Optimal. Leaf size=28 \[ a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9 \]
[Out]
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Rubi [A] time = 0.0330414, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9 \]
Antiderivative was successfully verified.
[In] Int[a*(e + f*x^4)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{2 a e f x^{5}}{5} + \frac{a f^{2} x^{9}}{9} + a \int e^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(a*(f*x**4+e)**2,x)
[Out]
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Mathematica [A] time = 0.00308368, size = 27, normalized size = 0.96 \[ a \left (e^2 x+\frac{2}{5} e f x^5+\frac{f^2 x^9}{9}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[a*(e + f*x^4)^2,x]
[Out]
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Maple [A] time = 0.002, size = 24, normalized size = 0.9 \[ a \left ({\frac{{f}^{2}{x}^{9}}{9}}+{\frac{2\,ef{x}^{5}}{5}}+{e}^{2}x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(a*(f*x^4+e)^2,x)
[Out]
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Maxima [A] time = 1.36085, size = 34, normalized size = 1.21 \[ \frac{1}{45} \,{\left (5 \, f^{2} x^{9} + 18 \, e f x^{5} + 45 \, e^{2} x\right )} a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((f*x^4 + e)^2*a,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.198251, size = 1, normalized size = 0.04 \[ \frac{1}{9} x^{9} f^{2} a + \frac{2}{5} x^{5} f e a + x e^{2} a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((f*x^4 + e)^2*a,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.043121, size = 27, normalized size = 0.96 \[ a e^{2} x + \frac{2 a e f x^{5}}{5} + \frac{a f^{2} x^{9}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(a*(f*x**4+e)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.20868, size = 34, normalized size = 1.21 \[ \frac{1}{45} \,{\left (5 \, f^{2} x^{9} + 18 \, f x^{5} e + 45 \, x e^{2}\right )} a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((f*x^4 + e)^2*a,x, algorithm="giac")
[Out]