Optimal. Leaf size=65 \[ -\frac{a^5}{2 x^2}+5 a^4 b x+\frac{5}{2} a^3 b^2 x^4+\frac{10}{7} a^2 b^3 x^7+\frac{1}{2} a b^4 x^{10}+\frac{b^5 x^{13}}{13} \]
[Out]
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Rubi [A] time = 0.0562805, antiderivative size = 65, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{a^5}{2 x^2}+5 a^4 b x+\frac{5}{2} a^3 b^2 x^4+\frac{10}{7} a^2 b^3 x^7+\frac{1}{2} a b^4 x^{10}+\frac{b^5 x^{13}}{13} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^5/x^3,x]
[Out]
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Rubi in Sympy [A] time = 10.864, size = 61, normalized size = 0.94 \[ - \frac{a^{5}}{2 x^{2}} + 5 a^{4} b x + \frac{5 a^{3} b^{2} x^{4}}{2} + \frac{10 a^{2} b^{3} x^{7}}{7} + \frac{a b^{4} x^{10}}{2} + \frac{b^{5} x^{13}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**5/x**3,x)
[Out]
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Mathematica [A] time = 0.00778775, size = 65, normalized size = 1. \[ -\frac{a^5}{2 x^2}+5 a^4 b x+\frac{5}{2} a^3 b^2 x^4+\frac{10}{7} a^2 b^3 x^7+\frac{1}{2} a b^4 x^{10}+\frac{b^5 x^{13}}{13} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^5/x^3,x]
[Out]
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Maple [A] time = 0.005, size = 56, normalized size = 0.9 \[ -{\frac{{a}^{5}}{2\,{x}^{2}}}+5\,{a}^{4}bx+{\frac{5\,{a}^{3}{b}^{2}{x}^{4}}{2}}+{\frac{10\,{a}^{2}{b}^{3}{x}^{7}}{7}}+{\frac{a{b}^{4}{x}^{10}}{2}}+{\frac{{b}^{5}{x}^{13}}{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^5/x^3,x)
[Out]
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Maxima [A] time = 1.44252, size = 74, normalized size = 1.14 \[ \frac{1}{13} \, b^{5} x^{13} + \frac{1}{2} \, a b^{4} x^{10} + \frac{10}{7} \, a^{2} b^{3} x^{7} + \frac{5}{2} \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x - \frac{a^{5}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203451, size = 80, normalized size = 1.23 \[ \frac{14 \, b^{5} x^{15} + 91 \, a b^{4} x^{12} + 260 \, a^{2} b^{3} x^{9} + 455 \, a^{3} b^{2} x^{6} + 910 \, a^{4} b x^{3} - 91 \, a^{5}}{182 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.20857, size = 61, normalized size = 0.94 \[ - \frac{a^{5}}{2 x^{2}} + 5 a^{4} b x + \frac{5 a^{3} b^{2} x^{4}}{2} + \frac{10 a^{2} b^{3} x^{7}}{7} + \frac{a b^{4} x^{10}}{2} + \frac{b^{5} x^{13}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**5/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.224384, size = 74, normalized size = 1.14 \[ \frac{1}{13} \, b^{5} x^{13} + \frac{1}{2} \, a b^{4} x^{10} + \frac{10}{7} \, a^{2} b^{3} x^{7} + \frac{5}{2} \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x - \frac{a^{5}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^3,x, algorithm="giac")
[Out]