Optimal. Leaf size=35 \[ a^3 x+a^2 c x^3+\frac{3}{5} a c^2 x^5+\frac{c^3 x^7}{7} \]
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Rubi [A] time = 0.0290113, antiderivative size = 35, 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 \[ a^3 x+a^2 c x^3+\frac{3}{5} a c^2 x^5+\frac{c^3 x^7}{7} \]
Antiderivative was successfully verified.
[In] Int[(a + c*x^2)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a^{2} c x^{3} + \frac{3 a c^{2} x^{5}}{5} + \frac{c^{3} x^{7}}{7} + \int a^{3}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**2+a)**3,x)
[Out]
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Mathematica [A] time = 0.00196918, size = 35, normalized size = 1. \[ a^3 x+a^2 c x^3+\frac{3}{5} a c^2 x^5+\frac{c^3 x^7}{7} \]
Antiderivative was successfully verified.
[In] Integrate[(a + c*x^2)^3,x]
[Out]
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Maple [A] time = 0.002, size = 32, normalized size = 0.9 \[{a}^{3}x+{a}^{2}c{x}^{3}+{\frac{3\,a{c}^{2}{x}^{5}}{5}}+{\frac{{c}^{3}{x}^{7}}{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^2+a)^3,x)
[Out]
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Maxima [A] time = 0.694496, size = 42, normalized size = 1.2 \[ \frac{1}{7} \, c^{3} x^{7} + \frac{3}{5} \, a c^{2} x^{5} + a^{2} c x^{3} + a^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.187323, size = 1, normalized size = 0.03 \[ \frac{1}{7} x^{7} c^{3} + \frac{3}{5} x^{5} c^{2} a + x^{3} c a^{2} + x a^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.098392, size = 32, normalized size = 0.91 \[ a^{3} x + a^{2} c x^{3} + \frac{3 a c^{2} x^{5}}{5} + \frac{c^{3} x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**2+a)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.207707, size = 42, normalized size = 1.2 \[ \frac{1}{7} \, c^{3} x^{7} + \frac{3}{5} \, a c^{2} x^{5} + a^{2} c x^{3} + a^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^3,x, algorithm="giac")
[Out]