Optimal. Leaf size=34 \[ \frac{\left (a+b x^2\right )^5}{10 b^2}-\frac{a \left (a+b x^2\right )^4}{8 b^2} \]
[Out]
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Rubi [A] time = 0.0848432, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{\left (a+b x^2\right )^5}{10 b^2}-\frac{a \left (a+b x^2\right )^4}{8 b^2} \]
Antiderivative was successfully verified.
[In] Int[x^3*(a + b*x^2)^3,x]
[Out]
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Rubi in Sympy [A] time = 8.96201, size = 27, normalized size = 0.79 \[ - \frac{a \left (a + b x^{2}\right )^{4}}{8 b^{2}} + \frac{\left (a + b x^{2}\right )^{5}}{10 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(b*x**2+a)**3,x)
[Out]
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Mathematica [A] time = 0.00322607, size = 43, normalized size = 1.26 \[ \frac{a^3 x^4}{4}+\frac{1}{2} a^2 b x^6+\frac{3}{8} a b^2 x^8+\frac{b^3 x^{10}}{10} \]
Antiderivative was successfully verified.
[In] Integrate[x^3*(a + b*x^2)^3,x]
[Out]
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Maple [A] time = 0., size = 36, normalized size = 1.1 \[{\frac{{b}^{3}{x}^{10}}{10}}+{\frac{3\,a{b}^{2}{x}^{8}}{8}}+{\frac{{a}^{2}b{x}^{6}}{2}}+{\frac{{a}^{3}{x}^{4}}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(b*x^2+a)^3,x)
[Out]
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Maxima [A] time = 1.35244, size = 47, normalized size = 1.38 \[ \frac{1}{10} \, b^{3} x^{10} + \frac{3}{8} \, a b^{2} x^{8} + \frac{1}{2} \, a^{2} b x^{6} + \frac{1}{4} \, a^{3} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.182997, size = 1, normalized size = 0.03 \[ \frac{1}{10} x^{10} b^{3} + \frac{3}{8} x^{8} b^{2} a + \frac{1}{2} x^{6} b a^{2} + \frac{1}{4} x^{4} a^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.099702, size = 37, normalized size = 1.09 \[ \frac{a^{3} x^{4}}{4} + \frac{a^{2} b x^{6}}{2} + \frac{3 a b^{2} x^{8}}{8} + \frac{b^{3} x^{10}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(b*x**2+a)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.206832, size = 47, normalized size = 1.38 \[ \frac{1}{10} \, b^{3} x^{10} + \frac{3}{8} \, a b^{2} x^{8} + \frac{1}{2} \, a^{2} b x^{6} + \frac{1}{4} \, a^{3} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3*x^3,x, algorithm="giac")
[Out]