Optimal. Leaf size=29 \[ \text{Int}\left (\frac{\left (a+b x^n+c x^{2 n}\right )^p}{\left (d+e x^n\right )^3},x\right ) \]
[Out]
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Rubi [A] time = 0.02769, 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. \[ \text{Int}\left (\frac{\left (a+b x^n+c x^{2 n}\right )^p}{\left (d+e x^n\right )^3},x\right ) \]
Verification is Not applicable to the result.
[In] Int[(a + b*x^n + c*x^(2*n))^p/(d + e*x^n)^3,x]
[Out]
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Rubi in Sympy [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (a + b x^{n} + c x^{2 n}\right )^{p}}{\left (d + e x^{n}\right )^{3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**n+c*x**(2*n))**p/(d+e*x**n)**3,x)
[Out]
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Mathematica [A] time = 1.01462, size = 0, normalized size = 0. \[ \int \frac{\left (a+b x^n+c x^{2 n}\right )^p}{\left (d+e x^n\right )^3} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[(a + b*x^n + c*x^(2*n))^p/(d + e*x^n)^3,x]
[Out]
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Maple [A] time = 0.11, size = 0, normalized size = 0. \[ \int{\frac{ \left ( a+b{x}^{n}+c{x}^{2\,n} \right ) ^{p}}{ \left ( d+e{x}^{n} \right ) ^{3}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^n+c*x^(2*n))^p/(d+e*x^n)^3,x)
[Out]
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Maxima [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (c x^{2 \, n} + b x^{n} + a\right )}^{p}}{{\left (e x^{n} + d\right )}^{3}}\,{d x} \]
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)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{{\left (c x^{2 \, n} + b x^{n} + a\right )}^{p}}{e^{3} x^{3 \, n} + 3 \, d e^{2} x^{2 \, n} + 3 \, d^{2} e x^{n} + d^{3}}, x\right ) \]
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)^3,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((a+b*x**n+c*x**(2*n))**p/(d+e*x**n)**3,x)
[Out]
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GIAC/XCAS [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (c x^{2 \, n} + b x^{n} + a\right )}^{p}}{{\left (e x^{n} + d\right )}^{3}}\,{d x} \]
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)^3,x, algorithm="giac")
[Out]