[next] [prev] [prev-tail] [tail] [up]

3.970 \(\int \frac{x^4 (A+B x)}{\left (a+b x+c x^2\right )^{5/2}} \, dx\)

Optimal. Leaf size=285 \[ -\frac{2 x \left (x \left (32 a^2 B c^2+16 a A b c^2-32 a b^2 B c-2 A b^3 c+5 b^4 B\right )+a \left (24 a A c^2-28 a b B c-2 A b^2 c+5 b^3 B\right )\right )}{3 c^2 \left (b^2-4 a c\right )^2 \sqrt{a+b x+c x^2}}+\frac{\sqrt{a+b x+c x^2} \left (128 a^2 B c^2+40 a A b c^2-100 a b^2 B c-6 A b^3 c+15 b^4 B\right )}{3 c^3 \left (b^2-4 a c\right )^2}-\frac{2 x^3 \left (x \left (-2 a B c-A b c+b^2 B\right )+a (b B-2 A c)\right )}{3 c \left (b^2-4 a c\right ) \left (a+b x+c x^2\right )^{3/2}}-\frac{(5 b B-2 A c) \tanh ^{-1}\left (\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right )}{2 c^{7/2}} \]

[Out]

(-2*x^3*(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x))/(3*c*(b^2 - 4*a*c)*(a +
 b*x + c*x^2)^(3/2)) - (2*x*(a*(5*b^3*B - 2*A*b^2*c - 28*a*b*B*c + 24*a*A*c^2) +
 (5*b^4*B - 2*A*b^3*c - 32*a*b^2*B*c + 16*a*A*b*c^2 + 32*a^2*B*c^2)*x))/(3*c^2*(
b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2]) + ((15*b^4*B - 6*A*b^3*c - 100*a*b^2*B*c +
 40*a*A*b*c^2 + 128*a^2*B*c^2)*Sqrt[a + b*x + c*x^2])/(3*c^3*(b^2 - 4*a*c)^2) -
((5*b*B - 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(7
/2))

_______________________________________________________________________________________

Rubi [A]  time = 0.680818, antiderivative size = 285, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 4, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.174 \[ -\frac{2 x \left (x \left (32 a^2 B c^2+16 a A b c^2-32 a b^2 B c-2 A b^3 c+5 b^4 B\right )+a \left (24 a A c^2-28 a b B c-2 A b^2 c+5 b^3 B\right )\right )}{3 c^2 \left (b^2-4 a c\right )^2 \sqrt{a+b x+c x^2}}+\frac{\sqrt{a+b x+c x^2} \left (128 a^2 B c^2+40 a A b c^2-100 a b^2 B c-6 A b^3 c+15 b^4 B\right )}{3 c^3 \left (b^2-4 a c\right )^2}-\frac{2 x^3 \left (x \left (-2 a B c-A b c+b^2 B\right )+a (b B-2 A c)\right )}{3 c \left (b^2-4 a c\right ) \left (a+b x+c x^2\right )^{3/2}}-\frac{(5 b B-2 A c) \tanh ^{-1}\left (\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right )}{2 c^{7/2}} \]

Antiderivative was successfully verified.

[In]  Int[(x^4*(A + B*x))/(a + b*x + c*x^2)^(5/2),x]

[Out]

(-2*x^3*(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x))/(3*c*(b^2 - 4*a*c)*(a +
 b*x + c*x^2)^(3/2)) - (2*x*(a*(5*b^3*B - 2*A*b^2*c - 28*a*b*B*c + 24*a*A*c^2) +
 (5*b^4*B - 2*A*b^3*c - 32*a*b^2*B*c + 16*a*A*b*c^2 + 32*a^2*B*c^2)*x))/(3*c^2*(
b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2]) + ((15*b^4*B - 6*A*b^3*c - 100*a*b^2*B*c +
 40*a*A*b*c^2 + 128*a^2*B*c^2)*Sqrt[a + b*x + c*x^2])/(3*c^3*(b^2 - 4*a*c)^2) -
((5*b*B - 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(7
/2))

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 96.502, size = 294, normalized size = 1.03 \[ \frac{2 x^{3} \left (a \left (2 A c - B b\right ) - x \left (- A b c - 2 B a c + B b^{2}\right )\right )}{3 c \left (- 4 a c + b^{2}\right ) \left (a + b x + c x^{2}\right )^{\frac{3}{2}}} - \frac{4 x \left (\frac{a \left (24 A a c^{2} - 2 A b^{2} c - 28 B a b c + 5 B b^{3}\right )}{2} + x \left (8 A a b c^{2} - A b^{3} c + 16 B a^{2} c^{2} - 16 B a b^{2} c + \frac{5 B b^{4}}{2}\right )\right )}{3 c^{2} \left (- 4 a c + b^{2}\right )^{2} \sqrt{a + b x + c x^{2}}} + \frac{\sqrt{a + b x + c x^{2}} \left (40 A a b c^{2} - 6 A b^{3} c + 128 B a^{2} c^{2} - 100 B a b^{2} c + 15 B b^{4}\right )}{3 c^{3} \left (- 4 a c + b^{2}\right )^{2}} + \frac{\left (2 A c - 5 B b\right ) \operatorname{atanh}{\left (\frac{b + 2 c x}{2 \sqrt{c} \sqrt{a + b x + c x^{2}}} \right )}}{2 c^{\frac{7}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**4*(B*x+A)/(c*x**2+b*x+a)**(5/2),x)

[Out]

2*x**3*(a*(2*A*c - B*b) - x*(-A*b*c - 2*B*a*c + B*b**2))/(3*c*(-4*a*c + b**2)*(a
 + b*x + c*x**2)**(3/2)) - 4*x*(a*(24*A*a*c**2 - 2*A*b**2*c - 28*B*a*b*c + 5*B*b
**3)/2 + x*(8*A*a*b*c**2 - A*b**3*c + 16*B*a**2*c**2 - 16*B*a*b**2*c + 5*B*b**4/
2))/(3*c**2*(-4*a*c + b**2)**2*sqrt(a + b*x + c*x**2)) + sqrt(a + b*x + c*x**2)*
(40*A*a*b*c**2 - 6*A*b**3*c + 128*B*a**2*c**2 - 100*B*a*b**2*c + 15*B*b**4)/(3*c
**3*(-4*a*c + b**2)**2) + (2*A*c - 5*B*b)*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a +
b*x + c*x**2)))/(2*c**(7/2))

_______________________________________________________________________________________

Mathematica [A]  time = 0.657332, size = 287, normalized size = 1.01 \[ \frac{128 a^4 B c^2-4 a^3 c \left (-2 b c (5 A+39 B x)+12 c^2 x (A-4 B x)+25 b^2 B\right )+a^2 \left (-6 b^3 c (A+35 B x)+12 b^2 c^2 x (7 A+4 B x)+16 c^4 x^3 (3 B x-4 A)+15 b^4 B+256 b B c^3 x^3\right )+2 a b^2 x \left (-3 b^2 c (2 A+15 B x)+2 b c^2 x (9 A-37 B x)+4 c^3 x^2 (7 A-3 B x)+15 b^3 B\right )+b^4 x^2 \left (b (20 B c x-6 A c)+c^2 x (3 B x-8 A)+15 b^2 B\right )}{3 c^3 \left (b^2-4 a c\right )^2 (a+x (b+c x))^{3/2}}+\frac{(2 A c-5 b B) \log \left (2 \sqrt{c} \sqrt{a+x (b+c x)}+b+2 c x\right )}{2 c^{7/2}} \]

Antiderivative was successfully verified.

[In]  Integrate[(x^4*(A + B*x))/(a + b*x + c*x^2)^(5/2),x]

[Out]

(128*a^4*B*c^2 + 2*a*b^2*x*(15*b^3*B + 2*b*c^2*x*(9*A - 37*B*x) + 4*c^3*x^2*(7*A
 - 3*B*x) - 3*b^2*c*(2*A + 15*B*x)) + a^2*(15*b^4*B + 256*b*B*c^3*x^3 + 16*c^4*x
^3*(-4*A + 3*B*x) + 12*b^2*c^2*x*(7*A + 4*B*x) - 6*b^3*c*(A + 35*B*x)) - 4*a^3*c
*(25*b^2*B + 12*c^2*x*(A - 4*B*x) - 2*b*c*(5*A + 39*B*x)) + b^4*x^2*(15*b^2*B +
c^2*x*(-8*A + 3*B*x) + b*(-6*A*c + 20*B*c*x)))/(3*c^3*(b^2 - 4*a*c)^2*(a + x*(b
+ c*x))^(3/2)) + ((-5*b*B + 2*A*c)*Log[b + 2*c*x + 2*Sqrt[c]*Sqrt[a + x*(b + c*x
)]])/(2*c^(7/2))

_______________________________________________________________________________________

Maple [B]  time = 0.016, size = 1262, normalized size = 4.4 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^4*(B*x+A)/(c*x^2+b*x+a)^(5/2),x)

[Out]

-1/48*A*b^5/c^4/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)+4*B*a/c^2*x^2/(c*x^2+b*x+a)^(3/2
)+5/6*B*b/c^2*x^3/(c*x^2+b*x+a)^(3/2)-5/4*B*b^2/c^3*x^2/(c*x^2+b*x+a)^(3/2)-5/16
*B*b^3/c^4*x/(c*x^2+b*x+a)^(3/2)+5/96*B*b^6/c^5/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)+
5/12*B*b^6/c^4/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)-1/6*A*b^5/c^3/(4*a*c-b^2)^2/(c*
x^2+b*x+a)^(1/2)+1/3*A*b/c^3*a/(c*x^2+b*x+a)^(3/2)+1/2*A/c^3*b^3/(4*a*c-b^2)/(c*
x^2+b*x+a)^(1/2)-38/3*B*b^3/c^2*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x+4*B*a^2/c^
2*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x-5/2*B*b/c^(7/2)*ln((1/2*b+c*x)/c^(1/2)+(c*
x^2+b*x+a)^(1/2))+B*x^4/c/(c*x^2+b*x+a)^(3/2)+5/96*B*b^4/c^5/(c*x^2+b*x+a)^(3/2)
-1/3*A*x^3/c/(c*x^2+b*x+a)^(3/2)-1/48*A*b^3/c^4/(c*x^2+b*x+a)^(3/2)-A/c^2*x/(c*x
^2+b*x+a)^(1/2)+1/2*A/c^3*b/(c*x^2+b*x+a)^(1/2)-5/4*B*b^2/c^4/(c*x^2+b*x+a)^(1/2
)-B*b^2/c^4*a/(c*x^2+b*x+a)^(3/2)+5/2*B*b/c^3*x/(c*x^2+b*x+a)^(1/2)-5/4*B*b^4/c^
4/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+1/2*A*b^2/c^2*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2
)*x+1/4*A*b^3/c^3*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)-1/3*A*b^4/c^2/(4*a*c-b^2)^2/
(c*x^2+b*x+a)^(1/2)*x+5/48*B*b^5/c^4/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x+5/6*B*b^5
/c^3/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x-1/24*A*b^4/c^3/(4*a*c-b^2)/(c*x^2+b*x+a
)^(3/2)*x+A/c^2*b^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+2*A*b^3/c^2*a/(4*a*c-b^2)^
2/(c*x^2+b*x+a)^(1/2)+16*B*a^2/c^2*b^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)-19/24*B
*b^4/c^4*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)-19/3*B*b^4/c^3*a/(4*a*c-b^2)^2/(c*x^2
+b*x+a)^(1/2)+A/c^(5/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+1/2*A*b/c^2*
x^2/(c*x^2+b*x+a)^(3/2)+4*A*b^2/c*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x+32*B*a^2
/c*b/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x-19/12*B*b^3/c^3*a/(4*a*c-b^2)/(c*x^2+b*
x+a)^(3/2)*x+8/3*B*a^2/c^3/(c*x^2+b*x+a)^(3/2)+1/8*A*b^2/c^3*x/(c*x^2+b*x+a)^(3/
2)-5/2*B*b^3/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+B*a/c^3*b*x/(c*x^2+b*x+a)^(3/
2)+2*B*a^2/c^3*b^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)

_______________________________________________________________________________________

Maxima [F]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)*x^4/(c*x^2 + b*x + a)^(5/2),x, algorithm="maxima")

[Out]

Exception raised: ValueError

_______________________________________________________________________________________

Fricas [A]  time = 0.594705, size = 1, normalized size = 0. \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)*x^4/(c*x^2 + b*x + a)^(5/2),x, algorithm="fricas")

[Out]

[1/12*(4*(15*B*a^2*b^4 + 3*(B*b^4*c^2 - 8*B*a*b^2*c^3 + 16*B*a^2*c^4)*x^4 + 4*(5
*B*b^5*c - 16*A*a^2*c^4 + 2*(32*B*a^2*b + 7*A*a*b^2)*c^3 - (37*B*a*b^3 + 2*A*b^4
)*c^2)*x^3 + 8*(16*B*a^4 + 5*A*a^3*b)*c^2 + 3*(5*B*b^6 + 64*B*a^3*c^3 + 4*(4*B*a
^2*b^2 + 3*A*a*b^3)*c^2 - 2*(15*B*a*b^4 + A*b^5)*c)*x^2 - 2*(50*B*a^3*b^2 + 3*A*
a^2*b^3)*c + 6*(5*B*a*b^5 - 8*A*a^3*c^3 + 2*(26*B*a^3*b + 7*A*a^2*b^2)*c^2 - (35
*B*a^2*b^3 + 2*A*a*b^4)*c)*x)*sqrt(c*x^2 + b*x + a)*sqrt(c) - 3*(5*B*a^2*b^5 - 3
2*A*a^4*c^3 + (5*B*b^5*c^2 - 32*A*a^2*c^5 + 16*(5*B*a^2*b + A*a*b^2)*c^4 - 2*(20
*B*a*b^3 + A*b^4)*c^3)*x^4 + 2*(5*B*b^6*c - 32*A*a^2*b*c^4 + 16*(5*B*a^2*b^2 + A
*a*b^3)*c^3 - 2*(20*B*a*b^4 + A*b^5)*c^2)*x^3 + 16*(5*B*a^4*b + A*a^3*b^2)*c^2 +
 (5*B*b^7 + 12*A*a*b^4*c^2 + 160*B*a^3*b*c^3 - 64*A*a^3*c^4 - 2*(15*B*a*b^5 + A*
b^6)*c)*x^2 - 2*(20*B*a^3*b^3 + A*a^2*b^4)*c + 2*(5*B*a*b^6 - 32*A*a^3*b*c^3 + 1
6*(5*B*a^3*b^2 + A*a^2*b^3)*c^2 - 2*(20*B*a^2*b^4 + A*a*b^5)*c)*x)*log(-4*(2*c^2
*x + b*c)*sqrt(c*x^2 + b*x + a) - (8*c^2*x^2 + 8*b*c*x + b^2 + 4*a*c)*sqrt(c)))/
((a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7
)*x^4 + 2*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*x^3 + (b^6*c^3 - 6*a*b^4*c^4 +
32*a^3*c^6)*x^2 + 2*(a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*x)*sqrt(c)), 1/6*
(2*(15*B*a^2*b^4 + 3*(B*b^4*c^2 - 8*B*a*b^2*c^3 + 16*B*a^2*c^4)*x^4 + 4*(5*B*b^5
*c - 16*A*a^2*c^4 + 2*(32*B*a^2*b + 7*A*a*b^2)*c^3 - (37*B*a*b^3 + 2*A*b^4)*c^2)
*x^3 + 8*(16*B*a^4 + 5*A*a^3*b)*c^2 + 3*(5*B*b^6 + 64*B*a^3*c^3 + 4*(4*B*a^2*b^2
 + 3*A*a*b^3)*c^2 - 2*(15*B*a*b^4 + A*b^5)*c)*x^2 - 2*(50*B*a^3*b^2 + 3*A*a^2*b^
3)*c + 6*(5*B*a*b^5 - 8*A*a^3*c^3 + 2*(26*B*a^3*b + 7*A*a^2*b^2)*c^2 - (35*B*a^2
*b^3 + 2*A*a*b^4)*c)*x)*sqrt(c*x^2 + b*x + a)*sqrt(-c) - 3*(5*B*a^2*b^5 - 32*A*a
^4*c^3 + (5*B*b^5*c^2 - 32*A*a^2*c^5 + 16*(5*B*a^2*b + A*a*b^2)*c^4 - 2*(20*B*a*
b^3 + A*b^4)*c^3)*x^4 + 2*(5*B*b^6*c - 32*A*a^2*b*c^4 + 16*(5*B*a^2*b^2 + A*a*b^
3)*c^3 - 2*(20*B*a*b^4 + A*b^5)*c^2)*x^3 + 16*(5*B*a^4*b + A*a^3*b^2)*c^2 + (5*B
*b^7 + 12*A*a*b^4*c^2 + 160*B*a^3*b*c^3 - 64*A*a^3*c^4 - 2*(15*B*a*b^5 + A*b^6)*
c)*x^2 - 2*(20*B*a^3*b^3 + A*a^2*b^4)*c + 2*(5*B*a*b^6 - 32*A*a^3*b*c^3 + 16*(5*
B*a^3*b^2 + A*a^2*b^3)*c^2 - 2*(20*B*a^2*b^4 + A*a*b^5)*c)*x)*arctan(1/2*(2*c*x
+ b)*sqrt(-c)/(sqrt(c*x^2 + b*x + a)*c)))/((a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4
*c^5 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*x^4 + 2*(b^5*c^4 - 8*a*b^3*c^5 + 16*
a^2*b*c^6)*x^3 + (b^6*c^3 - 6*a*b^4*c^4 + 32*a^3*c^6)*x^2 + 2*(a*b^5*c^3 - 8*a^2
*b^3*c^4 + 16*a^3*b*c^5)*x)*sqrt(-c))]

_______________________________________________________________________________________

Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**4*(B*x+A)/(c*x**2+b*x+a)**(5/2),x)

[Out]

Timed out

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.297333, size = 618, normalized size = 2.17 \[ \frac{{\left ({\left ({\left (\frac{3 \,{\left (B b^{4} c^{2} - 8 \, B a b^{2} c^{3} + 16 \, B a^{2} c^{4}\right )} x}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}} + \frac{4 \,{\left (5 \, B b^{5} c - 37 \, B a b^{3} c^{2} - 2 \, A b^{4} c^{2} + 64 \, B a^{2} b c^{3} + 14 \, A a b^{2} c^{3} - 16 \, A a^{2} c^{4}\right )}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}\right )} x + \frac{3 \,{\left (5 \, B b^{6} - 30 \, B a b^{4} c - 2 \, A b^{5} c + 16 \, B a^{2} b^{2} c^{2} + 12 \, A a b^{3} c^{2} + 64 \, B a^{3} c^{3}\right )}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}\right )} x + \frac{6 \,{\left (5 \, B a b^{5} - 35 \, B a^{2} b^{3} c - 2 \, A a b^{4} c + 52 \, B a^{3} b c^{2} + 14 \, A a^{2} b^{2} c^{2} - 8 \, A a^{3} c^{3}\right )}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}\right )} x + \frac{15 \, B a^{2} b^{4} - 100 \, B a^{3} b^{2} c - 6 \, A a^{2} b^{3} c + 128 \, B a^{4} c^{2} + 40 \, A a^{3} b c^{2}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}{3 \,{\left (c x^{2} + b x + a\right )}^{\frac{3}{2}}} + \frac{{\left (5 \, B b - 2 \, A c\right )}{\rm ln}\left ({\left | -2 \,{\left (\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right )} \sqrt{c} - b \right |}\right )}{2 \, c^{\frac{7}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)*x^4/(c*x^2 + b*x + a)^(5/2),x, algorithm="giac")

[Out]

1/3*((((3*(B*b^4*c^2 - 8*B*a*b^2*c^3 + 16*B*a^2*c^4)*x/(b^4*c^3 - 8*a*b^2*c^4 +
16*a^2*c^5) + 4*(5*B*b^5*c - 37*B*a*b^3*c^2 - 2*A*b^4*c^2 + 64*B*a^2*b*c^3 + 14*
A*a*b^2*c^3 - 16*A*a^2*c^4)/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))*x + 3*(5*B*b^6
 - 30*B*a*b^4*c - 2*A*b^5*c + 16*B*a^2*b^2*c^2 + 12*A*a*b^3*c^2 + 64*B*a^3*c^3)/
(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))*x + 6*(5*B*a*b^5 - 35*B*a^2*b^3*c - 2*A*a*
b^4*c + 52*B*a^3*b*c^2 + 14*A*a^2*b^2*c^2 - 8*A*a^3*c^3)/(b^4*c^3 - 8*a*b^2*c^4
+ 16*a^2*c^5))*x + (15*B*a^2*b^4 - 100*B*a^3*b^2*c - 6*A*a^2*b^3*c + 128*B*a^4*c
^2 + 40*A*a^3*b*c^2)/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))/(c*x^2 + b*x + a)^(3/
2) + 1/2*(5*B*b - 2*A*c)*ln(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) -
 b))/c^(7/2)

[next] [prev] [prev-tail] [front] [up]