3.90 \(\int \left (d+e x^n\right )^q \left (a+b x^n+c x^{2 n}\right )^p \, dx\)

Optimal. Leaf size=29 \[ \text{Int}\left (\left (d+e x^n\right )^q \left (a+b x^n+c x^{2 n}\right )^p,x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0259954, 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. \[ \text{Int}\left (\left (d+e x^n\right )^q \left (a+b x^n+c x^{2 n}\right )^p,x\right ) \]

Verification is Not applicable to the result.

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.321258, size = 0, normalized size = 0. \[ \int \left (d+e x^n\right )^q \left (a+b x^n+c x^{2 n}\right )^p \, dx \]

Verification is Not applicable to the result.

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

[Out]

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

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Maple [A]  time = 0.192, size = 0, normalized size = 0. \[ \int \left ( d+e{x}^{n} \right ) ^{q} \left ( a+b{x}^{n}+c{x}^{2\,n} \right ) ^{p}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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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((d+e*x**n)**q*(a+b*x**n+c*x**(2*n))**p,x)

[Out]

Timed out

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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