt {\frac {2}{3}}}{\sqrt {x}}\right )|\frac {3}{2}\right )-337 i \sqrt {2} \sqrt {1+\frac {1}{x}} \sqrt {3+\frac {2}{x}} x^{7/2} \operatorname {EllipticF}\left (i \text {arcsinh}\left (\frac {\sqrt {\frac {2}{3}}}{\sqrt {x}}\right ),\frac {3}{2}\right )}{15 x^{5/2} \sqrt {2+5 x+3 x^2}} \] Input:

Integrate[((2 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/x^(7/2),x]
 

Output:

(-2*(24 + 80*x + 906*x^2 + 2230*x^3 + 1605*x^4 + 225*x^5) - (1418*I)*Sqrt[ 
2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(7/2)*EllipticE[I*ArcSinh[Sqrt[2/3]/Sq 
rt[x]], 3/2] - (337*I)*Sqrt[2]*Sqrt[1 + x^(-1)]*Sqrt[3 + 2/x]*x^(7/2)*Elli 
pticF[I*ArcSinh[Sqrt[2/3]/Sqrt[x]], 3/2])/(15*x^(5/2)*Sqrt[2 + 5*x + 3*x^2 
])
 

Rubi [A] (verified)

Time = 0.38 (sec) , antiderivative size = 194, normalized size of antiderivative = 1.07, number of steps used = 8, number of rules used = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.280, Rules used = {1229, 1230, 27, 1240, 1503, 1413, 1456}

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.

\(\displaystyle \int \frac {(2-5 x) \left (3 x^2+5 x+2\right )^{3/2}}{x^{7/2}} \, dx\)

\(\Big \downarrow \) 1229

\(\displaystyle -\frac {1}{5} \int \frac {(105 x+89) \sqrt {3 x^2+5 x+2}}{x^{3/2}}dx-\frac {4 (3-5 x) \left (3 x^2+5 x+2\right )^{3/2}}{15 x^{5/2}}\)

\(\Big \downarrow \) 1230

\(\displaystyle \frac {1}{5} \left (\frac {2}{3} \int -\frac {3 (709 x+585)}{2 \sqrt {x} \sqrt {3 x^2+5 x+2}}dx+\frac {2 \sqrt {3 x^2+5 x+2} (89-35 x)}{\sqrt {x}}\right )-\frac {4 (3-5 x) \left (3 x^2+5 x+2\right )^{3/2}}{15 x^{5/2}}\)

\(\Big \downarrow \) 27

\(\displaystyle \frac {1}{5} \left (\frac {2 (89-35 x) \sqrt {3 x^2+5 x+2}}{\sqrt {x}}-\int \frac {709 x+585}{\sqrt {x} \sqrt {3 x^2+5 x+2}}dx\right )-\frac {4 (3-5 x) \left (3 x^2+5 x+2\right )^{3/2}}{15 x^{5/2}}\)

\(\Big \downarrow \) 1240

\(\displaystyle \frac {1}{5} \left (\frac {2 (89-35 x) \sqrt {3 x^2+5 x+2}}{\sqrt {x}}-2 \int \frac {709 x+585}{\sqrt {3 x^2+5 x+2}}d\sqrt {x}\right )-\frac {4 (3-5 x) \left (3 x^2+5 x+2\right )^{3/2}}{15 x^{5/2}}\)

\(\Big \downarrow \) 1503

\(\displaystyle \frac {1}{5} \left (\frac {2 (89-35 x) \sqrt {3 x^2+5 x+2}}{\sqrt {x}}-2 \left (585 \int \frac {1}{\sqrt {3 x^2+5 x+2}}d\sqrt {x}+709 \int \frac {x}{\sqrt {3 x^2+5 x+2}}d\sqrt {x}\right )\right )-\frac {4 (3-5 x) \left (3 x^2+5 x+2\right )^{3/2}}{15 x^{5/2}}\)

\(\Big \downarrow \) 1413

\(\displaystyle \frac {1}{5} \left (\frac {2 (89-35 x) \sqrt {3 x^2+5 x+2}}{\sqrt {x}}-2 \left (709 \int \frac {x}{\sqrt {3 x^2+5 x+2}}d\sqrt {x}+\frac {585 (x+1) \sqrt {\frac {3 x+2}{x+1}} \operatorname {EllipticF}\left (\arctan \left (\sqrt {x}\right ),-\frac {1}{2}\right )}{\sqrt {2} \sqrt {3 x^2+5 x+2}}\right )\right )-\frac {4 (3-5 x) \left (3 x^2+5 x+2\right )^{3/2}}{15 x^{5/2}}\)

\(\Big \downarrow \) 1456

\(\displaystyle \frac {1}{5} \left (\frac {2 (89-35 x) \sqrt {3 x^2+5 x+2}}{\sqrt {x}}-2 \left (\frac {585 (x+1) \sqrt {\frac {3 x+2}{x+1}} \operatorname {EllipticF}\left (\arctan \left (\sqrt {x}\right ),-\frac {1}{2}\right )}{\sqrt {2} \sqrt {3 x^2+5 x+2}}+709 \left (\frac {\sqrt {x} (3 x+2)}{3 \sqrt {3 x^2+5 x+2}}-\frac {\sqrt {2} (x+1) \sqrt {\frac {3 x+2}{x+1}} E\left (\arctan \left (\sqrt {x}\right )|-\frac {1}{2}\right )}{3 \sqrt {3 x^2+5 x+2}}\right )\right )\right )-\frac {4 (3-5 x) \left (3 x^2+5 x+2\right )^{3/2}}{15 x^{5/2}}\)

Input:

Int[((2 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/x^(7/2),x]
 

Output:

(-4*(3 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/(15*x^(5/2)) + ((2*(89 - 35*x)*Sqrt 
[2 + 5*x + 3*x^2])/Sqrt[x] - 2*(709*((Sqrt[x]*(2 + 3*x))/(3*Sqrt[2 + 5*x + 
 3*x^2]) - (Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[ 
x]], -1/2])/(3*Sqrt[2 + 5*x + 3*x^2])) + (585*(1 + x)*Sqrt[(2 + 3*x)/(1 + 
x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(Sqrt[2]*Sqrt[2 + 5*x + 3*x^2])))/5
 

Defintions of rubi rules used

rule 27

Int[(a_)*(Fx_), x_Symbol] :> Simp[a   Int[Fx, x], x] /; FreeQ[a, x] &&  !Ma 
tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
 

rule 1229

Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c 
_.)*(x_)^2)^(p_.), x_Symbol] :> Simp[(-(d + e*x)^(m + 1))*((a + b*x + c*x^2 
)^p/(e^2*(m + 1)*(m + 2)*(c*d^2 - b*d*e + a*e^2)))*((d*g - e*f*(m + 2))*(c* 
d^2 - b*d*e + a*e^2) - d*p*(2*c*d - b*e)*(e*f - d*g) - e*(g*(m + 1)*(c*d^2 
- b*d*e + a*e^2) + p*(2*c*d - b*e)*(e*f - d*g))*x), x] - Simp[p/(e^2*(m + 1 
)*(m + 2)*(c*d^2 - b*d*e + a*e^2))   Int[(d + e*x)^(m + 2)*(a + b*x + c*x^2 
)^(p - 1)*Simp[2*a*c*e*(e*f - d*g)*(m + 2) + b^2*e*(d*g*(p + 1) - e*f*(m + 
p + 2)) + b*(a*e^2*g*(m + 1) - c*d*(d*g*(2*p + 1) - e*f*(m + 2*p + 2))) - c 
*(2*c*d*(d*g*(2*p + 1) - e*f*(m + 2*p + 2)) - e*(2*a*e*g*(m + 1) - b*(d*g*( 
m - 2*p) + e*f*(m + 2*p + 2))))*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, g 
}, x] && GtQ[p, 0] && LtQ[m, -2] && LtQ[m + 2*p, 0] &&  !ILtQ[m + 2*p + 3, 
0]
 

rule 1230

Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c 
_.)*(x_)^2)^(p_.), x_Symbol] :> Simp[(d + e*x)^(m + 1)*(e*f*(m + 2*p + 2) - 
 d*g*(2*p + 1) + e*g*(m + 1)*x)*((a + b*x + c*x^2)^p/(e^2*(m + 1)*(m + 2*p 
+ 2))), x] + Simp[p/(e^2*(m + 1)*(m + 2*p + 2))   Int[(d + e*x)^(m + 1)*(a 
+ b*x + c*x^2)^(p - 1)*Simp[g*(b*d + 2*a*e + 2*a*e*m + 2*b*d*p) - f*b*e*(m 
+ 2*p + 2) + (g*(2*c*d + b*e + b*e*m + 4*c*d*p) - 2*c*e*f*(m + 2*p + 2))*x, 
 x], x], x] /; FreeQ[{a, b, c, d, e, f, g, m}, x] && GtQ[p, 0] && (LtQ[m, - 
1] || EqQ[p, 1] || (IntegerQ[p] &&  !RationalQ[m])) && NeQ[m, -1] &&  !ILtQ 
[m + 2*p + 1, 0] && (IntegerQ[m] || IntegerQ[p] || IntegersQ[2*m, 2*p])
 

rule 1240

Int[((f_) + (g_.)*(x_))/(Sqrt[x_]*Sqrt[(a_) + (b_.)*(x_) + (c_.)*(x_)^2]), 
x_Symbol] :> Simp[2   Subst[Int[(f + g*x^2)/Sqrt[a + b*x^2 + c*x^4], x], x, 
 Sqrt[x]], x] /; FreeQ[{a, b, c, f, g}, x]
 

rule 1413

Int[1/Sqrt[(a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4], x_Symbol] :> With[{q = Rt[b 
^2 - 4*a*c, 2]}, Simp[(2*a + (b - q)*x^2)*(Sqrt[(2*a + (b + q)*x^2)/(2*a + 
(b - q)*x^2)]/(2*a*Rt[(b - q)/(2*a), 2]*Sqrt[a + b*x^2 + c*x^4]))*EllipticF 
[ArcTan[Rt[(b - q)/(2*a), 2]*x], -2*(q/(b - q))], x] /; PosQ[(b - q)/a]] /; 
 FreeQ[{a, b, c}, x] && GtQ[b^2 - 4*a*c, 0]
 

rule 1456

Int[(x_)^2/Sqrt[(a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4], x_Symbol] :> With[{q = 
 Rt[b^2 - 4*a*c, 2]}, Simp[x*((b - q + 2*c*x^2)/(2*c*Sqrt[a + b*x^2 + c*x^4 
])), x] - Simp[Rt[(b - q)/(2*a), 2]*(2*a + (b - q)*x^2)*(Sqrt[(2*a + (b + q 
)*x^2)/(2*a + (b - q)*x^2)]/(2*c*Sqrt[a + b*x^2 + c*x^4]))*EllipticE[ArcTan 
[Rt[(b - q)/(2*a), 2]*x], -2*(q/(b - q))], x] /; PosQ[(b - q)/a]] /; FreeQ[ 
{a, b, c}, x] && GtQ[b^2 - 4*a*c, 0]
 

rule 1503

Int[((d_) + (e_.)*(x_)^2)/Sqrt[(a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4], x_Symbo 
l] :> With[{q = Rt[b^2 - 4*a*c, 2]}, Simp[d   Int[1/Sqrt[a + b*x^2 + c*x^4] 
, x], x] + Simp[e   Int[x^2/Sqrt[a + b*x^2 + c*x^4], x], x] /; PosQ[(b + q) 
/a] || PosQ[(b - q)/a]] /; FreeQ[{a, b, c, d, e}, x] && GtQ[b^2 - 4*a*c, 0]
 

Maple [A] (verified)

Time = 0.94 (sec) , antiderivative size = 129, normalized size of antiderivative = 0.71

method	result	size
default	\(\frac {372 \operatorname {EllipticF}\left (\frac {\sqrt {6 x +4}}{2}, i \sqrt {2}\right ) \sqrt {6 x +4}\, \sqrt {3+3 x}\, \sqrt {6}\, \sqrt {-x}\, x^{2}-709 \operatorname {EllipticE}\left (\frac {\sqrt {6 x +4}}{2}, i \sqrt {2}\right ) \sqrt {6 x +4}\, \sqrt {3+3 x}\, \sqrt {6}\, \sqrt {-x}\, x^{2}-1350 x^{5}+3132 x^{4}+7890 x^{3}+3072 x^{2}-480 x -144}{45 \sqrt {3 x^{2}+5 x +2}\, x^{\frac {5}{2}}}\)	\(129\)
elliptic	\(\frac {\sqrt {\left (3 x^{2}+5 x +2\right ) x}\, \left (-\frac {8 \sqrt {3 x^{3}+5 x^{2}+2 x}}{5 x^{3}}-\frac {4 \sqrt {3 x^{3}+5 x^{2}+2 x}}{3 x^{2}}+\frac {\frac {598}{5} x^{2}+\frac {598}{3} x +\frac {1196}{15}}{\sqrt {\left (3 x^{2}+5 x +2\right ) x}}-10 \sqrt {3 x^{3}+5 x^{2}+2 x}-\frac {39 \sqrt {6 x +4}\, \sqrt {3+3 x}\, \sqrt {-6 x}\, \operatorname {EllipticF}\left (\frac {\sqrt {6 x +4}}{2}, i \sqrt {2}\right )}{\sqrt {3 x^{3}+5 x^{2}+2 x}}-\frac {709 \sqrt {6 x +4}\, \sqrt {3+3 x}\, \sqrt {-6 x}\, \left (\frac {\operatorname {EllipticE}\left (\frac {\sqrt {6 x +4}}{2}, i \sqrt {2}\right )}{3}-\operatorname {EllipticF}\left (\frac {\sqrt {6 x +4}}{2}, i \sqrt {2}\right )\right )}{15 \sqrt {3 x^{3}+5 x^{2}+2 x}}\right )}{\sqrt {x}\, \sqrt {3 x^{2}+5 x +2}}\)	\(245\)

Input:

int((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(7/2),x,method=_RETURNVERBOSE)
 

Output:

1/45*(372*EllipticF(1/2*(6*x+4)^(1/2),I*2^(1/2))*(6*x+4)^(1/2)*(3+3*x)^(1/ 
2)*6^(1/2)*(-x)^(1/2)*x^2-709*EllipticE(1/2*(6*x+4)^(1/2),I*2^(1/2))*(6*x+ 
4)^(1/2)*(3+3*x)^(1/2)*6^(1/2)*(-x)^(1/2)*x^2-1350*x^5+3132*x^4+7890*x^3+3 
072*x^2-480*x-144)/(3*x^2+5*x+2)^(1/2)/x^(5/2)
 

Fricas [A] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 69, normalized size of antiderivative = 0.38 \[ \int \frac {(2-5 x) \left (2+5 x+3 x^2\right )^{3/2}}{x^{7/2}} \, dx=-\frac {2 \, {\left (1720 \, \sqrt {3} x^{3} {\rm weierstrassPInverse}\left (\frac {28}{27}, \frac {80}{729}, x + \frac {5}{9}\right ) - 6381 \, \sqrt {3} x^{3} {\rm weierstrassZeta}\left (\frac {28}{27}, \frac {80}{729}, {\rm weierstrassPInverse}\left (\frac {28}{27}, \frac {80}{729}, x + \frac {5}{9}\right )\right ) + 9 \, {\left (75 \, x^{3} - 299 \, x^{2} + 10 \, x + 12\right )} \sqrt {3 \, x^{2} + 5 \, x + 2} \sqrt {x}\right )}}{135 \, x^{3}} \] Input:

integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(7/2),x, algorithm="fricas")
 

Output:

-2/135*(1720*sqrt(3)*x^3*weierstrassPInverse(28/27, 80/729, x + 5/9) - 638 
1*sqrt(3)*x^3*weierstrassZeta(28/27, 80/729, weierstrassPInverse(28/27, 80 
/729, x + 5/9)) + 9*(75*x^3 - 299*x^2 + 10*x + 12)*sqrt(3*x^2 + 5*x + 2)*s 
qrt(x))/x^3
 

Sympy [F]

\[ \int \frac {(2-5 x) \left (2+5 x+3 x^2\right )^{3/2}}{x^{7/2}} \, dx=- \int \left (- \frac {4 \sqrt {3 x^{2} + 5 x + 2}}{x^{\frac {7}{2}}}\right )\, dx - \int \frac {19 \sqrt {3 x^{2} + 5 x + 2}}{x^{\frac {3}{2}}}\, dx - \int \frac {15 \sqrt {3 x^{2} + 5 x + 2}}{\sqrt {x}}\, dx \] Input:

integrate((2-5*x)*(3*x**2+5*x+2)**(3/2)/x**(7/2),x)
 

Output:

-Integral(-4*sqrt(3*x**2 + 5*x + 2)/x**(7/2), x) - Integral(19*sqrt(3*x**2 
 + 5*x + 2)/x**(3/2), x) - Integral(15*sqrt(3*x**2 + 5*x + 2)/sqrt(x), x)
 

Maxima [F]

\[ \int \frac {(2-5 x) \left (2+5 x+3 x^2\right )^{3/2}}{x^{7/2}} \, dx=\int { -\frac {{\left (3 \, x^{2} + 5 \, x + 2\right )}^{\frac {3}{2}} {\left (5 \, x - 2\right )}}{x^{\frac {7}{2}}} \,d x } \] Input:

integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(7/2),x, algorithm="maxima")
 

Output:

-integrate((3*x^2 + 5*x + 2)^(3/2)*(5*x - 2)/x^(7/2), x)
 

Giac [F]

\[ \int \frac {(2-5 x) \left (2+5 x+3 x^2\right )^{3/2}}{x^{7/2}} \, dx=\int { -\frac {{\left (3 \, x^{2} + 5 \, x + 2\right )}^{\frac {3}{2}} {\left (5 \, x - 2\right )}}{x^{\frac {7}{2}}} \,d x } \] Input:

integrate((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(7/2),x, algorithm="giac")
 

Output:

integrate(-(3*x^2 + 5*x + 2)^(3/2)*(5*x - 2)/x^(7/2), x)
 

Mupad [F(-1)]

Timed out. \[ \int \frac {(2-5 x) \left (2+5 x+3 x^2\right )^{3/2}}{x^{7/2}} \, dx=\int -\frac {\left (5\,x-2\right )\,{\left (3\,x^2+5\,x+2\right )}^{3/2}}{x^{7/2}} \,d x \] Input:

int(-((5*x - 2)*(5*x + 3*x^2 + 2)^(3/2))/x^(7/2),x)
 

Output:

int(-((5*x - 2)*(5*x + 3*x^2 + 2)^(3/2))/x^(7/2), x)
 

Reduce [F]

\[ \int \frac {(2-5 x) \left (2+5 x+3 x^2\right )^{3/2}}{x^{7/2}} \, dx=\frac {-600 \sqrt {3 x^{2}+5 x +2}\, x^{3}-21008 \sqrt {3 x^{2}+5 x +2}\, x^{2}+4600 \sqrt {3 x^{2}+5 x +2}\, x -96 \sqrt {3 x^{2}+5 x +2}+14040 \sqrt {x}\, \left (\int \frac {\sqrt {3 x^{2}+5 x +2}}{3 \sqrt {x}\, x^{4}+5 \sqrt {x}\, x^{3}+2 \sqrt {x}\, x^{2}}d x \right ) x^{2}+9477 \sqrt {x}\, \left (\int \frac {\sqrt {3 x^{2}+5 x +2}\, x}{3 \sqrt {x}\, x^{2}+5 \sqrt {x}\, x +2 \sqrt {x}}d x \right ) x^{2}+17115 \sqrt {x}\, \left (\int \frac {\sqrt {x}\, \sqrt {3 x^{2}+5 x +2}}{3 x^{2}+5 x +2}d x \right ) x^{2}}{60 \sqrt {x}\, x^{2}} \] Input:

int((2-5*x)*(3*x^2+5*x+2)^(3/2)/x^(7/2),x)
 

Output:

( - 600*sqrt(3*x**2 + 5*x + 2)*x**3 - 21008*sqrt(3*x**2 + 5*x + 2)*x**2 + 
4600*sqrt(3*x**2 + 5*x + 2)*x - 96*sqrt(3*x**2 + 5*x + 2) + 14040*sqrt(x)* 
int(sqrt(3*x**2 + 5*x + 2)/(3*sqrt(x)*x**4 + 5*sqrt(x)*x**3 + 2*sqrt(x)*x* 
*2),x)*x**2 + 9477*sqrt(x)*int((sqrt(3*x**2 + 5*x + 2)*x)/(3*sqrt(x)*x**2 
+ 5*sqrt(x)*x + 2*sqrt(x)),x)*x**2 + 17115*sqrt(x)*int((sqrt(x)*sqrt(3*x** 
2 + 5*x + 2))/(3*x**2 + 5*x + 2),x)*x**2)/(60*sqrt(x)*x**2)