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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]