∖int(f+gx)∖left(a+bx+cx2∖right)3∕2 ___________________________________________________d+ex∖,dx

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

Optimal. Leaf size=441 \[ \frac{\tanh ^{-1}\left (\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right ) \left (48 c^2 e^2 \left (a^2 e^2 g+2 a b e (e f-d g)+b^2 (-d) (e f-d g)\right )-8 b^2 c e^3 (3 a e g-b d g+b e f)+192 c^3 d e (b d-a e) (e f-d g)+3 b^4 e^4 g-128 c^4 d^3 (e f-d g)\right )}{128 c^{5/2} e^5}-\frac{\sqrt{a+b x+c x^2} \left (2 c e x \left (-4 c e (3 a e g-2 b d g+2 b e f)+3 b^2 e^2 g+16 c^2 d (e f-d g)\right )+16 c^2 e (5 b d-4 a e) (e f-d g)-4 b c e^2 (3 a e g-2 b d g+2 b e f)+3 b^3 e^3 g-64 c^3 d^2 (e f-d g)\right )}{64 c^2 e^4}+\frac{(e f-d g) \left (a e^2-b d e+c d^2\right )^{3/2} \tanh ^{-1}\left (\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right )}{e^5}+\frac{\left (a+b x+c x^2\right )^{3/2} (3 b e g-8 c d g+8 c e f+6 c e g x)}{24 c e^2} \]

[Out]

-((3*b^3*e^3*g - 64*c^3*d^2*(e*f - d*g) + 16*c^2*e*(5*b*d - 4*a*e)*(e*f - d*g) -

4*b*c*e^2*(2*b*e*f - 2*b*d*g + 3*a*e*g) + 2*c*e*(3*b^2*e^2*g + 16*c^2*d*(e*f -

d*g) - 4*c*e*(2*b*e*f - 2*b*d*g + 3*a*e*g))*x)*Sqrt[a + b*x + c*x^2])/(64*c^2*e^

4) + ((8*c*e*f - 8*c*d*g + 3*b*e*g + 6*c*e*g*x)*(a + b*x + c*x^2)^(3/2))/(24*c*e

^2) + ((3*b^4*e^4*g - 128*c^4*d^3*(e*f - d*g) + 192*c^3*d*e*(b*d - a*e)*(e*f - d

*g) - 8*b^2*c*e^3*(b*e*f - b*d*g + 3*a*e*g) + 48*c^2*e^2*(a^2*e^2*g - b^2*d*(e*f

- d*g) + 2*a*b*e*(e*f - d*g)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*

x^2])])/(128*c^(5/2)*e^5) + ((c*d^2 - b*d*e + a*e^2)^(3/2)*(e*f - d*g)*ArcTanh[(

b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x

^2])])/e^5

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Rubi [A] time = 1.68833, antiderivative size = 441, normalized size of antiderivative = 1., number of steps used = 7, number of rules used = 5, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.185 \[ \frac{\tanh ^{-1}\left (\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right ) \left (48 c^2 e^2 \left (a^2 e^2 g+2 a b e (e f-d g)+b^2 (-d) (e f-d g)\right )-8 b^2 c e^3 (3 a e g-b d g+b e f)+192 c^3 d e (b d-a e) (e f-d g)+3 b^4 e^4 g-128 c^4 d^3 (e f-d g)\right )}{128 c^{5/2} e^5}-\frac{\sqrt{a+b x+c x^2} \left (2 c e x \left (-4 c e (3 a e g-2 b d g+2 b e f)+3 b^2 e^2 g+16 c^2 d (e f-d g)\right )+16 c^2 e (5 b d-4 a e) (e f-d g)-4 b c e^2 (3 a e g-2 b d g+2 b e f)+3 b^3 e^3 g-64 c^3 d^2 (e f-d g)\right )}{64 c^2 e^4}+\frac{(e f-d g) \left (a e^2-b d e+c d^2\right )^{3/2} \tanh ^{-1}\left (\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right )}{e^5}+\frac{\left (a+b x+c x^2\right )^{3/2} (3 b e g-8 c d g+8 c e f+6 c e g x)}{24 c e^2} \]

Antiderivative was successfully veriﬁed.

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

[Out]

-((3*b^3*e^3*g - 64*c^3*d^2*(e*f - d*g) + 16*c^2*e*(5*b*d - 4*a*e)*(e*f - d*g) -

4*b*c*e^2*(2*b*e*f - 2*b*d*g + 3*a*e*g) + 2*c*e*(3*b^2*e^2*g + 16*c^2*d*(e*f -

d*g) - 4*c*e*(2*b*e*f - 2*b*d*g + 3*a*e*g))*x)*Sqrt[a + b*x + c*x^2])/(64*c^2*e^

4) + ((8*c*e*f - 8*c*d*g + 3*b*e*g + 6*c*e*g*x)*(a + b*x + c*x^2)^(3/2))/(24*c*e

^2) + ((3*b^4*e^4*g - 128*c^4*d^3*(e*f - d*g) + 192*c^3*d*e*(b*d - a*e)*(e*f - d

*g) - 8*b^2*c*e^3*(b*e*f - b*d*g + 3*a*e*g) + 48*c^2*e^2*(a^2*e^2*g - b^2*d*(e*f

- d*g) + 2*a*b*e*(e*f - d*g)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*

x^2])])/(128*c^(5/2)*e^5) + ((c*d^2 - b*d*e + a*e^2)^(3/2)*(e*f - d*g)*ArcTanh[(

b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x

^2])])/e^5

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

[Out]

Timed out

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Mathematica [A] time = 1.42208, size = 449, normalized size = 1.02 \[ \frac{\frac{3 \log \left (2 \sqrt{c} \sqrt{a+x (b+c x)}+b+2 c x\right ) \left (48 c^2 e^2 \left (a^2 e^2 g+2 a b e (e f-d g)+b^2 d (d g-e f)\right )-8 b^2 c e^3 (3 a e g-b d g+b e f)-192 c^3 d e (b d-a e) (d g-e f)+3 b^4 e^4 g+128 c^4 d^3 (d g-e f)\right )}{c^{5/2}}+\frac{2 e \sqrt{a+x (b+c x)} \left (8 c^2 e \left (a e (-32 d g+32 e f+15 e g x)+b \left (30 d^2 g-2 d e (15 f+7 g x)+e^2 x (14 f+9 g x)\right )\right )+6 b c e^2 (10 a e g+b (-4 d g+4 e f+e g x))-9 b^3 e^3 g-16 c^3 \left (12 d^3 g-6 d^2 e (2 f+g x)+2 d e^2 x (3 f+2 g x)-e^3 x^2 (4 f+3 g x)\right )\right )}{c^2}+384 (e f-d g) \log (d+e x) \left (e (a e-b d)+c d^2\right )^{3/2}+384 (d g-e f) \left (e (a e-b d)+c d^2\right )^{3/2} \log \left (2 \sqrt{a+x (b+c x)} \sqrt{e (a e-b d)+c d^2}+2 a e-b d+b e x-2 c d x\right )}{384 e^5} \]

Antiderivative was successfully veriﬁed.

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

[Out]

((2*e*Sqrt[a + x*(b + c*x)]*(-9*b^3*e^3*g - 16*c^3*(12*d^3*g - 6*d^2*e*(2*f + g*

x) + 2*d*e^2*x*(3*f + 2*g*x) - e^3*x^2*(4*f + 3*g*x)) + 6*b*c*e^2*(10*a*e*g + b*

(4*e*f - 4*d*g + e*g*x)) + 8*c^2*e*(a*e*(32*e*f - 32*d*g + 15*e*g*x) + b*(30*d^2

*g - 2*d*e*(15*f + 7*g*x) + e^2*x*(14*f + 9*g*x)))))/c^2 + 384*(c*d^2 + e*(-(b*d

) + a*e))^(3/2)*(e*f - d*g)*Log[d + e*x] + (3*(3*b^4*e^4*g + 128*c^4*d^3*(-(e*f)

+ d*g) - 192*c^3*d*e*(b*d - a*e)*(-(e*f) + d*g) - 8*b^2*c*e^3*(b*e*f - b*d*g +

3*a*e*g) + 48*c^2*e^2*(a^2*e^2*g + 2*a*b*e*(e*f - d*g) + b^2*d*(-(e*f) + d*g)))*

Log[b + 2*c*x + 2*Sqrt[c]*Sqrt[a + x*(b + c*x)]])/c^(5/2) + 384*(c*d^2 + e*(-(b*

d) + a*e))^(3/2)*(-(e*f) + d*g)*Log[-(b*d) + 2*a*e - 2*c*d*x + b*e*x + 2*Sqrt[c*

d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)]])/(384*e^5)

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Maple [B] time = 0.014, size = 4188, normalized size = 9.5 \[ \text{output too large to display} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

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

[Out]

1/e^3*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c*d^2*f-

1/e^4*ln((1/2*(b*e-2*c*d)/e+c*(x+d/e))/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e

)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(3/2)*d^3*f-1/e^4*((x+d/e)^2*c+(b*e-2*c*d)/e

*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c*d^3*g-1/16/e/c^(3/2)*ln((1/2*(b*e-2*c*

d)/e+c*(x+d/e))/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e

^2)^(1/2))*b^3*f+1/4/e*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^

2)^(1/2)*x*b*f-5/4/e^2*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^

2)^(1/2)*b*d*f+3/128/e*g/c^(5/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^4

+1/4/e*g*(c*x^2+b*x+a)^(3/2)*x-1/3/e^2*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2

-b*d*e+c*d^2)/e^2)^(3/2)*d*g+1/e*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e

+c*d^2)/e^2)^(1/2)*a*f+3/8/e*g*(c*x^2+b*x+a)^(1/2)*x*a+1/8/e*g/c*(c*x^2+b*x+a)^(

3/2)*b+1/e^5*ln((1/2*(b*e-2*c*d)/e+c*(x+d/e))/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e

*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(3/2)*d^4*g-1/e/((a*e^2-b*d*e+c*d^2)/

e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c

*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/

2))/(x+d/e))*a^2*f-1/e^2*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/

e^2)^(1/2)*a*d*g+1/3/e*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^

2)^(3/2)*f+1/8/e/c*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(

1/2)*b^2*f+5/4/e^3*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(

1/2)*b*d^2*g-3/64/e*g/c^2*(c*x^2+b*x+a)^(1/2)*b^3+3/8/e*g/c^(1/2)*ln((1/2*b+c*x)

/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2+2/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a

*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((

x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d^3*

c*f-3/4/e^2/c^(1/2)*ln((1/2*(b*e-2*c*d)/e+c*(x+d/e))/c^(1/2)+((x+d/e)^2*c+(b*e-2

*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*a*b*d*g-2/e^3/((a*e^2-b*d*e+c*d^

2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*

e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^

(1/2))/(x+d/e))*a*b*d^2*g-2/e^5/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d

*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2

*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d^4*c*g+2/e^

2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x

+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^

2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*b*d*f+2/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2

)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2

)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/

e))*a*c*d^3*g-2/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^

2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*

d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*c*d^2*f+1/e^4/((a*e^2-b*

d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*

e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^

2)/e^2)^(1/2))/(x+d/e))*b^2*d^3*g-1/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a

*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((

x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^2*d^

2*f+1/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c

*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/

e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2*d*g+1/e^6/((a*e^2-b*d*e+c*d^2)/e

^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*

d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2

))/(x+d/e))*c^2*d^5*g-1/e^5/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c

*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(

b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c^2*d^4*f-3/8/e^2*

ln((1/2*(b*e-2*c*d)/e+c*(x+d/e))/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e

^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b^2*d*f-1/2/e^2*((x+d/e)^2*c+(b*e-2*c*d)/e*(

x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c*d*f+1/2/e^3*((x+d/e)^2*c+(b*e-2*c*d)/e

*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c*d^2*g-1/4/e^2*((x+d/e)^2*c+(b*e-2*c*

d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*d*g-1/8/e^2/c*((x+d/e)^2*c+(b*e-

2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*d*g+1/16/e^2/c^(3/2)*ln((1/2

*(b*e-2*c*d)/e+c*(x+d/e))/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*

e+c*d^2)/e^2)^(1/2))*b^3*d*g+3/2/e^3*ln((1/2*(b*e-2*c*d)/e+c*(x+d/e))/c^(1/2)+((

x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d^2*a*g

-3/2/e^2*ln((1/2*(b*e-2*c*d)/e+c*(x+d/e))/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+

d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d*a*f+3/8/e^3*ln((1/2*(b*e-2*c*d)/e

+c*(x+d/e))/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^

(1/2))/c^(1/2)*b^2*d^2*g+3/16/e*g/c*(c*x^2+b*x+a)^(1/2)*b*a-3/16/e*g/c^(3/2)*ln(

(1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2*a-3/32/e*g/c*(c*x^2+b*x+a)^(1/2)*x*

b^2+3/4/e/c^(1/2)*ln((1/2*(b*e-2*c*d)/e+c*(x+d/e))/c^(1/2)+((x+d/e)^2*c+(b*e-2*c

*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*a*b*f-3/2/e^4*ln((1/2*(b*e-2*c*d)/

e+c*(x+d/e))/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)

^(1/2))*c^(1/2)*d^3*b*g+3/2/e^3*ln((1/2*(b*e-2*c*d)/e+c*(x+d/e))/c^(1/2)+((x+d/e

)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d^2*b*f

_______________________________________________________________________________________

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

[Out]

Timed out

_______________________________________________________________________________________

GIAC/XCAS [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

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

[Out]

Exception raised: TypeError

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