3.1016 \(\int \frac{A+B x}{x^{9/2} \left (a+b x+c x^2\right )} \, dx\)

Optimal. Leaf size=381 \[ -\frac{2 \left (a B \left (b^2-a c\right )-A \left (b^3-2 a b c\right )\right )}{a^4 \sqrt{x}}-\frac{2 \left (-a A c-a b B+A b^2\right )}{3 a^3 x^{3/2}}+\frac{2 (A b-a B)}{5 a^2 x^{5/2}}-\frac{\sqrt{2} \sqrt{c} \left (\frac{a b B \left (b^2-3 a c\right )-A \left (2 a^2 c^2-4 a b^2 c+b^4\right )}{\sqrt{b^2-4 a c}}-A \left (b^3-2 a b c\right )+a B \left (b^2-a c\right )\right ) \tan ^{-1}\left (\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right )}{a^4 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \sqrt{c} \left (-\frac{a b B \left (b^2-3 a c\right )-A \left (2 a^2 c^2-4 a b^2 c+b^4\right )}{\sqrt{b^2-4 a c}}-A \left (b^3-2 a b c\right )+a B \left (b^2-a c\right )\right ) \tan ^{-1}\left (\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right )}{a^4 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{2 A}{7 a x^{7/2}} \]

[Out]

(-2*A)/(7*a*x^(7/2)) + (2*(A*b - a*B))/(5*a^2*x^(5/2)) - (2*(A*b^2 - a*b*B - a*A
*c))/(3*a^3*x^(3/2)) - (2*(a*B*(b^2 - a*c) - A*(b^3 - 2*a*b*c)))/(a^4*Sqrt[x]) -
(Sqrt[2]*Sqrt[c]*(a*B*(b^2 - a*c) - A*(b^3 - 2*a*b*c) + (a*b*B*(b^2 - 3*a*c) -
A*(b^4 - 4*a*b^2*c + 2*a^2*c^2))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt
[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(a^4*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[2]*
Sqrt[c]*(a*B*(b^2 - a*c) - A*(b^3 - 2*a*b*c) - (a*b*B*(b^2 - 3*a*c) - A*(b^4 - 4
*a*b^2*c + 2*a^2*c^2))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[
b + Sqrt[b^2 - 4*a*c]]])/(a^4*Sqrt[b + Sqrt[b^2 - 4*a*c]])

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Rubi [A]  time = 4.09329, antiderivative size = 381, normalized size of antiderivative = 1., number of steps used = 8, number of rules used = 4, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.174 \[ -\frac{2 \left (a B \left (b^2-a c\right )-A \left (b^3-2 a b c\right )\right )}{a^4 \sqrt{x}}-\frac{2 \left (-a A c-a b B+A b^2\right )}{3 a^3 x^{3/2}}+\frac{2 (A b-a B)}{5 a^2 x^{5/2}}-\frac{\sqrt{2} \sqrt{c} \left (\frac{a b B \left (b^2-3 a c\right )-A \left (2 a^2 c^2-4 a b^2 c+b^4\right )}{\sqrt{b^2-4 a c}}-A \left (b^3-2 a b c\right )+a B \left (b^2-a c\right )\right ) \tan ^{-1}\left (\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right )}{a^4 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \sqrt{c} \left (-\frac{a b B \left (b^2-3 a c\right )-A \left (2 a^2 c^2-4 a b^2 c+b^4\right )}{\sqrt{b^2-4 a c}}-A \left (b^3-2 a b c\right )+a B \left (b^2-a c\right )\right ) \tan ^{-1}\left (\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right )}{a^4 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{2 A}{7 a x^{7/2}} \]

Antiderivative was successfully verified.

[In]  Int[(A + B*x)/(x^(9/2)*(a + b*x + c*x^2)),x]

[Out]

(-2*A)/(7*a*x^(7/2)) + (2*(A*b - a*B))/(5*a^2*x^(5/2)) - (2*(A*b^2 - a*b*B - a*A
*c))/(3*a^3*x^(3/2)) - (2*(a*B*(b^2 - a*c) - A*(b^3 - 2*a*b*c)))/(a^4*Sqrt[x]) -
(Sqrt[2]*Sqrt[c]*(a*B*(b^2 - a*c) - A*(b^3 - 2*a*b*c) + (a*b*B*(b^2 - 3*a*c) -
A*(b^4 - 4*a*b^2*c + 2*a^2*c^2))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt
[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(a^4*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[2]*
Sqrt[c]*(a*B*(b^2 - a*c) - A*(b^3 - 2*a*b*c) - (a*b*B*(b^2 - 3*a*c) - A*(b^4 - 4
*a*b^2*c + 2*a^2*c^2))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[
b + Sqrt[b^2 - 4*a*c]]])/(a^4*Sqrt[b + Sqrt[b^2 - 4*a*c]])

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((B*x+A)/x**(9/2)/(c*x**2+b*x+a),x)

[Out]

Timed out

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Mathematica [A]  time = 1.22693, size = 451, normalized size = 1.18 \[ \frac{-\frac{30 a^3 A}{x^{7/2}}+\frac{105 \sqrt{2} \sqrt{c} \left (A \left (2 a^2 c^2-4 a b^2 c-2 a b c \sqrt{b^2-4 a c}+b^3 \sqrt{b^2-4 a c}+b^4\right )+a B \left (-b^2 \sqrt{b^2-4 a c}+a c \sqrt{b^2-4 a c}+3 a b c-b^3\right )\right ) \tan ^{-1}\left (\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right )}{\sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{105 \sqrt{2} \sqrt{c} \left (A \left (-2 a^2 c^2+4 a b^2 c-2 a b c \sqrt{b^2-4 a c}+b^3 \sqrt{b^2-4 a c}-b^4\right )+a B \left (-b^2 \sqrt{b^2-4 a c}+a c \sqrt{b^2-4 a c}-3 a b c+b^3\right )\right ) \tan ^{-1}\left (\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right )}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{42 a^2 (A b-a B)}{x^{5/2}}+\frac{70 a \left (a A c+a b B-A b^2\right )}{x^{3/2}}+\frac{210 \left (A \left (b^3-2 a b c\right )+a B \left (a c-b^2\right )\right )}{\sqrt{x}}}{105 a^4} \]

Antiderivative was successfully verified.

[In]  Integrate[(A + B*x)/(x^(9/2)*(a + b*x + c*x^2)),x]

[Out]

((-30*a^3*A)/x^(7/2) + (42*a^2*(A*b - a*B))/x^(5/2) + (70*a*(-(A*b^2) + a*b*B +
a*A*c))/x^(3/2) + (210*(a*B*(-b^2 + a*c) + A*(b^3 - 2*a*b*c)))/Sqrt[x] + (105*Sq
rt[2]*Sqrt[c]*(a*B*(-b^3 + 3*a*b*c - b^2*Sqrt[b^2 - 4*a*c] + a*c*Sqrt[b^2 - 4*a*
c]) + A*(b^4 - 4*a*b^2*c + 2*a^2*c^2 + b^3*Sqrt[b^2 - 4*a*c] - 2*a*b*c*Sqrt[b^2
- 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[
b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (105*Sqrt[2]*Sqrt[c]*(a*B*(b^3 - 3*a
*b*c - b^2*Sqrt[b^2 - 4*a*c] + a*c*Sqrt[b^2 - 4*a*c]) + A*(-b^4 + 4*a*b^2*c - 2*
a^2*c^2 + b^3*Sqrt[b^2 - 4*a*c] - 2*a*b*c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sq
rt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^
2 - 4*a*c]]))/(105*a^4)

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Maple [B]  time = 0.062, size = 1210, normalized size = 3.2 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((B*x+A)/x^(9/2)/(c*x^2+b*x+a),x)

[Out]

2/5/x^(5/2)/a^2*A*b-2/3/a^3/x^(3/2)*b^2*A+2/3/a^2/x^(3/2)*b*B+2/a^4/x^(1/2)*A*b^
3-2/a^3/x^(1/2)*b^2*B+2/3*A*c/a^2/x^(3/2)+2/a^3*c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1
/2))*c)^(1/2)*arctanh(c*x^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*A*b-1
/a^4*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(c*x^(1/2)*2^(1/2)/((-b+
(-4*a*c+b^2)^(1/2))*c)^(1/2))*A*b^3-2/a^2*c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-
4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(c*x^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)
^(1/2))*A+1/a^3*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(c*x^(1/2)*2^
(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b^2*B-2/a^3*c^2*2^(1/2)/((b+(-4*a*c+b^2
)^(1/2))*c)^(1/2)*arctan(c*x^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*A*b
+1/a^4*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(c*x^(1/2)*2^(1/2)/((b+(
-4*a*c+b^2)^(1/2))*c)^(1/2))*A*b^3-2/a^2*c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*
a*c+b^2)^(1/2))*c)^(1/2)*arctan(c*x^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/
2))*A-1/a^3*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(c*x^(1/2)*2^(1/2)/
((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b^2*B-1/a^2*c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2
))*c)^(1/2)*arctanh(c*x^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*B+1/a^2
*c^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(c*x^(1/2)*2^(1/2)/((b+(-4*a
*c+b^2)^(1/2))*c)^(1/2))*B-3/a^2*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)
^(1/2))*c)^(1/2)*arctan(c*x^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b*B+
1/a^3*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(c*x
^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*B*b^3-4/a^3/x^(1/2)*A*b*c+4/a^
3*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(c*x^(1/
2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*A*b^2+4/a^3*c^2/(-4*a*c+b^2)^(1/2)*
2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(c*x^(1/2)*2^(1/2)/((-b+(-4*a*c
+b^2)^(1/2))*c)^(1/2))*A*b^2-1/a^4*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2
)^(1/2))*c)^(1/2)*arctanh(c*x^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*A
*b^4-2/7*A/a/x^(7/2)-2/5*B/a/x^(5/2)-3/a^2*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(
-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(c*x^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c
)^(1/2))*b*B+1/a^3*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)
*arctan(c*x^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*B*b^3-1/a^4*c/(-4*a*
c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(c*x^(1/2)*2^(1/2)/(
(b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*A*b^4+2*B*c/a^2/x^(1/2)

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Maxima [F]  time = 0., size = 0, normalized size = 0. \[ -\frac{2 \,{\left (\frac{15 \, A a^{4}}{x^{\frac{7}{2}}} - 105 \,{\left ({\left (b^{4} - 3 \, a b^{2} c + a^{2} c^{2}\right )} A -{\left (a b^{3} - 2 \, a^{2} b c\right )} B\right )} \sqrt{x} - \frac{105 \,{\left ({\left (a b^{3} - 2 \, a^{2} b c\right )} A -{\left (a^{2} b^{2} - a^{3} c\right )} B\right )}}{\sqrt{x}} - \frac{35 \,{\left (B a^{3} b -{\left (a^{2} b^{2} - a^{3} c\right )} A\right )}}{x^{\frac{3}{2}}} + \frac{21 \,{\left (B a^{4} - A a^{3} b\right )}}{x^{\frac{5}{2}}}\right )}}{105 \, a^{5}} - \int \frac{{\left ({\left (b^{4} c - 3 \, a b^{2} c^{2} + a^{2} c^{3}\right )} A -{\left (a b^{3} c - 2 \, a^{2} b c^{2}\right )} B\right )} x^{\frac{3}{2}} +{\left ({\left (b^{5} - 4 \, a b^{3} c + 3 \, a^{2} b c^{2}\right )} A -{\left (a b^{4} - 3 \, a^{2} b^{2} c + a^{3} c^{2}\right )} B\right )} \sqrt{x}}{a^{5} c x^{2} + a^{5} b x + a^{6}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)/((c*x^2 + b*x + a)*x^(9/2)),x, algorithm="maxima")

[Out]

-2/105*(15*A*a^4/x^(7/2) - 105*((b^4 - 3*a*b^2*c + a^2*c^2)*A - (a*b^3 - 2*a^2*b
*c)*B)*sqrt(x) - 105*((a*b^3 - 2*a^2*b*c)*A - (a^2*b^2 - a^3*c)*B)/sqrt(x) - 35*
(B*a^3*b - (a^2*b^2 - a^3*c)*A)/x^(3/2) + 21*(B*a^4 - A*a^3*b)/x^(5/2))/a^5 - in
tegrate((((b^4*c - 3*a*b^2*c^2 + a^2*c^3)*A - (a*b^3*c - 2*a^2*b*c^2)*B)*x^(3/2)
+ ((b^5 - 4*a*b^3*c + 3*a^2*b*c^2)*A - (a*b^4 - 3*a^2*b^2*c + a^3*c^2)*B)*sqrt(
x))/(a^5*c*x^2 + a^5*b*x + a^6), x)

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Fricas [A]  time = 4.94098, size = 14186, normalized size = 37.23 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)/((c*x^2 + b*x + a)*x^(9/2)),x, algorithm="fricas")

[Out]

1/210*(105*sqrt(2)*a^4*x^(7/2)*sqrt(-(B^2*a^2*b^7 - 2*A*B*a*b^8 + A^2*b^9 - (4*A
*B*a^5 - 9*A^2*a^4*b)*c^4 - (7*B^2*a^5*b - 32*A*B*a^4*b^2 + 30*A^2*a^3*b^3)*c^3
+ (14*B^2*a^4*b^3 - 40*A*B*a^3*b^4 + 27*A^2*a^2*b^5)*c^2 - (7*B^2*a^3*b^5 - 16*A
*B*a^2*b^6 + 9*A^2*a*b^7)*c + (a^9*b^2 - 4*a^10*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3*
a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^2
*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 96
*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2 -
68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*c
^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*b
^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2*
a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B^
3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 - 2
*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13 +
7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c)))/(a^9*b^2 - 4*a^10*c))*log(sqrt(2)*(B^3
*a^3*b^11 - 3*A*B^2*a^2*b^12 + 3*A^2*B*a*b^13 - A^3*b^14 + 4*A^3*a^7*c^7 - (4*A*
B^2*a^8 - 40*A^2*B*a^7*b + 53*A^3*a^6*b^2)*c^6 - (8*B^3*a^8*b - 101*A*B^2*a^7*b^
2 + 270*A^2*B*a^6*b^3 - 197*A^3*a^5*b^4)*c^5 + (54*B^3*a^7*b^3 - 313*A*B^2*a^6*b
^4 + 545*A^2*B*a^5*b^5 - 294*A^3*a^4*b^6)*c^4 - (77*B^3*a^6*b^5 - 336*A*B^2*a^5*
b^6 + 468*A^2*B*a^4*b^7 - 210*A^3*a^3*b^8)*c^3 + (44*B^3*a^5*b^7 - 162*A*B^2*a^4
*b^8 + 195*A^2*B*a^3*b^9 - 77*A^3*a^2*b^10)*c^2 - (11*B^3*a^4*b^9 - 36*A*B^2*a^3
*b^10 + 39*A^2*B*a^2*b^11 - 14*A^3*a*b^12)*c - (B*a^10*b^6 - A*a^9*b^7 - 4*(2*B*
a^13 - 5*A*a^12*b)*c^3 + (18*B*a^12*b^2 - 25*A*a^11*b^3)*c^2 - (8*B*a^11*b^4 - 9
*A*a^10*b^5)*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A
^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a
^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^
3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7
*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^
7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B
^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A
^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 -
268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^1
1 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^1
9*c)))*sqrt(-(B^2*a^2*b^7 - 2*A*B*a*b^8 + A^2*b^9 - (4*A*B*a^5 - 9*A^2*a^4*b)*c^
4 - (7*B^2*a^5*b - 32*A*B*a^4*b^2 + 30*A^2*a^3*b^3)*c^3 + (14*B^2*a^4*b^3 - 40*A
*B*a^3*b^4 + 27*A^2*a^2*b^5)*c^2 - (7*B^2*a^3*b^5 - 16*A*B*a^2*b^6 + 9*A^2*a*b^7
)*c + (a^9*b^2 - 4*a^10*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2
*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b
+ 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*A
^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240*
A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 - 3
44*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c^
4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4*
b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2*
a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A*
B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18*
b^2 - 4*a^19*c)))/(a^9*b^2 - 4*a^10*c)) + 4*(A^4*a^4*c^9 + (7*A^3*B*a^4*b - 10*A
^4*a^3*b^2)*c^8 - (B^4*a^6 - 9*A*B^3*a^5*b + 12*A^2*B^2*a^4*b^2 + 10*A^3*B*a^3*b
^3 - 15*A^4*a^2*b^4)*c^7 + (6*B^4*a^5*b^2 - 26*A*B^3*a^4*b^3 + 30*A^2*B^2*a^3*b^
4 - 3*A^3*B*a^2*b^5 - 7*A^4*a*b^6)*c^6 - (5*B^4*a^4*b^4 - 17*A*B^3*a^3*b^5 + 18*
A^2*B^2*a^2*b^6 - 5*A^3*B*a*b^7 - A^4*b^8)*c^5 + (B^4*a^3*b^6 - 3*A*B^3*a^2*b^7
+ 3*A^2*B^2*a*b^8 - A^3*B*b^9)*c^4)*sqrt(x)) - 105*sqrt(2)*a^4*x^(7/2)*sqrt(-(B^
2*a^2*b^7 - 2*A*B*a*b^8 + A^2*b^9 - (4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - (7*B^2*a^5*b
- 32*A*B*a^4*b^2 + 30*A^2*a^3*b^3)*c^3 + (14*B^2*a^4*b^3 - 40*A*B*a^3*b^4 + 27*
A^2*a^2*b^5)*c^2 - (7*B^2*a^3*b^5 - 16*A*B*a^2*b^6 + 9*A^2*a*b^7)*c + (a^9*b^2 -
4*a^10*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B*
a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b^
2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 + 1
30*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4
- 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^5
+ 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a^
7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a^
3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*A
^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 + 3
6*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c))
)/(a^9*b^2 - 4*a^10*c))*log(-sqrt(2)*(B^3*a^3*b^11 - 3*A*B^2*a^2*b^12 + 3*A^2*B*
a*b^13 - A^3*b^14 + 4*A^3*a^7*c^7 - (4*A*B^2*a^8 - 40*A^2*B*a^7*b + 53*A^3*a^6*b
^2)*c^6 - (8*B^3*a^8*b - 101*A*B^2*a^7*b^2 + 270*A^2*B*a^6*b^3 - 197*A^3*a^5*b^4
)*c^5 + (54*B^3*a^7*b^3 - 313*A*B^2*a^6*b^4 + 545*A^2*B*a^5*b^5 - 294*A^3*a^4*b^
6)*c^4 - (77*B^3*a^6*b^5 - 336*A*B^2*a^5*b^6 + 468*A^2*B*a^4*b^7 - 210*A^3*a^3*b
^8)*c^3 + (44*B^3*a^5*b^7 - 162*A*B^2*a^4*b^8 + 195*A^2*B*a^3*b^9 - 77*A^3*a^2*b
^10)*c^2 - (11*B^3*a^4*b^9 - 36*A*B^2*a^3*b^10 + 39*A^2*B*a^2*b^11 - 14*A^3*a*b^
12)*c - (B*a^10*b^6 - A*a^9*b^7 - 4*(2*B*a^13 - 5*A*a^12*b)*c^3 + (18*B*a^12*b^2
- 25*A*a^11*b^3)*c^2 - (8*B*a^11*b^4 - 9*A*a^10*b^5)*c)*sqrt((B^4*a^4*b^12 - 4*
A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 -
2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*
b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9
*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5*
b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B
*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^
2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 18
4*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c
^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*
b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c)))*sqrt(-(B^2*a^2*b^7 - 2*A*B*a*b^8
+ A^2*b^9 - (4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - (7*B^2*a^5*b - 32*A*B*a^4*b^2 + 30*
A^2*a^3*b^3)*c^3 + (14*B^2*a^4*b^3 - 40*A*B*a^3*b^4 + 27*A^2*a^2*b^5)*c^2 - (7*B
^2*a^3*b^5 - 16*A*B*a^2*b^6 + 9*A^2*a*b^7)*c + (a^9*b^2 - 4*a^10*c)*sqrt((B^4*a^
4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^4
*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 16
*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 - 2
*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 + 1
57*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6
- 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*b
^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*a
^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4*
a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 26
*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c)))/(a^9*b^2 - 4*a^10*c))
+ 4*(A^4*a^4*c^9 + (7*A^3*B*a^4*b - 10*A^4*a^3*b^2)*c^8 - (B^4*a^6 - 9*A*B^3*a^
5*b + 12*A^2*B^2*a^4*b^2 + 10*A^3*B*a^3*b^3 - 15*A^4*a^2*b^4)*c^7 + (6*B^4*a^5*b
^2 - 26*A*B^3*a^4*b^3 + 30*A^2*B^2*a^3*b^4 - 3*A^3*B*a^2*b^5 - 7*A^4*a*b^6)*c^6
- (5*B^4*a^4*b^4 - 17*A*B^3*a^3*b^5 + 18*A^2*B^2*a^2*b^6 - 5*A^3*B*a*b^7 - A^4*b
^8)*c^5 + (B^4*a^3*b^6 - 3*A*B^3*a^2*b^7 + 3*A^2*B^2*a*b^8 - A^3*B*b^9)*c^4)*sqr
t(x)) + 105*sqrt(2)*a^4*x^(7/2)*sqrt(-(B^2*a^2*b^7 - 2*A*B*a*b^8 + A^2*b^9 - (4*
A*B*a^5 - 9*A^2*a^4*b)*c^4 - (7*B^2*a^5*b - 32*A*B*a^4*b^2 + 30*A^2*a^3*b^3)*c^3
+ (14*B^2*a^4*b^3 - 40*A*B*a^3*b^4 + 27*A^2*a^2*b^5)*c^2 - (7*B^2*a^3*b^5 - 16*
A*B*a^2*b^6 + 9*A^2*a*b^7)*c - (a^9*b^2 - 4*a^10*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3
*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^
2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 9
6*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2
- 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*
c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*
b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2
*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B
^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 -
2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13
+ 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c)))/(a^9*b^2 - 4*a^10*c))*log(sqrt(2)*(B^
3*a^3*b^11 - 3*A*B^2*a^2*b^12 + 3*A^2*B*a*b^13 - A^3*b^14 + 4*A^3*a^7*c^7 - (4*A
*B^2*a^8 - 40*A^2*B*a^7*b + 53*A^3*a^6*b^2)*c^6 - (8*B^3*a^8*b - 101*A*B^2*a^7*b
^2 + 270*A^2*B*a^6*b^3 - 197*A^3*a^5*b^4)*c^5 + (54*B^3*a^7*b^3 - 313*A*B^2*a^6*
b^4 + 545*A^2*B*a^5*b^5 - 294*A^3*a^4*b^6)*c^4 - (77*B^3*a^6*b^5 - 336*A*B^2*a^5
*b^6 + 468*A^2*B*a^4*b^7 - 210*A^3*a^3*b^8)*c^3 + (44*B^3*a^5*b^7 - 162*A*B^2*a^
4*b^8 + 195*A^2*B*a^3*b^9 - 77*A^3*a^2*b^10)*c^2 - (11*B^3*a^4*b^9 - 36*A*B^2*a^
3*b^10 + 39*A^2*B*a^2*b^11 - 14*A^3*a*b^12)*c + (B*a^10*b^6 - A*a^9*b^7 - 4*(2*B
*a^13 - 5*A*a^12*b)*c^3 + (18*B*a^12*b^2 - 25*A*a^11*b^3)*c^2 - (8*B*a^11*b^4 -
9*A*a^10*b^5)*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*
A^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*
a^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b
^3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^
7*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a
^7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*
B^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*
A^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 -
268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^
11 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^
19*c)))*sqrt(-(B^2*a^2*b^7 - 2*A*B*a*b^8 + A^2*b^9 - (4*A*B*a^5 - 9*A^2*a^4*b)*c
^4 - (7*B^2*a^5*b - 32*A*B*a^4*b^2 + 30*A^2*a^3*b^3)*c^3 + (14*B^2*a^4*b^3 - 40*
A*B*a^3*b^4 + 27*A^2*a^2*b^5)*c^2 - (7*B^2*a^3*b^5 - 16*A*B*a^2*b^6 + 9*A^2*a*b^
7)*c - (a^9*b^2 - 4*a^10*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^
2*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*
b + 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*
A^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240
*A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 -
344*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c
^4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4
*b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2
*a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A
*B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18
*b^2 - 4*a^19*c)))/(a^9*b^2 - 4*a^10*c)) + 4*(A^4*a^4*c^9 + (7*A^3*B*a^4*b - 10*
A^4*a^3*b^2)*c^8 - (B^4*a^6 - 9*A*B^3*a^5*b + 12*A^2*B^2*a^4*b^2 + 10*A^3*B*a^3*
b^3 - 15*A^4*a^2*b^4)*c^7 + (6*B^4*a^5*b^2 - 26*A*B^3*a^4*b^3 + 30*A^2*B^2*a^3*b
^4 - 3*A^3*B*a^2*b^5 - 7*A^4*a*b^6)*c^6 - (5*B^4*a^4*b^4 - 17*A*B^3*a^3*b^5 + 18
*A^2*B^2*a^2*b^6 - 5*A^3*B*a*b^7 - A^4*b^8)*c^5 + (B^4*a^3*b^6 - 3*A*B^3*a^2*b^7
+ 3*A^2*B^2*a*b^8 - A^3*B*b^9)*c^4)*sqrt(x)) - 105*sqrt(2)*a^4*x^(7/2)*sqrt(-(B
^2*a^2*b^7 - 2*A*B*a*b^8 + A^2*b^9 - (4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - (7*B^2*a^5*
b - 32*A*B*a^4*b^2 + 30*A^2*a^3*b^3)*c^3 + (14*B^2*a^4*b^3 - 40*A*B*a^3*b^4 + 27
*A^2*a^2*b^5)*c^2 - (7*B^2*a^3*b^5 - 16*A*B*a^2*b^6 + 9*A^2*a*b^7)*c - (a^9*b^2
- 4*a^10*c)*sqrt((B^4*a^4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B
*a*b^15 + A^4*b^16 + A^4*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b
^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 +
130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4
- 332*A^3*B*a^6*b^5 + 157*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^
5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a
^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a
^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*
A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 +
36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c)
))/(a^9*b^2 - 4*a^10*c))*log(-sqrt(2)*(B^3*a^3*b^11 - 3*A*B^2*a^2*b^12 + 3*A^2*B
*a*b^13 - A^3*b^14 + 4*A^3*a^7*c^7 - (4*A*B^2*a^8 - 40*A^2*B*a^7*b + 53*A^3*a^6*
b^2)*c^6 - (8*B^3*a^8*b - 101*A*B^2*a^7*b^2 + 270*A^2*B*a^6*b^3 - 197*A^3*a^5*b^
4)*c^5 + (54*B^3*a^7*b^3 - 313*A*B^2*a^6*b^4 + 545*A^2*B*a^5*b^5 - 294*A^3*a^4*b
^6)*c^4 - (77*B^3*a^6*b^5 - 336*A*B^2*a^5*b^6 + 468*A^2*B*a^4*b^7 - 210*A^3*a^3*
b^8)*c^3 + (44*B^3*a^5*b^7 - 162*A*B^2*a^4*b^8 + 195*A^2*B*a^3*b^9 - 77*A^3*a^2*
b^10)*c^2 - (11*B^3*a^4*b^9 - 36*A*B^2*a^3*b^10 + 39*A^2*B*a^2*b^11 - 14*A^3*a*b
^12)*c + (B*a^10*b^6 - A*a^9*b^7 - 4*(2*B*a^13 - 5*A*a^12*b)*c^3 + (18*B*a^12*b^
2 - 25*A*a^11*b^3)*c^2 - (8*B*a^11*b^4 - 9*A*a^10*b^5)*c)*sqrt((B^4*a^4*b^12 - 4
*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^4*a^8*c^8 -
2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 16*A*B^3*a^9
*b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 - 2*(6*B^4*a^
9*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 + 157*A^4*a^5
*b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6 - 956*A^3*
B*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*b^7 + 384*A
^2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*a^6*b^8 - 1
84*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4*a^2*b^12)*
c^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 26*A^3*B*a^2
*b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c)))*sqrt(-(B^2*a^2*b^7 - 2*A*B*a*b^
8 + A^2*b^9 - (4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - (7*B^2*a^5*b - 32*A*B*a^4*b^2 + 30
*A^2*a^3*b^3)*c^3 + (14*B^2*a^4*b^3 - 40*A*B*a^3*b^4 + 27*A^2*a^2*b^5)*c^2 - (7*
B^2*a^3*b^5 - 16*A*B*a^2*b^6 + 9*A^2*a*b^7)*c - (a^9*b^2 - 4*a^10*c)*sqrt((B^4*a
^4*b^12 - 4*A*B^3*a^3*b^13 + 6*A^2*B^2*a^2*b^14 - 4*A^3*B*a*b^15 + A^4*b^16 + A^
4*a^8*c^8 - 2*(A^2*B^2*a^9 - 8*A^3*B*a^8*b + 10*A^4*a^7*b^2)*c^7 + (B^4*a^10 - 1
6*A*B^3*a^9*b + 96*A^2*B^2*a^8*b^2 - 200*A^3*B*a^7*b^3 + 130*A^4*a^6*b^4)*c^6 -
2*(6*B^4*a^9*b^2 - 68*A*B^3*a^8*b^3 + 240*A^2*B^2*a^7*b^4 - 332*A^3*B*a^6*b^5 +
157*A^4*a^5*b^6)*c^5 + (46*B^4*a^8*b^4 - 344*A*B^3*a^7*b^5 + 888*A^2*B^2*a^6*b^6
- 956*A^3*B*a^5*b^7 + 367*A^4*a^4*b^8)*c^4 - 2*(31*B^4*a^7*b^6 - 182*A*B^3*a^6*
b^7 + 384*A^2*B^2*a^5*b^8 - 348*A^3*B*a^4*b^9 + 115*A^4*a^3*b^10)*c^3 + (37*B^4*
a^6*b^8 - 184*A*B^3*a^5*b^9 + 336*A^2*B^2*a^4*b^10 - 268*A^3*B*a^3*b^11 + 79*A^4
*a^2*b^12)*c^2 - 2*(5*B^4*a^5*b^10 - 22*A*B^3*a^4*b^11 + 36*A^2*B^2*a^3*b^12 - 2
6*A^3*B*a^2*b^13 + 7*A^4*a*b^14)*c)/(a^18*b^2 - 4*a^19*c)))/(a^9*b^2 - 4*a^10*c)
) + 4*(A^4*a^4*c^9 + (7*A^3*B*a^4*b - 10*A^4*a^3*b^2)*c^8 - (B^4*a^6 - 9*A*B^3*a
^5*b + 12*A^2*B^2*a^4*b^2 + 10*A^3*B*a^3*b^3 - 15*A^4*a^2*b^4)*c^7 + (6*B^4*a^5*
b^2 - 26*A*B^3*a^4*b^3 + 30*A^2*B^2*a^3*b^4 - 3*A^3*B*a^2*b^5 - 7*A^4*a*b^6)*c^6
- (5*B^4*a^4*b^4 - 17*A*B^3*a^3*b^5 + 18*A^2*B^2*a^2*b^6 - 5*A^3*B*a*b^7 - A^4*
b^8)*c^5 + (B^4*a^3*b^6 - 3*A*B^3*a^2*b^7 + 3*A^2*B^2*a*b^8 - A^3*B*b^9)*c^4)*sq
rt(x)) - 60*A*a^3 - 420*(B*a*b^2 - A*b^3 - (B*a^2 - 2*A*a*b)*c)*x^3 + 140*(B*a^2
*b - A*a*b^2 + A*a^2*c)*x^2 - 84*(B*a^3 - A*a^2*b)*x)/(a^4*x^(7/2))

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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((B*x+A)/x**(9/2)/(c*x**2+b*x+a),x)

[Out]

Timed out

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)/((c*x^2 + b*x + a)*x^(9/2)),x, algorithm="giac")

[Out]

Timed out