Optimal. Leaf size=62 \[ -\frac{a^5}{7 x^7}-\frac{5 a^4 b}{4 x^4}-\frac{10 a^3 b^2}{x}+5 a^2 b^3 x^2+a b^4 x^5+\frac{b^5 x^8}{8} \]
[Out]
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Rubi [A] time = 0.0671913, antiderivative size = 62, 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 \[ -\frac{a^5}{7 x^7}-\frac{5 a^4 b}{4 x^4}-\frac{10 a^3 b^2}{x}+5 a^2 b^3 x^2+a b^4 x^5+\frac{b^5 x^8}{8} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^5/x^8,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{5}}{7 x^{7}} - \frac{5 a^{4} b}{4 x^{4}} - \frac{10 a^{3} b^{2}}{x} + 10 a^{2} b^{3} \int x\, dx + a b^{4} x^{5} + \frac{b^{5} x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**5/x**8,x)
[Out]
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Mathematica [A] time = 0.00724857, size = 62, normalized size = 1. \[ -\frac{a^5}{7 x^7}-\frac{5 a^4 b}{4 x^4}-\frac{10 a^3 b^2}{x}+5 a^2 b^3 x^2+a b^4 x^5+\frac{b^5 x^8}{8} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^5/x^8,x]
[Out]
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Maple [A] time = 0.008, size = 57, normalized size = 0.9 \[ -{\frac{{a}^{5}}{7\,{x}^{7}}}-{\frac{5\,{a}^{4}b}{4\,{x}^{4}}}-10\,{\frac{{a}^{3}{b}^{2}}{x}}+5\,{a}^{2}{b}^{3}{x}^{2}+a{b}^{4}{x}^{5}+{\frac{{b}^{5}{x}^{8}}{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^5/x^8,x)
[Out]
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Maxima [A] time = 1.42869, size = 80, normalized size = 1.29 \[ \frac{1}{8} \, b^{5} x^{8} + a b^{4} x^{5} + 5 \, a^{2} b^{3} x^{2} - \frac{280 \, a^{3} b^{2} x^{6} + 35 \, a^{4} b x^{3} + 4 \, a^{5}}{28 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206535, size = 80, normalized size = 1.29 \[ \frac{7 \, b^{5} x^{15} + 56 \, a b^{4} x^{12} + 280 \, a^{2} b^{3} x^{9} - 560 \, a^{3} b^{2} x^{6} - 70 \, a^{4} b x^{3} - 8 \, a^{5}}{56 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.6108, size = 60, normalized size = 0.97 \[ 5 a^{2} b^{3} x^{2} + a b^{4} x^{5} + \frac{b^{5} x^{8}}{8} - \frac{4 a^{5} + 35 a^{4} b x^{3} + 280 a^{3} b^{2} x^{6}}{28 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**5/x**8,x)
[Out]
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GIAC/XCAS [A] time = 0.217634, size = 80, normalized size = 1.29 \[ \frac{1}{8} \, b^{5} x^{8} + a b^{4} x^{5} + 5 \, a^{2} b^{3} x^{2} - \frac{280 \, a^{3} b^{2} x^{6} + 35 \, a^{4} b x^{3} + 4 \, a^{5}}{28 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^8,x, algorithm="giac")
[Out]