3.630 \(\int \frac{\sqrt{d+e x}}{\left (a-c x^2\right )^3} \, dx\)
Optimal. Leaf size=281 \[ -\frac{\left (-18 \sqrt{a} \sqrt{c} d e+5 a e^2+12 c d^2\right ) \tanh ^{-1}\left (\frac{\sqrt [4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right )}{32 a^{5/2} c^{3/4} \left (\sqrt{c} d-\sqrt{a} e\right )^{3/2}}+\frac{\left (18 \sqrt{a} \sqrt{c} d e+5 a e^2+12 c d^2\right ) \tanh ^{-1}\left (\frac{\sqrt [4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right )}{32 a^{5/2} c^{3/4} \left (\sqrt{a} e+\sqrt{c} d\right )^{3/2}}-\frac{\sqrt{d+e x} \left (a d e-x \left (6 c d^2-5 a e^2\right )\right )}{16 a^2 \left (a-c x^2\right ) \left (c d^2-a e^2\right )}+\frac{x \sqrt{d+e x}}{4 a \left (a-c x^2\right )^2} \]
[Out]
(x*Sqrt[d + e*x])/(4*a*(a - c*x^2)^2) - (Sqrt[d + e*x]*(a*d*e - (6*c*d^2 - 5*a*e
^2)*x))/(16*a^2*(c*d^2 - a*e^2)*(a - c*x^2)) - ((12*c*d^2 - 18*Sqrt[a]*Sqrt[c]*d
*e + 5*a*e^2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(32*
a^(5/2)*c^(3/4)*(Sqrt[c]*d - Sqrt[a]*e)^(3/2)) + ((12*c*d^2 + 18*Sqrt[a]*Sqrt[c]
*d*e + 5*a*e^2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(3
2*a^(5/2)*c^(3/4)*(Sqrt[c]*d + Sqrt[a]*e)^(3/2))
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Rubi [A] time = 1.17905, antiderivative size = 281, normalized size of antiderivative = 1.,
number of steps used = 6, number of rules used = 5, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25
\[ -\frac{\left (-18 \sqrt{a} \sqrt{c} d e+5 a e^2+12 c d^2\right ) \tanh ^{-1}\left (\frac{\sqrt [4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right )}{32 a^{5/2} c^{3/4} \left (\sqrt{c} d-\sqrt{a} e\right )^{3/2}}+\frac{\left (18 \sqrt{a} \sqrt{c} d e+5 a e^2+12 c d^2\right ) \tanh ^{-1}\left (\frac{\sqrt [4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right )}{32 a^{5/2} c^{3/4} \left (\sqrt{a} e+\sqrt{c} d\right )^{3/2}}-\frac{\sqrt{d+e x} \left (a d e-x \left (6 c d^2-5 a e^2\right )\right )}{16 a^2 \left (a-c x^2\right ) \left (c d^2-a e^2\right )}+\frac{x \sqrt{d+e x}}{4 a \left (a-c x^2\right )^2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[d + e*x]/(a - c*x^2)^3,x]
[Out]
(x*Sqrt[d + e*x])/(4*a*(a - c*x^2)^2) - (Sqrt[d + e*x]*(a*d*e - (6*c*d^2 - 5*a*e
^2)*x))/(16*a^2*(c*d^2 - a*e^2)*(a - c*x^2)) - ((12*c*d^2 - 18*Sqrt[a]*Sqrt[c]*d
*e + 5*a*e^2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(32*
a^(5/2)*c^(3/4)*(Sqrt[c]*d - Sqrt[a]*e)^(3/2)) + ((12*c*d^2 + 18*Sqrt[a]*Sqrt[c]
*d*e + 5*a*e^2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(3
2*a^(5/2)*c^(3/4)*(Sqrt[c]*d + Sqrt[a]*e)^(3/2))
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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((e*x+d)**(1/2)/(-c*x**2+a)**3,x)
[Out]
Timed out
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Mathematica [A] time = 0.525458, size = 304, normalized size = 1.08 \[ -\frac{\left (-18 \sqrt{a} \sqrt{c} d e+5 a e^2+12 c d^2\right ) \tanh ^{-1}\left (\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-\sqrt{a} \sqrt{c} e}}\right )}{32 a^{5/2} \sqrt{c} \left (\sqrt{c} d-\sqrt{a} e\right ) \sqrt{c d-\sqrt{a} \sqrt{c} e}}+\frac{\left (18 \sqrt{a} \sqrt{c} d e+5 a e^2+12 c d^2\right ) \tanh ^{-1}\left (\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} \sqrt{c} e+c d}}\right )}{32 a^{5/2} \sqrt{c} \left (\sqrt{a} e+\sqrt{c} d\right ) \sqrt{\sqrt{a} \sqrt{c} e+c d}}+\frac{\sqrt{d+e x} \left (4 a x-\frac{\left (a-c x^2\right ) \left (a e (d+5 e x)-6 c d^2 x\right )}{c d^2-a e^2}\right )}{16 a^2 \left (a-c x^2\right )^2} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[d + e*x]/(a - c*x^2)^3,x]
[Out]
(Sqrt[d + e*x]*(4*a*x - ((a - c*x^2)*(-6*c*d^2*x + a*e*(d + 5*e*x)))/(c*d^2 - a*
e^2)))/(16*a^2*(a - c*x^2)^2) - ((12*c*d^2 - 18*Sqrt[a]*Sqrt[c]*d*e + 5*a*e^2)*A
rcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - Sqrt[a]*Sqrt[c]*e]])/(32*a^(5/2)*Sqrt[
c]*(Sqrt[c]*d - Sqrt[a]*e)*Sqrt[c*d - Sqrt[a]*Sqrt[c]*e]) + ((12*c*d^2 + 18*Sqrt
[a]*Sqrt[c]*d*e + 5*a*e^2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d + Sqrt[a]*Sq
rt[c]*e]])/(32*a^(5/2)*Sqrt[c]*(Sqrt[c]*d + Sqrt[a]*e)*Sqrt[c*d + Sqrt[a]*Sqrt[c
]*e])
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Maple [B] time = 0.149, size = 806, normalized size = 2.9 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)^(1/2)/(-c*x^2+a)^3,x)
[Out]
-3/16*e/a^2/(e*x+(a*c*e^2)^(1/2)/c)^2/(c*d-(a*c*e^2)^(1/2))*(e*x+d)^(3/2)*d+5/32
*e/c/a^2*(a*c*e^2)^(1/2)/(e*x+(a*c*e^2)^(1/2)/c)^2/(c*d-(a*c*e^2)^(1/2))*(e*x+d)
^(3/2)+3/16*e/c/a^2/(e*x+(a*c*e^2)^(1/2)/c)^2*(e*x+d)^(1/2)*d-7/32*e/c^2/a^2*(a*
c*e^2)^(1/2)/(e*x+(a*c*e^2)^(1/2)/c)^2*(e*x+d)^(1/2)+5/32*e^3*c/a/(a*c*e^2)^(1/2
)/(c*d-(a*c*e^2)^(1/2))/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)/
((-c*d+(a*c*e^2)^(1/2))*c)^(1/2))+3/8*e*c^2/a^2/(a*c*e^2)^(1/2)/(c*d-(a*c*e^2)^(
1/2))/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(
1/2))*c)^(1/2))*d^2-9/16*e*c/a^2/(c*d-(a*c*e^2)^(1/2))/((-c*d+(a*c*e^2)^(1/2))*c
)^(1/2)*arctan(c*(e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2))*d-3/16*e/a^2/(e
*x-(a*c*e^2)^(1/2)/c)^2/(c*d+(a*c*e^2)^(1/2))*(e*x+d)^(3/2)*d-5/32*e/c/a^2*(a*c*
e^2)^(1/2)/(e*x-(a*c*e^2)^(1/2)/c)^2/(c*d+(a*c*e^2)^(1/2))*(e*x+d)^(3/2)+3/16*e/
c/a^2/(e*x-(a*c*e^2)^(1/2)/c)^2*(e*x+d)^(1/2)*d+7/32*e/c^2/a^2*(a*c*e^2)^(1/2)/(
e*x-(a*c*e^2)^(1/2)/c)^2*(e*x+d)^(1/2)+5/32*e^3*c/a/(a*c*e^2)^(1/2)/(c*d+(a*c*e^
2)^(1/2))/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)/((c*d+(a*c*e^2
)^(1/2))*c)^(1/2))+3/8*e*c^2/a^2/(a*c*e^2)^(1/2)/(c*d+(a*c*e^2)^(1/2))/((c*d+(a*
c*e^2)^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2))*
d^2+9/16*e*c/a^2/(c*d+(a*c*e^2)^(1/2))/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh(c
*(e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2))*d
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ -\int \frac{\sqrt{e x + d}}{{\left (c x^{2} - a\right )}^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-sqrt(e*x + d)/(c*x^2 - a)^3,x, algorithm="maxima")
[Out]
-integrate(sqrt(e*x + d)/(c*x^2 - a)^3, x)
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Fricas [A] time = 0.47331, size = 5112, normalized size = 18.19 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-sqrt(e*x + d)/(c*x^2 - a)^3,x, algorithm="fricas")
[Out]
-1/64*((a^4*c*d^2 - a^5*e^2 + (a^2*c^3*d^2 - a^3*c^2*e^2)*x^4 - 2*(a^3*c^2*d^2 -
a^4*c*e^2)*x^2)*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105
*a^3*d*e^6 + (a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6)*s
qrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*
c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*
a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^
2*d^2*e^4 - a^8*c*e^6))*log(-(3024*c^3*d^6*e^5 - 7884*a*c^2*d^4*e^7 + 5625*a^2*c
*d^2*e^9 - 625*a^3*e^11)*sqrt(e*x + d) + (126*a^3*c^3*d^5*e^6 - 318*a^4*c^2*d^3*
e^8 + 200*a^5*c*d*e^10 + (12*a^5*c^7*d^10 - 55*a^6*c^6*d^8*e^2 + 98*a^7*c^5*d^6*
e^4 - 84*a^8*c^4*d^4*e^6 + 34*a^9*c^3*d^2*e^8 - 5*a^10*c^2*e^10)*sqrt((441*c^2*d
^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*c^8*d^10*e^2 +
15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*a^10*c^4*d^2*e
^10 + a^11*c^3*e^12)))*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4
- 105*a^3*d*e^6 + (a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*
e^6)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 -
6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^
8 - 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*
a^7*c^2*d^2*e^4 - a^8*c*e^6))) - (a^4*c*d^2 - a^5*e^2 + (a^2*c^3*d^2 - a^3*c^2*e
^2)*x^4 - 2*(a^3*c^2*d^2 - a^4*c*e^2)*x^2)*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2
+ 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 + (a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*
c^2*d^2*e^4 - a^8*c*e^6)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^
14)/(a^5*c^9*d^12 - 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6
+ 15*a^9*c^5*d^4*e^8 - 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 - 3*
a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6))*log(-(3024*c^3*d^6*e^5 - 7884*
a*c^2*d^4*e^7 + 5625*a^2*c*d^2*e^9 - 625*a^3*e^11)*sqrt(e*x + d) - (126*a^3*c^3*
d^5*e^6 - 318*a^4*c^2*d^3*e^8 + 200*a^5*c*d*e^10 + (12*a^5*c^7*d^10 - 55*a^6*c^6
*d^8*e^2 + 98*a^7*c^5*d^6*e^4 - 84*a^8*c^4*d^4*e^6 + 34*a^9*c^3*d^2*e^8 - 5*a^10
*c^2*e^10)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d
^12 - 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*
d^4*e^8 - 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))*sqrt((144*c^3*d^7 - 420*a*c^2*d
^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 + (a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 +
3*a^7*c^2*d^2*e^4 - a^8*c*e^6)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*
a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d
^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^
6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6))) + (a^4*c*d^2 - a^5*e^2
+ (a^2*c^3*d^2 - a^3*c^2*e^2)*x^4 - 2*(a^3*c^2*d^2 - a^4*c*e^2)*x^2)*sqrt((144*c
^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 - (a^5*c^4*d^6 -
3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6)*sqrt((441*c^2*d^4*e^10 - 1050
*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^
8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*a^10*c^4*d^2*e^10 + a^11*c^3
*e^12)))/(a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6))*log(
-(3024*c^3*d^6*e^5 - 7884*a*c^2*d^4*e^7 + 5625*a^2*c*d^2*e^9 - 625*a^3*e^11)*sqr
t(e*x + d) + (126*a^3*c^3*d^5*e^6 - 318*a^4*c^2*d^3*e^8 + 200*a^5*c*d*e^10 - (12
*a^5*c^7*d^10 - 55*a^6*c^6*d^8*e^2 + 98*a^7*c^5*d^6*e^4 - 84*a^8*c^4*d^4*e^6 + 3
4*a^9*c^3*d^2*e^8 - 5*a^10*c^2*e^10)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12
+ 625*a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8
*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))*sqrt(
(144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 - (a^5*c^4*
d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6)*sqrt((441*c^2*d^4*e^10
- 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*c^8*d^10*e^2 + 15*a^7*
c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*a^10*c^4*d^2*e^10 + a^
11*c^3*e^12)))/(a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6)
)) - (a^4*c*d^2 - a^5*e^2 + (a^2*c^3*d^2 - a^3*c^2*e^2)*x^4 - 2*(a^3*c^2*d^2 - a
^4*c*e^2)*x^2)*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a
^3*d*e^6 - (a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6)*sqr
t((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*c^
8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*a^
10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*
d^2*e^4 - a^8*c*e^6))*log(-(3024*c^3*d^6*e^5 - 7884*a*c^2*d^4*e^7 + 5625*a^2*c*d
^2*e^9 - 625*a^3*e^11)*sqrt(e*x + d) - (126*a^3*c^3*d^5*e^6 - 318*a^4*c^2*d^3*e^
8 + 200*a^5*c*d*e^10 - (12*a^5*c^7*d^10 - 55*a^6*c^6*d^8*e^2 + 98*a^7*c^5*d^6*e^
4 - 84*a^8*c^4*d^4*e^6 + 34*a^9*c^3*d^2*e^8 - 5*a^10*c^2*e^10)*sqrt((441*c^2*d^4
*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*c^8*d^10*e^2 + 1
5*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*a^10*c^4*d^2*e^1
0 + a^11*c^3*e^12)))*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 -
105*a^3*d*e^6 - (a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^
6)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 - 6*
a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8
- 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^
7*c^2*d^2*e^4 - a^8*c*e^6))) - 4*(a*c*d*e*x^2 - a^2*d*e - (6*c^2*d^2 - 5*a*c*e^2
)*x^3 + (10*a*c*d^2 - 9*a^2*e^2)*x)*sqrt(e*x + d))/(a^4*c*d^2 - a^5*e^2 + (a^2*c
^3*d^2 - a^3*c^2*e^2)*x^4 - 2*(a^3*c^2*d^2 - a^4*c*e^2)*x^2)
_______________________________________________________________________________________
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((e*x+d)**(1/2)/(-c*x**2+a)**3,x)
[Out]
Timed out
_______________________________________________________________________________________
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(-sqrt(e*x + d)/(c*x^2 - a)^3,x, algorithm="giac")
[Out]
Timed out