3.403 \(\int \left (c+e x^2\right )^q \left (a+c x^2+b x^4\right )^p \, dx\)

Optimal. Leaf size=27 \[ \text{Int}\left (\left (c+e x^2\right )^q \left (a+b x^4+c x^2\right )^p,x\right ) \]

[Out]

Unintegrable[(c + e*x^2)^q*(a + c*x^2 + b*x^4)^p, x]

_______________________________________________________________________________________

Rubi [A]  time = 0.0285223, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \text{Int}\left (\left (c+e x^2\right )^q \left (a+c x^2+b x^4\right )^p,x\right ) \]

Verification is Not applicable to the result.

[In]  Int[(c + e*x^2)^q*(a + c*x^2 + b*x^4)^p,x]

[Out]

Defer[Int][(c + e*x^2)^q*(a + c*x^2 + b*x^4)^p, x]

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 0., size = 0, normalized size = 0. \[ \int \left (c + e x^{2}\right )^{q} \left (a + b x^{4} + c x^{2}\right )^{p}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((e*x**2+c)**q*(b*x**4+c*x**2+a)**p,x)

[Out]

Integral((c + e*x**2)**q*(a + b*x**4 + c*x**2)**p, x)

_______________________________________________________________________________________

Mathematica [A]  time = 0.113788, size = 0, normalized size = 0. \[ \int \left (c+e x^2\right )^q \left (a+c x^2+b x^4\right )^p \, dx \]

Verification is Not applicable to the result.

[In]  Integrate[(c + e*x^2)^q*(a + c*x^2 + b*x^4)^p,x]

[Out]

Integrate[(c + e*x^2)^q*(a + c*x^2 + b*x^4)^p, x]

_______________________________________________________________________________________

Maple [A]  time = 0.109, size = 0, normalized size = 0. \[ \int \left ( e{x}^{2}+c \right ) ^{q} \left ( b{x}^{4}+c{x}^{2}+a \right ) ^{p}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((e*x^2+c)^q*(b*x^4+c*x^2+a)^p,x)

[Out]

int((e*x^2+c)^q*(b*x^4+c*x^2+a)^p,x)

_______________________________________________________________________________________

Maxima [A]  time = 0., size = 0, normalized size = 0. \[ \int{\left (b x^{4} + c x^{2} + a\right )}^{p}{\left (e x^{2} + c\right )}^{q}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + c*x^2 + a)^p*(e*x^2 + c)^q,x, algorithm="maxima")

[Out]

integrate((b*x^4 + c*x^2 + a)^p*(e*x^2 + c)^q, x)

_______________________________________________________________________________________

Fricas [A]  time = 0., size = 0, normalized size = 0. \[{\rm integral}\left ({\left (b x^{4} + c x^{2} + a\right )}^{p}{\left (e x^{2} + c\right )}^{q}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + c*x^2 + a)^p*(e*x^2 + c)^q,x, algorithm="fricas")

[Out]

integral((b*x^4 + c*x^2 + a)^p*(e*x^2 + c)^q, x)

_______________________________________________________________________________________

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**2+c)**q*(b*x**4+c*x**2+a)**p,x)

[Out]

Timed out

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0., size = 0, normalized size = 0. \[ \int{\left (b x^{4} + c x^{2} + a\right )}^{p}{\left (e x^{2} + c\right )}^{q}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + c*x^2 + a)^p*(e*x^2 + c)^q,x, algorithm="giac")

[Out]

integrate((b*x^4 + c*x^2 + a)^p*(e*x^2 + c)^q, x)