∖int (ex)7∕2 ___________________________________________∖left(a−bx2 ∖right)2√ ____ c−dx2 ∖,dx

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

3.911 \(\int \frac{(e x)^{7/2}}{\left (a-b x^2\right )^2 \sqrt{c-d x^2}} \, dx\)

Optimal. Leaf size=376 \[ \frac{\sqrt [4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (4 b c-3 a d) F\left (\left .\sin ^{-1}\left (\frac{\sqrt [4]{d} \sqrt{e x}}{\sqrt [4]{c} \sqrt{e}}\right )\right |-1\right )}{2 b^2 \sqrt [4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt [4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (5 b c-3 a d) \Pi \left (-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left .\sin ^{-1}\left (\frac{\sqrt [4]{d} \sqrt{e x}}{\sqrt [4]{c} \sqrt{e}}\right )\right |-1\right )}{4 b^2 \sqrt [4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt [4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (5 b c-3 a d) \Pi \left (\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left .\sin ^{-1}\left (\frac{\sqrt [4]{d} \sqrt{e x}}{\sqrt [4]{c} \sqrt{e}}\right )\right |-1\right )}{4 b^2 \sqrt [4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{a e^3 \sqrt{e x} \sqrt{c-d x^2}}{2 b \left (a-b x^2\right ) (b c-a d)} \]

[Out]

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

c - 3*a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(

1/4)*Sqrt[e])], -1])/(2*b^2*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2]) - (c^(1/4)*(5*b

*c - 3*a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*

Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*b^2*d^(1/4)*(b

*c - a*d)*Sqrt[c - d*x^2]) - (c^(1/4)*(5*b*c - 3*a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c

]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^

(1/4)*Sqrt[e])], -1])/(4*b^2*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2])

_______________________________________________________________________________________

Rubi [A] time = 1.46624, antiderivative size = 376, normalized size of antiderivative = 1., number of steps used = 10, number of rules used = 8, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.267 \[ \frac{\sqrt [4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (4 b c-3 a d) F\left (\left .\sin ^{-1}\left (\frac{\sqrt [4]{d} \sqrt{e x}}{\sqrt [4]{c} \sqrt{e}}\right )\right |-1\right )}{2 b^2 \sqrt [4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt [4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (5 b c-3 a d) \Pi \left (-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left .\sin ^{-1}\left (\frac{\sqrt [4]{d} \sqrt{e x}}{\sqrt [4]{c} \sqrt{e}}\right )\right |-1\right )}{4 b^2 \sqrt [4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt [4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (5 b c-3 a d) \Pi \left (\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left .\sin ^{-1}\left (\frac{\sqrt [4]{d} \sqrt{e x}}{\sqrt [4]{c} \sqrt{e}}\right )\right |-1\right )}{4 b^2 \sqrt [4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{a e^3 \sqrt{e x} \sqrt{c-d x^2}}{2 b \left (a-b x^2\right ) (b c-a d)} \]

Antiderivative was successfully veriﬁed.

[In] Int[(e*x)^(7/2)/((a - b*x^2)^2*Sqrt[c - d*x^2]),x]

[Out]

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

c - 3*a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(

1/4)*Sqrt[e])], -1])/(2*b^2*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2]) - (c^(1/4)*(5*b

*c - 3*a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*

Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*b^2*d^(1/4)*(b

*c - a*d)*Sqrt[c - d*x^2]) - (c^(1/4)*(5*b*c - 3*a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c

]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^

(1/4)*Sqrt[e])], -1])/(4*b^2*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2])

_______________________________________________________________________________________

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)**(7/2)/(-b*x**2+a)**2/(-d*x**2+c)**(1/2),x)

[Out]

Timed out

_______________________________________________________________________________________

Mathematica [C] time = 0.597887, size = 414, normalized size = 1.1 \[ \frac{a (e x)^{7/2} \left (\frac{25 a c^2 F_1\left (\frac{1}{4};\frac{1}{2},1;\frac{5}{4};\frac{d x^2}{c},\frac{b x^2}{a}\right )}{2 x^2 \left (2 b c F_1\left (\frac{5}{4};\frac{1}{2},2;\frac{9}{4};\frac{d x^2}{c},\frac{b x^2}{a}\right )+a d F_1\left (\frac{5}{4};\frac{3}{2},1;\frac{9}{4};\frac{d x^2}{c},\frac{b x^2}{a}\right )\right )+5 a c F_1\left (\frac{1}{4};\frac{1}{2},1;\frac{5}{4};\frac{d x^2}{c},\frac{b x^2}{a}\right )}+\frac{10 x^2 \left (d x^2-c\right ) \left (2 b c F_1\left (\frac{9}{4};\frac{1}{2},2;\frac{13}{4};\frac{d x^2}{c},\frac{b x^2}{a}\right )+a d F_1\left (\frac{9}{4};\frac{3}{2},1;\frac{13}{4};\frac{d x^2}{c},\frac{b x^2}{a}\right )\right )-9 c \left (5 a c-2 a d x^2-4 b c x^2\right ) F_1\left (\frac{5}{4};\frac{1}{2},1;\frac{9}{4};\frac{d x^2}{c},\frac{b x^2}{a}\right )}{2 x^2 \left (2 b c F_1\left (\frac{9}{4};\frac{1}{2},2;\frac{13}{4};\frac{d x^2}{c},\frac{b x^2}{a}\right )+a d F_1\left (\frac{9}{4};\frac{3}{2},1;\frac{13}{4};\frac{d x^2}{c},\frac{b x^2}{a}\right )\right )+9 a c F_1\left (\frac{5}{4};\frac{1}{2},1;\frac{9}{4};\frac{d x^2}{c},\frac{b x^2}{a}\right )}\right )}{10 b x^3 \left (b x^2-a\right ) \sqrt{c-d x^2} (b c-a d)} \]

Warning: Unable to verify antiderivative.

[In] Integrate[(e*x)^(7/2)/((a - b*x^2)^2*Sqrt[c - d*x^2]),x]

[Out]

(a*(e*x)^(7/2)*((25*a*c^2*AppellF1[1/4, 1/2, 1, 5/4, (d*x^2)/c, (b*x^2)/a])/(5*a

*c*AppellF1[1/4, 1/2, 1, 5/4, (d*x^2)/c, (b*x^2)/a] + 2*x^2*(2*b*c*AppellF1[5/4,

1/2, 2, 9/4, (d*x^2)/c, (b*x^2)/a] + a*d*AppellF1[5/4, 3/2, 1, 9/4, (d*x^2)/c,

(b*x^2)/a])) + (-9*c*(5*a*c - 4*b*c*x^2 - 2*a*d*x^2)*AppellF1[5/4, 1/2, 1, 9/4,

(d*x^2)/c, (b*x^2)/a] + 10*x^2*(-c + d*x^2)*(2*b*c*AppellF1[9/4, 1/2, 2, 13/4, (

d*x^2)/c, (b*x^2)/a] + a*d*AppellF1[9/4, 3/2, 1, 13/4, (d*x^2)/c, (b*x^2)/a]))/(

9*a*c*AppellF1[5/4, 1/2, 1, 9/4, (d*x^2)/c, (b*x^2)/a] + 2*x^2*(2*b*c*AppellF1[9

/4, 1/2, 2, 13/4, (d*x^2)/c, (b*x^2)/a] + a*d*AppellF1[9/4, 3/2, 1, 13/4, (d*x^2

)/c, (b*x^2)/a]))))/(10*b*(b*c - a*d)*x^3*(-a + b*x^2)*Sqrt[c - d*x^2])

_______________________________________________________________________________________

Maple [B] time = 0.044, size = 2520, normalized size = 6.7 \[ \text{result too large to display} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In] int((e*x)^(7/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x)

[Out]

1/8/b*(8*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/2*2^(1/2))*2^(1/2)*x^

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

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

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

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

c*d)^(1/2)*(a*b)^(1/2)+3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^

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

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

(c*d)^(1/2))^(1/2)-5*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2

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

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

(1/2))^(1/2)-3*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)*b/((

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

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

))^(1/2)+5*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)*b/((c*d)

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

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

2)+4*x*a^2*b*c*d^2*(a*b)^(1/2)-4*x*a*b^2*c^2*d*(a*b)^(1/2)-14*EllipticF(((d*x+(c

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

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

^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+5*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2

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

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

x*d/(c*d)^(1/2))^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+5*EllipticPi(((d*x+(c*d)^(1/2))/(

c*d)^(1/2))^(1/2),(c*d)^(1/2)*b/((c*d)^(1/2)*b-(a*b)^(1/2)*d),1/2*2^(1/2))*2^(1/

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

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

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

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

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

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

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

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

(c*d)^(1/2))^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+6*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^

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

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

)*(a*b)^(1/2)-5*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)*b/(

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

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

)*(c*d)^(1/2)*(a*b)^(1/2)-5*EllipticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*

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

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

^(1/2))^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+14*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2

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

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

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

^(1/2),(c*d)^(1/2)*b/((c*d)^(1/2)*b-(a*b)^(1/2)*d),1/2*2^(1/2))*2^(1/2)*a^2*b^2*

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

2)*(-x*d/(c*d)^(1/2))^(1/2)-6*EllipticF(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),1/

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

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

ticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)*b/((a*b)^(1/2)*d+(c*d)^(

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

(-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-x*d/(c*d)^(1/2))^(1/2)+3*EllipticPi(((d*

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

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

/2))/(c*d)^(1/2))^(1/2)*(-x*d/(c*d)^(1/2))^(1/2)*(c*d)^(1/2)*(a*b)^(1/2)+5*Ellip

ticPi(((d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)*b/((a*b)^(1/2)*d+(c*d)^(

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

*((-d*x+(c*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-x*d/(c*d)^(1/2))^(1/2)+3*EllipticPi(((

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

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

*d)^(1/2))/(c*d)^(1/2))^(1/2)*(-x*d/(c*d)^(1/2))^(1/2)+3*EllipticPi(((d*x+(c*d)^

(1/2))/(c*d)^(1/2))^(1/2),(c*d)^(1/2)*b/((c*d)^(1/2)*b-(a*b)^(1/2)*d),1/2*2^(1/2

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

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

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

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

_______________________________________________________________________________________

Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (e x\right )^{\frac{7}{2}}}{{\left (b x^{2} - a\right )}^{2} \sqrt{-d x^{2} + c}}\,{d x} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In] integrate((e*x)^(7/2)/((b*x^2 - a)^2*sqrt(-d*x^2 + c)),x, algorithm="maxima")

[Out]

integrate((e*x)^(7/2)/((b*x^2 - a)^2*sqrt(-d*x^2 + c)), x)

_______________________________________________________________________________________

Fricas [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((e*x)^(7/2)/((b*x^2 - a)^2*sqrt(-d*x^2 + c)),x, algorithm="fricas")

[Out]

Exception raised: TypeError

_______________________________________________________________________________________

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)**(7/2)/(-b*x**2+a)**2/(-d*x**2+c)**(1/2),x)

[Out]

Timed out

_______________________________________________________________________________________

GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (e x\right )^{\frac{7}{2}}}{{\left (b x^{2} - a\right )}^{2} \sqrt{-d x^{2} + c}}\,{d x} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In] integrate((e*x)^(7/2)/((b*x^2 - a)^2*sqrt(-d*x^2 + c)),x, algorithm="giac")

[Out]

integrate((e*x)^(7/2)/((b*x^2 - a)^2*sqrt(-d*x^2 + c)), x)

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