3.2376 \(\int \frac{f+g x}{(d+e x)^2 \left (a+b x+c x^2\right )^3} \, dx\)

Optimal. Leaf size=1043 \[ \frac{(c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \log (d+e x) e^4}{\left (c d^2-b e d+a e^2\right )^4}-\frac{(c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \log \left (c x^2+b x+a\right ) e^4}{2 \left (c d^2-b e d+a e^2\right )^4}+\frac{\left (6 c^4 f d^4+c^3 (4 a e (6 e f-d g)-3 b d (4 e f+d g)) d^2-b^3 e^3 (3 b e f-2 b d g-a e g)-b c e^2 \left (-3 d (e f-d g) b^2-a e (21 e f-13 d g) b+7 a^2 e^2 g\right )-c^2 e \left (-b^2 (3 e f+7 d g) d^2+6 a b e (4 e f+d g) d+2 a^2 e^2 (15 e f-22 d g)\right )\right ) e}{\left (b^2-4 a c\right )^2 \left (c d^2-b e d+a e^2\right )^3 (d+e x)}-\frac{\left (12 c^6 f d^6+2 c^5 (2 a e (15 e f-2 d g)-3 b d (6 e f+d g)) d^4+10 c^4 e \left (b^2 (3 e f+2 d g) d^2-a b e (12 e f+d g) d+2 a^2 e^2 (9 e f-4 d g)\right ) d^2+b^5 e^5 (3 b e f-2 b d g-a e g)+b^3 c e^4 \left (-d (6 e f-5 d g) b^2-10 a e (3 e f-2 d g) b+10 a^2 e^2 g\right )-10 a b c^2 e^4 \left (-d (6 e f-5 d g) b^2-3 a e (3 e f-2 d g) b+3 a^2 e^2 g\right )-10 c^3 e^2 \left (2 b^3 g d^4-8 a b^2 e g d^3+3 a^2 b e^2 (6 e f-d g) d+6 a^3 e^3 (e f-2 d g)\right )\right ) \tanh ^{-1}\left (\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right )}{\left (b^2-4 a c\right )^{5/2} \left (c d^2-b e d+a e^2\right )^4}-\frac{4 a c e (2 c d-b e) (2 c d f+2 a e g-b (e f+d g))-\left (-e b^2+c d b+2 a c e\right ) \left (6 c^2 f d^2-b e (3 b e f-2 b d g-a e g)+c (2 a e (5 e f-2 d g)-b d (2 e f+3 d g))\right )-c \left (12 c^3 f d^3+2 c^2 (2 a e (9 e f-2 d g)-3 b d (3 e f+d g)) d+b^2 e^2 (3 b e f-2 b d g-a e g)+c e \left (11 b^2 g d^2+16 a^2 e^2 g-2 a b e (9 e f+5 d g)\right )\right ) x}{2 \left (b^2-4 a c\right )^2 \left (c d^2-b e d+a e^2\right )^2 (d+e x) \left (c x^2+b x+a\right )}-\frac{-e f b^2+c d f b+a e g b+2 a c e f-2 a c d g+c (2 c d f+2 a e g-b (e f+d g)) x}{2 \left (b^2-4 a c\right ) \left (c d^2-b e d+a e^2\right ) (d+e x) \left (c x^2+b x+a\right )^2} \]

[Out]

(e*(6*c^4*d^4*f - b^3*e^3*(3*b*e*f - 2*b*d*g - a*e*g) - b*c*e^2*(7*a^2*e^2*g - a
*b*e*(21*e*f - 13*d*g) - 3*b^2*d*(e*f - d*g)) + c^3*d^2*(4*a*e*(6*e*f - d*g) - 3
*b*d*(4*e*f + d*g)) - c^2*e*(2*a^2*e^2*(15*e*f - 22*d*g) + 6*a*b*d*e*(4*e*f + d*
g) - b^2*d^2*(3*e*f + 7*d*g))))/((b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^3*(d +
e*x)) - (b*c*d*f - b^2*e*f + 2*a*c*e*f - 2*a*c*d*g + a*b*e*g + c*(2*c*d*f + 2*a*
e*g - b*(e*f + d*g))*x)/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)*(a +
b*x + c*x^2)^2) - (4*a*c*e*(2*c*d - b*e)*(2*c*d*f + 2*a*e*g - b*(e*f + d*g)) - (
b*c*d - b^2*e + 2*a*c*e)*(6*c^2*d^2*f - b*e*(3*b*e*f - 2*b*d*g - a*e*g) + c*(2*a
*e*(5*e*f - 2*d*g) - b*d*(2*e*f + 3*d*g))) - c*(12*c^3*d^3*f + b^2*e^2*(3*b*e*f
- 2*b*d*g - a*e*g) + 2*c^2*d*(2*a*e*(9*e*f - 2*d*g) - 3*b*d*(3*e*f + d*g)) + c*e
*(11*b^2*d^2*g + 16*a^2*e^2*g - 2*a*b*e*(9*e*f + 5*d*g)))*x)/(2*(b^2 - 4*a*c)^2*
(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)*(a + b*x + c*x^2)) - ((12*c^6*d^6*f + b^5*e^
5*(3*b*e*f - 2*b*d*g - a*e*g) + b^3*c*e^4*(10*a^2*e^2*g - b^2*d*(6*e*f - 5*d*g)
- 10*a*b*e*(3*e*f - 2*d*g)) - 10*a*b*c^2*e^4*(3*a^2*e^2*g - b^2*d*(6*e*f - 5*d*g
) - 3*a*b*e*(3*e*f - 2*d*g)) - 10*c^3*e^2*(2*b^3*d^4*g - 8*a*b^2*d^3*e*g + 6*a^3
*e^3*(e*f - 2*d*g) + 3*a^2*b*d*e^2*(6*e*f - d*g)) + 2*c^5*d^4*(2*a*e*(15*e*f - 2
*d*g) - 3*b*d*(6*e*f + d*g)) + 10*c^4*d^2*e*(2*a^2*e^2*(9*e*f - 4*d*g) - a*b*d*e
*(12*e*f + d*g) + b^2*d^2*(3*e*f + 2*d*g)))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c
]])/((b^2 - 4*a*c)^(5/2)*(c*d^2 - b*d*e + a*e^2)^4) + (e^4*(c*d*(6*e*f - 5*d*g)
- e*(3*b*e*f - 2*b*d*g - a*e*g))*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^4 - (e^4*
(c*d*(6*e*f - 5*d*g) - e*(3*b*e*f - 2*b*d*g - a*e*g))*Log[a + b*x + c*x^2])/(2*(
c*d^2 - b*d*e + a*e^2)^4)

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Rubi [A]  time = 16.3366, antiderivative size = 1043, normalized size of antiderivative = 1., number of steps used = 8, number of rules used = 6, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.24 \[ \frac{(c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \log (d+e x) e^4}{\left (c d^2-b e d+a e^2\right )^4}-\frac{(c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \log \left (c x^2+b x+a\right ) e^4}{2 \left (c d^2-b e d+a e^2\right )^4}+\frac{\left (6 c^4 f d^4+c^3 (4 a e (6 e f-d g)-3 b d (4 e f+d g)) d^2-b^3 e^3 (3 b e f-2 b d g-a e g)-b c e^2 \left (-3 d (e f-d g) b^2-a e (21 e f-13 d g) b+7 a^2 e^2 g\right )-c^2 e \left (-b^2 (3 e f+7 d g) d^2+6 a b e (4 e f+d g) d+2 a^2 e^2 (15 e f-22 d g)\right )\right ) e}{\left (b^2-4 a c\right )^2 \left (c d^2-b e d+a e^2\right )^3 (d+e x)}-\frac{\left (12 c^6 f d^6+2 c^5 (2 a e (15 e f-2 d g)-3 b d (6 e f+d g)) d^4+10 c^4 e \left (b^2 (3 e f+2 d g) d^2-a b e (12 e f+d g) d+2 a^2 e^2 (9 e f-4 d g)\right ) d^2+b^5 e^5 (3 b e f-2 b d g-a e g)+b^3 c e^4 \left (-d (6 e f-5 d g) b^2-10 a e (3 e f-2 d g) b+10 a^2 e^2 g\right )-10 a b c^2 e^4 \left (-d (6 e f-5 d g) b^2-3 a e (3 e f-2 d g) b+3 a^2 e^2 g\right )-10 c^3 e^2 \left (2 b^3 g d^4-8 a b^2 e g d^3+3 a^2 b e^2 (6 e f-d g) d+6 a^3 e^3 (e f-2 d g)\right )\right ) \tanh ^{-1}\left (\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right )}{\left (b^2-4 a c\right )^{5/2} \left (c d^2-b e d+a e^2\right )^4}-\frac{4 a c e (2 c d-b e) (2 c d f+2 a e g-b (e f+d g))-\left (-e b^2+c d b+2 a c e\right ) \left (6 c^2 f d^2-b e (3 b e f-2 b d g-a e g)+c (2 a e (5 e f-2 d g)-b d (2 e f+3 d g))\right )-c \left (12 c^3 f d^3+2 c^2 (2 a e (9 e f-2 d g)-3 b d (3 e f+d g)) d+b^2 e^2 (3 b e f-2 b d g-a e g)+c e \left (11 b^2 g d^2+16 a^2 e^2 g-2 a b e (9 e f+5 d g)\right )\right ) x}{2 \left (b^2-4 a c\right )^2 \left (c d^2-b e d+a e^2\right )^2 (d+e x) \left (c x^2+b x+a\right )}-\frac{-e f b^2+c d f b+a e g b+2 a c e f-2 a c d g+c (2 c d f+2 a e g-b (e f+d g)) x}{2 \left (b^2-4 a c\right ) \left (c d^2-b e d+a e^2\right ) (d+e x) \left (c x^2+b x+a\right )^2} \]

Antiderivative was successfully verified.

[In]  Int[(f + g*x)/((d + e*x)^2*(a + b*x + c*x^2)^3),x]

[Out]

(e*(6*c^4*d^4*f - b^3*e^3*(3*b*e*f - 2*b*d*g - a*e*g) - b*c*e^2*(7*a^2*e^2*g - a
*b*e*(21*e*f - 13*d*g) - 3*b^2*d*(e*f - d*g)) + c^3*d^2*(4*a*e*(6*e*f - d*g) - 3
*b*d*(4*e*f + d*g)) - c^2*e*(2*a^2*e^2*(15*e*f - 22*d*g) + 6*a*b*d*e*(4*e*f + d*
g) - b^2*d^2*(3*e*f + 7*d*g))))/((b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^3*(d +
e*x)) - (b*c*d*f - b^2*e*f + 2*a*c*e*f - 2*a*c*d*g + a*b*e*g + c*(2*c*d*f + 2*a*
e*g - b*(e*f + d*g))*x)/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)*(a +
b*x + c*x^2)^2) - (4*a*c*e*(2*c*d - b*e)*(2*c*d*f + 2*a*e*g - b*(e*f + d*g)) - (
b*c*d - b^2*e + 2*a*c*e)*(6*c^2*d^2*f - b*e*(3*b*e*f - 2*b*d*g - a*e*g) + c*(2*a
*e*(5*e*f - 2*d*g) - b*d*(2*e*f + 3*d*g))) - c*(12*c^3*d^3*f + b^2*e^2*(3*b*e*f
- 2*b*d*g - a*e*g) + 2*c^2*d*(2*a*e*(9*e*f - 2*d*g) - 3*b*d*(3*e*f + d*g)) + c*e
*(11*b^2*d^2*g + 16*a^2*e^2*g - 2*a*b*e*(9*e*f + 5*d*g)))*x)/(2*(b^2 - 4*a*c)^2*
(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)*(a + b*x + c*x^2)) - ((12*c^6*d^6*f + b^5*e^
5*(3*b*e*f - 2*b*d*g - a*e*g) + b^3*c*e^4*(10*a^2*e^2*g - b^2*d*(6*e*f - 5*d*g)
- 10*a*b*e*(3*e*f - 2*d*g)) - 10*a*b*c^2*e^4*(3*a^2*e^2*g - b^2*d*(6*e*f - 5*d*g
) - 3*a*b*e*(3*e*f - 2*d*g)) - 10*c^3*e^2*(2*b^3*d^4*g - 8*a*b^2*d^3*e*g + 6*a^3
*e^3*(e*f - 2*d*g) + 3*a^2*b*d*e^2*(6*e*f - d*g)) + 2*c^5*d^4*(2*a*e*(15*e*f - 2
*d*g) - 3*b*d*(6*e*f + d*g)) + 10*c^4*d^2*e*(2*a^2*e^2*(9*e*f - 4*d*g) - a*b*d*e
*(12*e*f + d*g) + b^2*d^2*(3*e*f + 2*d*g)))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c
]])/((b^2 - 4*a*c)^(5/2)*(c*d^2 - b*d*e + a*e^2)^4) + (e^4*(c*d*(6*e*f - 5*d*g)
- e*(3*b*e*f - 2*b*d*g - a*e*g))*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^4 - (e^4*
(c*d*(6*e*f - 5*d*g) - e*(3*b*e*f - 2*b*d*g - a*e*g))*Log[a + b*x + c*x^2])/(2*(
c*d^2 - b*d*e + a*e^2)^4)

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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((g*x+f)/(e*x+d)**2/(c*x**2+b*x+a)**3,x)

[Out]

Timed out

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Mathematica [A]  time = 7.55736, size = 1409, normalized size = 1.35 \[ -\frac{(e f-d g) e^4}{\left (c d^2-b e d+a e^2\right )^3 (d+e x)}+\frac{\left (3 e^6 f b^6-2 d e^5 g b^6-6 c d e^5 f b^5-a e^6 g b^5+5 c d^2 e^4 g b^5-30 a c e^6 f b^4+20 a c d e^5 g b^4+60 a c^2 d e^5 f b^3+10 a^2 c e^6 g b^3-50 a c^2 d^2 e^4 g b^3-20 c^3 d^4 e^2 g b^3+90 a^2 c^2 e^6 f b^2+30 c^4 d^4 e^2 f b^2-60 a^2 c^2 d e^5 g b^2+80 a c^3 d^3 e^3 g b^2+20 c^4 d^5 e g b^2-180 a^2 c^3 d e^5 f b-120 a c^4 d^3 e^3 f b-36 c^5 d^5 e f b-6 c^5 d^6 g b-30 a^3 c^2 e^6 g b+30 a^2 c^3 d^2 e^4 g b-10 a c^4 d^4 e^2 g b+12 c^6 d^6 f-60 a^3 c^3 e^6 f+180 a^2 c^4 d^2 e^4 f+60 a c^5 d^4 e^2 f+120 a^3 c^3 d e^5 g-80 a^2 c^4 d^3 e^3 g-8 a c^5 d^5 e g\right ) \tan ^{-1}\left (\frac{b+2 c x}{\sqrt{4 a c-b^2}}\right )}{\left (b^2-4 a c\right )^2 \sqrt{4 a c-b^2} \left (-c d^2+b e d-a e^2\right )^4}+\frac{\left (-3 b f e^6+a g e^6+6 c d f e^5+2 b d g e^5-5 c d^2 g e^4\right ) \log (d+e x)}{\left (c d^2-b e d+a e^2\right )^4}+\frac{\left (3 b f e^6-a g e^6-6 c d f e^5-2 b d g e^5+5 c d^2 g e^4\right ) \log \left (c x^2+b x+a\right )}{2 \left (c d^2-b e d+a e^2\right )^4}+\frac{-4 e^4 f b^5+2 d e^3 g b^5+7 c d e^3 f b^4+2 a e^4 g b^4-6 c d^2 e^2 g b^4-4 c e^4 f x b^4+2 c d e^3 g x b^4+29 a c e^4 f b^3+3 c^2 d^2 e^2 f b^3-13 a c d e^3 g b^3+7 c^2 d^3 e g b^3+6 c^2 d e^3 f x b^3+2 a c e^4 g x b^3-6 c^2 d^2 e^2 g x b^3-56 a c^2 d e^3 f b^2-12 c^3 d^3 e f b^2-3 c^3 d^4 g b^2-15 a^2 c e^4 g b^2+18 a c^2 d^2 e^2 g b^2+26 a c^2 e^4 f x b^2+6 c^3 d^2 e^2 f x b^2-10 a c^2 d e^3 g x b^2+14 c^3 d^3 e g x b^2+6 c^4 d^4 f b-46 a^2 c^2 e^4 f b+24 a c^3 d^2 e^2 f b+44 a^2 c^2 d e^3 g b-4 a c^3 d^3 e g b-48 a c^3 d e^3 f x b-24 c^4 d^3 e f x b-6 c^4 d^4 g x b-14 a^2 c^2 e^4 g x b-12 a c^3 d^2 e^2 g x b+64 a^2 c^3 d e^3 f+16 a^3 c^2 e^4 g-48 a^2 c^3 d^2 e^2 g+12 c^5 d^4 f x-28 a^2 c^3 e^4 f x+48 a c^4 d^2 e^2 f x+56 a^2 c^3 d e^3 g x-8 a c^4 d^3 e g x}{2 \left (4 a c-b^2\right )^2 \left (c d^2-b e d+a e^2\right )^3 \left (c x^2+b x+a\right )}+\frac{e^2 f b^3-2 c d e f b^2-a e^2 g b^2+c e^2 f x b^2+c^2 d^2 f b-3 a c e^2 f b+2 a c d e g b-2 c^2 d e f x b-c^2 d^2 g x b-a c e^2 g x b+4 a c^2 d e f-2 a c^2 d^2 g+2 a^2 c e^2 g+2 c^3 d^2 f x-2 a c^2 e^2 f x+4 a c^2 d e g x}{2 \left (4 a c-b^2\right ) \left (c d^2-b e d+a e^2\right )^2 \left (c x^2+b x+a\right )^2} \]

Antiderivative was successfully verified.

[In]  Integrate[(f + g*x)/((d + e*x)^2*(a + b*x + c*x^2)^3),x]

[Out]

-((e^4*(e*f - d*g))/((c*d^2 - b*d*e + a*e^2)^3*(d + e*x))) + (b*c^2*d^2*f - 2*b^
2*c*d*e*f + 4*a*c^2*d*e*f + b^3*e^2*f - 3*a*b*c*e^2*f - 2*a*c^2*d^2*g + 2*a*b*c*
d*e*g - a*b^2*e^2*g + 2*a^2*c*e^2*g + 2*c^3*d^2*f*x - 2*b*c^2*d*e*f*x + b^2*c*e^
2*f*x - 2*a*c^2*e^2*f*x - b*c^2*d^2*g*x + 4*a*c^2*d*e*g*x - a*b*c*e^2*g*x)/(2*(-
b^2 + 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x + c*x^2)^2) + (6*b*c^4*d^4*f - 1
2*b^2*c^3*d^3*e*f + 3*b^3*c^2*d^2*e^2*f + 24*a*b*c^3*d^2*e^2*f + 7*b^4*c*d*e^3*f
- 56*a*b^2*c^2*d*e^3*f + 64*a^2*c^3*d*e^3*f - 4*b^5*e^4*f + 29*a*b^3*c*e^4*f -
46*a^2*b*c^2*e^4*f - 3*b^2*c^3*d^4*g + 7*b^3*c^2*d^3*e*g - 4*a*b*c^3*d^3*e*g - 6
*b^4*c*d^2*e^2*g + 18*a*b^2*c^2*d^2*e^2*g - 48*a^2*c^3*d^2*e^2*g + 2*b^5*d*e^3*g
- 13*a*b^3*c*d*e^3*g + 44*a^2*b*c^2*d*e^3*g + 2*a*b^4*e^4*g - 15*a^2*b^2*c*e^4*
g + 16*a^3*c^2*e^4*g + 12*c^5*d^4*f*x - 24*b*c^4*d^3*e*f*x + 6*b^2*c^3*d^2*e^2*f
*x + 48*a*c^4*d^2*e^2*f*x + 6*b^3*c^2*d*e^3*f*x - 48*a*b*c^3*d*e^3*f*x - 4*b^4*c
*e^4*f*x + 26*a*b^2*c^2*e^4*f*x - 28*a^2*c^3*e^4*f*x - 6*b*c^4*d^4*g*x + 14*b^2*
c^3*d^3*e*g*x - 8*a*c^4*d^3*e*g*x - 6*b^3*c^2*d^2*e^2*g*x - 12*a*b*c^3*d^2*e^2*g
*x + 2*b^4*c*d*e^3*g*x - 10*a*b^2*c^2*d*e^3*g*x + 56*a^2*c^3*d*e^3*g*x + 2*a*b^3
*c*e^4*g*x - 14*a^2*b*c^2*e^4*g*x)/(2*(-b^2 + 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^3
*(a + b*x + c*x^2)) + ((12*c^6*d^6*f - 36*b*c^5*d^5*e*f + 30*b^2*c^4*d^4*e^2*f +
60*a*c^5*d^4*e^2*f - 120*a*b*c^4*d^3*e^3*f + 180*a^2*c^4*d^2*e^4*f - 6*b^5*c*d*
e^5*f + 60*a*b^3*c^2*d*e^5*f - 180*a^2*b*c^3*d*e^5*f + 3*b^6*e^6*f - 30*a*b^4*c*
e^6*f + 90*a^2*b^2*c^2*e^6*f - 60*a^3*c^3*e^6*f - 6*b*c^5*d^6*g + 20*b^2*c^4*d^5
*e*g - 8*a*c^5*d^5*e*g - 20*b^3*c^3*d^4*e^2*g - 10*a*b*c^4*d^4*e^2*g + 80*a*b^2*
c^3*d^3*e^3*g - 80*a^2*c^4*d^3*e^3*g + 5*b^5*c*d^2*e^4*g - 50*a*b^3*c^2*d^2*e^4*
g + 30*a^2*b*c^3*d^2*e^4*g - 2*b^6*d*e^5*g + 20*a*b^4*c*d*e^5*g - 60*a^2*b^2*c^2
*d*e^5*g + 120*a^3*c^3*d*e^5*g - a*b^5*e^6*g + 10*a^2*b^3*c*e^6*g - 30*a^3*b*c^2
*e^6*g)*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/((b^2 - 4*a*c)^2*Sqrt[-b^2 + 4*a
*c]*(-(c*d^2) + b*d*e - a*e^2)^4) + ((6*c*d*e^5*f - 3*b*e^6*f - 5*c*d^2*e^4*g +
2*b*d*e^5*g + a*e^6*g)*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^4 + ((-6*c*d*e^5*f
+ 3*b*e^6*f + 5*c*d^2*e^4*g - 2*b*d*e^5*g - a*e^6*g)*Log[a + b*x + c*x^2])/(2*(c
*d^2 - b*d*e + a*e^2)^4)

_______________________________________________________________________________________

Maple [B]  time = 0.062, size = 17159, normalized size = 16.5 \[ \text{output too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((g*x+f)/(e*x+d)^2/(c*x^2+b*x+a)^3,x)

[Out]

result too large to display

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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((g*x + f)/((c*x^2 + b*x + a)^3*(e*x + d)^2),x, algorithm="maxima")

[Out]

Exception raised: ValueError

_______________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((g*x + f)/((c*x^2 + b*x + a)^3*(e*x + d)^2),x, algorithm="fricas")

[Out]

Timed out

_______________________________________________________________________________________

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((g*x+f)/(e*x+d)**2/(c*x**2+b*x+a)**3,x)

[Out]

Timed out

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 8.82745, size = 1, normalized size = 0. \[ \mathit{Done} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((g*x + f)/((c*x^2 + b*x + a)^3*(e*x + d)^2),x, algorithm="giac")

[Out]

Done