Optimal. Leaf size=45 \[ a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{d \left (e+f x^4\right )^3}{12 f} \]
[Out]
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Rubi [A] time = 0.0619573, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.176 \[ a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{d \left (e+f x^4\right )^3}{12 f} \]
Antiderivative was successfully verified.
[In] Int[(a + d*x^3)*(e + f*x^4)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{2 a e f x^{5}}{5} + \frac{a f^{2} x^{9}}{9} + a \int e^{2}\, dx + \frac{d \left (e + f x^{4}\right )^{3}}{12 f} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((d*x**3+a)*(f*x**4+e)**2,x)
[Out]
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Mathematica [A] time = 0.00411818, size = 60, normalized size = 1.33 \[ a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{1}{4} d e^2 x^4+\frac{1}{4} d e f x^8+\frac{1}{12} d f^2 x^{12} \]
Antiderivative was successfully verified.
[In] Integrate[(a + d*x^3)*(e + f*x^4)^2,x]
[Out]
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Maple [A] time = 0.001, size = 51, normalized size = 1.1 \[{\frac{d{f}^{2}{x}^{12}}{12}}+{\frac{a{f}^{2}{x}^{9}}{9}}+{\frac{def{x}^{8}}{4}}+{\frac{2\,aef{x}^{5}}{5}}+{\frac{d{e}^{2}{x}^{4}}{4}}+a{e}^{2}x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((d*x^3+a)*(f*x^4+e)^2,x)
[Out]
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Maxima [A] time = 1.4422, size = 68, normalized size = 1.51 \[ \frac{1}{12} \, d f^{2} x^{12} + \frac{1}{9} \, a f^{2} x^{9} + \frac{1}{4} \, d e f x^{8} + \frac{2}{5} \, a e f x^{5} + \frac{1}{4} \, d e^{2} x^{4} + a e^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((f*x^4 + e)^2*(d*x^3 + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.2041, size = 1, normalized size = 0.02 \[ \frac{1}{12} x^{12} f^{2} d + \frac{1}{9} x^{9} f^{2} a + \frac{1}{4} x^{8} f e d + \frac{2}{5} x^{5} f e a + \frac{1}{4} x^{4} e^{2} d + x e^{2} a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((f*x^4 + e)^2*(d*x^3 + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.05881, size = 58, normalized size = 1.29 \[ a e^{2} x + \frac{2 a e f x^{5}}{5} + \frac{a f^{2} x^{9}}{9} + \frac{d e^{2} x^{4}}{4} + \frac{d e f x^{8}}{4} + \frac{d f^{2} x^{12}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x**3+a)*(f*x**4+e)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.209483, size = 68, normalized size = 1.51 \[ \frac{1}{12} \, d f^{2} x^{12} + \frac{1}{9} \, a f^{2} x^{9} + \frac{1}{4} \, d f x^{8} e + \frac{2}{5} \, a f x^{5} e + \frac{1}{4} \, d x^{4} e^{2} + a x e^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((f*x^4 + e)^2*(d*x^3 + a),x, algorithm="giac")
[Out]