Optimal. Leaf size=25 \[ a^2 x+\frac{2}{3} a c x^3+\frac{c^2 x^5}{5} \]
[Out]
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Rubi [A] time = 0.0193471, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ a^2 x+\frac{2}{3} a c x^3+\frac{c^2 x^5}{5} \]
Antiderivative was successfully verified.
[In] Int[(a + c*x^2)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{2 a c x^{3}}{3} + \frac{c^{2} x^{5}}{5} + \int a^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**2+a)**2,x)
[Out]
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Mathematica [A] time = 0.00170871, size = 25, normalized size = 1. \[ a^2 x+\frac{2}{3} a c x^3+\frac{c^2 x^5}{5} \]
Antiderivative was successfully verified.
[In] Integrate[(a + c*x^2)^2,x]
[Out]
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Maple [A] time = 0.002, size = 22, normalized size = 0.9 \[{a}^{2}x+{\frac{2\,a{x}^{3}c}{3}}+{\frac{{c}^{2}{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^2+a)^2,x)
[Out]
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Maxima [A] time = 0.703682, size = 28, normalized size = 1.12 \[ \frac{1}{5} \, c^{2} x^{5} + \frac{2}{3} \, a c x^{3} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.191099, size = 1, normalized size = 0.04 \[ \frac{1}{5} x^{5} c^{2} + \frac{2}{3} x^{3} c a + x a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.087772, size = 22, normalized size = 0.88 \[ a^{2} x + \frac{2 a c x^{3}}{3} + \frac{c^{2} x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**2+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.209627, size = 28, normalized size = 1.12 \[ \frac{1}{5} \, c^{2} x^{5} + \frac{2}{3} \, a c x^{3} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^2,x, algorithm="giac")
[Out]