3.1024 \(\int \frac{x}{\sqrt{-44375 b^4+576000 b^3 c x+576000 b^2 c^2 x^2+5308416 c^4 x^4}} \, dx\)
Optimal. Leaf size=177 \[ \frac{\log \left (32462531054272512000 b^2 c^{10} x^6+21641687369515008000 b^3 c^9 x^5+951050714480640000 b^4 c^8 x^4+2583100705996800000 b^5 c^7 x^3+597005697024000000 b^6 c^6 x^2+5308416 \sqrt{576000 b^2 c^2 x^2+576000 b^3 c x-44375 b^4+5308416 c^4 x^4} \left (1990656000 b^2 c^8 x^4+1105920000 b^3 c^7 x^3+38880000 b^4 c^6 x^2+79200000 b^5 c^5 x+12203125 b^6 c^4+12230590464 c^{10} x^6\right )+20738073600000000 b^8 c^4+149587343098087735296 c^{12} x^8\right )}{18432 c^2} \]
[Out]
Log[20738073600000000*b^8*c^4 + 597005697024000000*b^6*c^6*x^2 + 2583100705996800000*b^5*c^7*x^3 + 95105071448
0640000*b^4*c^8*x^4 + 21641687369515008000*b^3*c^9*x^5 + 32462531054272512000*b^2*c^10*x^6 + 14958734309808773
5296*c^12*x^8 + 5308416*Sqrt[-44375*b^4 + 576000*b^3*c*x + 576000*b^2*c^2*x^2 + 5308416*c^4*x^4]*(12203125*b^6
*c^4 + 79200000*b^5*c^5*x + 38880000*b^4*c^6*x^2 + 1105920000*b^3*c^7*x^3 + 1990656000*b^2*c^8*x^4 + 122305904
64*c^10*x^6)]/(18432*c^2)
________________________________________________________________________________________
Rubi [A] time = 0.0888565, antiderivative size = 177, normalized size of antiderivative = 1.,
number of steps used = 1, number of rules used = 1, integrand size = 38, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.026, Rules used =
{2082} \[ \frac{\log \left (32462531054272512000 b^2 c^{10} x^6+21641687369515008000 b^3 c^9 x^5+951050714480640000 b^4 c^8 x^4+2583100705996800000 b^5 c^7 x^3+597005697024000000 b^6 c^6 x^2+5308416 \sqrt{576000 b^2 c^2 x^2+576000 b^3 c x-44375 b^4+5308416 c^4 x^4} \left (1990656000 b^2 c^8 x^4+1105920000 b^3 c^7 x^3+38880000 b^4 c^6 x^2+79200000 b^5 c^5 x+12203125 b^6 c^4+12230590464 c^{10} x^6\right )+20738073600000000 b^8 c^4+149587343098087735296 c^{12} x^8\right )}{18432 c^2} \]
Antiderivative was successfully verified.
[In]
Int[x/Sqrt[-44375*b^4 + 576000*b^3*c*x + 576000*b^2*c^2*x^2 + 5308416*c^4*x^4],x]
[Out]
Log[20738073600000000*b^8*c^4 + 597005697024000000*b^6*c^6*x^2 + 2583100705996800000*b^5*c^7*x^3 + 95105071448
0640000*b^4*c^8*x^4 + 21641687369515008000*b^3*c^9*x^5 + 32462531054272512000*b^2*c^10*x^6 + 14958734309808773
5296*c^12*x^8 + 5308416*Sqrt[-44375*b^4 + 576000*b^3*c*x + 576000*b^2*c^2*x^2 + 5308416*c^4*x^4]*(12203125*b^6
*c^4 + 79200000*b^5*c^5*x + 38880000*b^4*c^6*x^2 + 1105920000*b^3*c^7*x^3 + 1990656000*b^2*c^8*x^4 + 122305904
64*c^10*x^6)]/(18432*c^2)
Rule 2082
Int[(x_)/Sqrt[(a_) + (b_.)*(x_) + (c_.)*(x_)^2 + (e_.)*(x_)^4], x_Symbol] :> With[{Px = (1*(33*b^2*c + 6*a*c^2
+ 40*a^2*e))/320 - (22*a*c*e*x^2)/5 + (22*b*c*e*x^3)/15 + (1*e*(5*c^2 + 4*a*e)*x^4)/4 + (4*b*e^2*x^5)/3 + 2*c
*e^2*x^6 + e^3*x^8}, Simp[(1*Log[Px + Dist[1/(8*Rt[e, 2]*x), D[Px, x], x]*Sqrt[a + b*x + c*x^2 + e*x^4]])/(8*R
t[e, 2]), x]] /; FreeQ[{a, b, c, e}, x] && EqQ[71*c^2 + 100*a*e, 0] && EqQ[1152*c^3 - 125*b^2*e, 0]
Rubi steps
\begin{align*} \int \frac{x}{\sqrt{-44375 b^4+576000 b^3 c x+576000 b^2 c^2 x^2+5308416 c^4 x^4}} \, dx &=\frac{\log \left (20738073600000000 b^8 c^4+597005697024000000 b^6 c^6 x^2+2583100705996800000 b^5 c^7 x^3+951050714480640000 b^4 c^8 x^4+21641687369515008000 b^3 c^9 x^5+32462531054272512000 b^2 c^{10} x^6+149587343098087735296 c^{12} x^8+5308416 \sqrt{-44375 b^4+576000 b^3 c x+576000 b^2 c^2 x^2+5308416 c^4 x^4} \left (12203125 b^6 c^4+79200000 b^5 c^5 x+38880000 b^4 c^6 x^2+1105920000 b^3 c^7 x^3+1990656000 b^2 c^8 x^4+12230590464 c^{10} x^6\right )\right )}{18432 c^2}\\ \end{align*}
Mathematica [C] time = 6.19329, size = 1671, normalized size = 9.44 \[ \text{result too large to display} \]
Warning: Unable to verify antiderivative.
[In]
Integrate[x/Sqrt[-44375*b^4 + 576000*b^3*c*x + 576000*b^2*c^2*x^2 + 5308416*c^4*x^4],x]
[Out]
(2*(x - (b*Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 2, 0])/c)^2*(-((b*EllipticF[ArcSin[Sqrt[((
c*x - b*Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 1, 0])*(Root[-44375 + 576000*#1 + 576000*#1^2
+ 5308416*#1^4 & , 2, 0] - Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 4, 0]))/((c*x - b*Root[-4
4375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 2, 0])*(Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4
& , 1, 0] - Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 4, 0]))]], -(((Root[-44375 + 576000*#1 +
576000*#1^2 + 5308416*#1^4 & , 2, 0] - Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 3, 0])*(Root[
-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 1, 0] - Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1
^4 & , 4, 0]))/((-Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 1, 0] + Root[-44375 + 576000*#1 + 5
76000*#1^2 + 5308416*#1^4 & , 3, 0])*(Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 2, 0] - Root[-4
4375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 4, 0])))]*Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1
^4 & , 2, 0])/c) + (EllipticPi[(-((b*Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 1, 0])/c) + (b*R
oot[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 4, 0])/c)/(-((b*Root[-44375 + 576000*#1 + 576000*#1^2
+ 5308416*#1^4 & , 2, 0])/c) + (b*Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 4, 0])/c), ArcSin[S
qrt[((c*x - b*Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 1, 0])*(Root[-44375 + 576000*#1 + 57600
0*#1^2 + 5308416*#1^4 & , 2, 0] - Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 4, 0]))/((c*x - b*R
oot[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 2, 0])*(Root[-44375 + 576000*#1 + 576000*#1^2 + 530841
6*#1^4 & , 1, 0] - Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 4, 0]))]], -(((Root[-44375 + 57600
0*#1 + 576000*#1^2 + 5308416*#1^4 & , 2, 0] - Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 3, 0])*
(Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 1, 0] - Root[-44375 + 576000*#1 + 576000*#1^2 + 5308
416*#1^4 & , 4, 0]))/((-Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 1, 0] + Root[-44375 + 576000*
#1 + 576000*#1^2 + 5308416*#1^4 & , 3, 0])*(Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 2, 0] - R
oot[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 4, 0])))]*(-(b*Root[-44375 + 576000*#1 + 576000*#1^2 +
5308416*#1^4 & , 1, 0]) + b*Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 2, 0]))/c)*Sqrt[((-(b*Ro
ot[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 1, 0]) + b*Root[-44375 + 576000*#1 + 576000*#1^2 + 5308
416*#1^4 & , 2, 0])*(x - (b*Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 3, 0])/c))/(c*(x - (b*Roo
t[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 2, 0])/c)*(-((b*Root[-44375 + 576000*#1 + 576000*#1^2 +
5308416*#1^4 & , 1, 0])/c) + (b*Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 3, 0])/c))]*Sqrt[((c*
x - b*Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 1, 0])*(Root[-44375 + 576000*#1 + 576000*#1^2 +
5308416*#1^4 & , 2, 0] - Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 4, 0]))/((c*x - b*Root[-443
75 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 2, 0])*(Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 &
, 1, 0] - Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 4, 0]))]*((b*Root[-44375 + 576000*#1 + 576
000*#1^2 + 5308416*#1^4 & , 1, 0])/c - (b*Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 4, 0])/c)*S
qrt[((-(b*Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 1, 0]) + b*Root[-44375 + 576000*#1 + 576000
*#1^2 + 5308416*#1^4 & , 2, 0])*(x - (b*Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 4, 0])/c))/(c
*(x - (b*Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 2, 0])/c)*(-((b*Root[-44375 + 576000*#1 + 57
6000*#1^2 + 5308416*#1^4 & , 1, 0])/c) + (b*Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 4, 0])/c)
)])/(Sqrt[-44375*b^4 + 576000*b^3*c*x + 576000*b^2*c^2*x^2 + 5308416*c^4*x^4]*(-((b*Root[-44375 + 576000*#1 +
576000*#1^2 + 5308416*#1^4 & , 1, 0])/c) + (b*Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 2, 0])/
c)*((b*Root[-44375 + 576000*#1 + 576000*#1^2 + 5308416*#1^4 & , 2, 0])/c - (b*Root[-44375 + 576000*#1 + 576000
*#1^2 + 5308416*#1^4 & , 4, 0])/c))
________________________________________________________________________________________
Maple [C] time = 0.568, size = 1597, normalized size = 9. \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(x/(5308416*c^4*x^4+576000*b^2*c^2*x^2+576000*b^3*c*x-44375*b^4)^(1/2),x)
[Out]
1/1152*(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c)*((5/48*
RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c)*(x-5/48*RootOf(_Z^4+
10*_Z^2+96*_Z-71,index=1)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-
71,index=1)*b/c)/(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c))^(1/2)*(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-7
1,index=2)*b/c)^2*((5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*
b/c)*(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=3)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=3)*b/c-5/48*R
ootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)/(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c))^(1/2)*((5/48*Roo
tOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)*(x-5/48*RootOf(_Z^4+10*
_Z^2+96*_Z-71,index=4)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,
index=1)*b/c)/(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c))^(1/2)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,ind
ex=4)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c-5/48
*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)/(c^4*(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)*(x-5/48*Ro
otOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c)*(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=3)*b/c)*(x-5/48*RootOf(_Z^
4+10*_Z^2+96*_Z-71,index=4)*b/c))^(1/2)*(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c*EllipticF(((5/48*RootO
f(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c)*(x-5/48*RootOf(_Z^4+10*_Z
^2+96*_Z-71,index=1)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,in
dex=1)*b/c)/(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c))^(1/2),((5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,inde
x=2)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=3)*b/c)*(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c-5/48*
RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c-5/48*RootOf(_Z^4+10
*_Z^2+96*_Z-71,index=3)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71
,index=4)*b/c))^(1/2))+(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index
=2)*b/c)*EllipticPi(((5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2
)*b/c)*(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c-5/48
*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)/(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c))^(1/2),(5/48*Ro
otOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)/(5/48*RootOf(_Z^4+10*_
Z^2+96*_Z-71,index=4)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c),((5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,
index=2)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=3)*b/c)*(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c-5
/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c-5/48*RootOf(_Z^
4+10*_Z^2+96*_Z-71,index=3)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_
Z-71,index=4)*b/c))^(1/2)))
________________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x}{\sqrt{5308416 \, c^{4} x^{4} + 576000 \, b^{2} c^{2} x^{2} + 576000 \, b^{3} c x - 44375 \, b^{4}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x/(5308416*c^4*x^4+576000*b^2*c^2*x^2+576000*b^3*c*x-44375*b^4)^(1/2),x, algorithm="maxima")
[Out]
integrate(x/sqrt(5308416*c^4*x^4 + 576000*b^2*c^2*x^2 + 576000*b^3*c*x - 44375*b^4), x)
________________________________________________________________________________________
Fricas [A] time = 2.57616, size = 537, normalized size = 3.03 \begin{align*} \frac{\log \left (28179280429056 \, c^{8} x^{8} + 6115295232000 \, b^{2} c^{6} x^{6} + 4076863488000 \, b^{3} c^{5} x^{5} + 179159040000 \, b^{4} c^{4} x^{4} + 486604800000 \, b^{5} c^{3} x^{3} + 112464000000 \, b^{6} c^{2} x^{2} + 3906640625 \, b^{8} +{\left (12230590464 \, c^{6} x^{6} + 1990656000 \, b^{2} c^{4} x^{4} + 1105920000 \, b^{3} c^{3} x^{3} + 38880000 \, b^{4} c^{2} x^{2} + 79200000 \, b^{5} c x + 12203125 \, b^{6}\right )} \sqrt{5308416 \, c^{4} x^{4} + 576000 \, b^{2} c^{2} x^{2} + 576000 \, b^{3} c x - 44375 \, b^{4}}\right )}{18432 \, c^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x/(5308416*c^4*x^4+576000*b^2*c^2*x^2+576000*b^3*c*x-44375*b^4)^(1/2),x, algorithm="fricas")
[Out]
1/18432*log(28179280429056*c^8*x^8 + 6115295232000*b^2*c^6*x^6 + 4076863488000*b^3*c^5*x^5 + 179159040000*b^4*
c^4*x^4 + 486604800000*b^5*c^3*x^3 + 112464000000*b^6*c^2*x^2 + 3906640625*b^8 + (12230590464*c^6*x^6 + 199065
6000*b^2*c^4*x^4 + 1105920000*b^3*c^3*x^3 + 38880000*b^4*c^2*x^2 + 79200000*b^5*c*x + 12203125*b^6)*sqrt(53084
16*c^4*x^4 + 576000*b^2*c^2*x^2 + 576000*b^3*c*x - 44375*b^4))/c^2
________________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x}{\sqrt{- 44375 b^{4} + 576000 b^{3} c x + 576000 b^{2} c^{2} x^{2} + 5308416 c^{4} x^{4}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x/(5308416*c**4*x**4+576000*b**2*c**2*x**2+576000*b**3*c*x-44375*b**4)**(1/2),x)
[Out]
Integral(x/sqrt(-44375*b**4 + 576000*b**3*c*x + 576000*b**2*c**2*x**2 + 5308416*c**4*x**4), x)
________________________________________________________________________________________
Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x}{\sqrt{5308416 \, c^{4} x^{4} + 576000 \, b^{2} c^{2} x^{2} + 576000 \, b^{3} c x - 44375 \, b^{4}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x/(5308416*c^4*x^4+576000*b^2*c^2*x^2+576000*b^3*c*x-44375*b^4)^(1/2),x, algorithm="giac")
[Out]
integrate(x/sqrt(5308416*c^4*x^4 + 576000*b^2*c^2*x^2 + 576000*b^3*c*x - 44375*b^4), x)