Optimal. Leaf size=16 \[ \frac{\left (a+b x^2\right )^6}{12 b} \]
[Out]
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Rubi [A] time = 0.0127081, 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 \[ \frac{\left (a+b x^2\right )^6}{12 b} \]
Antiderivative was successfully verified.
[In] Int[x*(a + b*x^2)^5,x]
[Out]
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Rubi in Sympy [A] time = 2.19247, size = 10, normalized size = 0.62 \[ \frac{\left (a + b x^{2}\right )^{6}}{12 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(b*x**2+a)**5,x)
[Out]
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Mathematica [A] time = 0.00421162, size = 16, normalized size = 1. \[ \frac{\left (a+b x^2\right )^6}{12 b} \]
Antiderivative was successfully verified.
[In] Integrate[x*(a + b*x^2)^5,x]
[Out]
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Maple [B] time = 0.003, size = 58, normalized size = 3.6 \[{\frac{{b}^{5}{x}^{12}}{12}}+{\frac{a{b}^{4}{x}^{10}}{2}}+{\frac{5\,{a}^{2}{b}^{3}{x}^{8}}{4}}+{\frac{5\,{a}^{3}{b}^{2}{x}^{6}}{3}}+{\frac{5\,{a}^{4}b{x}^{4}}{4}}+{\frac{{a}^{5}{x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(b*x^2+a)^5,x)
[Out]
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Maxima [A] time = 1.33089, size = 19, normalized size = 1.19 \[ \frac{{\left (b x^{2} + a\right )}^{6}}{12 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^5*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.19162, size = 1, normalized size = 0.06 \[ \frac{1}{12} x^{12} b^{5} + \frac{1}{2} x^{10} b^{4} a + \frac{5}{4} x^{8} b^{3} a^{2} + \frac{5}{3} x^{6} b^{2} a^{3} + \frac{5}{4} x^{4} b a^{4} + \frac{1}{2} x^{2} a^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^5*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.116997, size = 65, normalized size = 4.06 \[ \frac{a^{5} x^{2}}{2} + \frac{5 a^{4} b x^{4}}{4} + \frac{5 a^{3} b^{2} x^{6}}{3} + \frac{5 a^{2} b^{3} x^{8}}{4} + \frac{a b^{4} x^{10}}{2} + \frac{b^{5} x^{12}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(b*x**2+a)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.205511, size = 19, normalized size = 1.19 \[ \frac{{\left (b x^{2} + a\right )}^{6}}{12 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^5*x,x, algorithm="giac")
[Out]