Optimal. Leaf size=16 \[ \frac{\left (a+b x^2\right )^4}{8 b} \]
[Out]
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Rubi [A] time = 0.012089, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{\left (a+b x^2\right )^4}{8 b} \]
Antiderivative was successfully verified.
[In] Int[x*(a + b*x^2)^3,x]
[Out]
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Rubi in Sympy [A] time = 2.24312, size = 10, normalized size = 0.62 \[ \frac{\left (a + b x^{2}\right )^{4}}{8 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(b*x**2+a)**3,x)
[Out]
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Mathematica [A] time = 0.00356205, size = 16, normalized size = 1. \[ \frac{\left (a+b x^2\right )^4}{8 b} \]
Antiderivative was successfully verified.
[In] Integrate[x*(a + b*x^2)^3,x]
[Out]
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Maple [B] time = 0.001, size = 36, normalized size = 2.3 \[{\frac{{b}^{3}{x}^{8}}{8}}+{\frac{a{b}^{2}{x}^{6}}{2}}+{\frac{3\,{a}^{2}b{x}^{4}}{4}}+{\frac{{a}^{3}{x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(b*x^2+a)^3,x)
[Out]
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Maxima [A] time = 1.3496, size = 19, normalized size = 1.19 \[ \frac{{\left (b x^{2} + a\right )}^{4}}{8 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.179606, size = 1, normalized size = 0.06 \[ \frac{1}{8} x^{8} b^{3} + \frac{1}{2} x^{6} b^{2} a + \frac{3}{4} x^{4} b a^{2} + \frac{1}{2} x^{2} a^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.098184, size = 37, normalized size = 2.31 \[ \frac{a^{3} x^{2}}{2} + \frac{3 a^{2} b x^{4}}{4} + \frac{a b^{2} x^{6}}{2} + \frac{b^{3} x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(b*x**2+a)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.207988, size = 19, normalized size = 1.19 \[ \frac{{\left (b x^{2} + a\right )}^{4}}{8 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3*x,x, algorithm="giac")
[Out]