Optimal. Leaf size=40 \[ \frac{b \left (a+b x^3\right )^4}{60 a^2 x^{12}}-\frac{\left (a+b x^3\right )^4}{15 a x^{15}} \]
[Out]
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Rubi [A] time = 0.0522817, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{b \left (a+b x^3\right )^4}{60 a^2 x^{12}}-\frac{\left (a+b x^3\right )^4}{15 a x^{15}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^3/x^16,x]
[Out]
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Rubi in Sympy [A] time = 8.75949, size = 37, normalized size = 0.92 \[ - \frac{a^{3}}{15 x^{15}} - \frac{a^{2} b}{4 x^{12}} - \frac{a b^{2}}{3 x^{9}} - \frac{b^{3}}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**3/x**16,x)
[Out]
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Mathematica [A] time = 0.00671068, size = 43, normalized size = 1.08 \[ -\frac{a^3}{15 x^{15}}-\frac{a^2 b}{4 x^{12}}-\frac{a b^2}{3 x^9}-\frac{b^3}{6 x^6} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^3/x^16,x]
[Out]
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Maple [A] time = 0.008, size = 36, normalized size = 0.9 \[ -{\frac{{a}^{2}b}{4\,{x}^{12}}}-{\frac{{a}^{3}}{15\,{x}^{15}}}-{\frac{{b}^{3}}{6\,{x}^{6}}}-{\frac{a{b}^{2}}{3\,{x}^{9}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^3/x^16,x)
[Out]
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Maxima [A] time = 1.4368, size = 50, normalized size = 1.25 \[ -\frac{10 \, b^{3} x^{9} + 20 \, a b^{2} x^{6} + 15 \, a^{2} b x^{3} + 4 \, a^{3}}{60 \, x^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^16,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205513, size = 50, normalized size = 1.25 \[ -\frac{10 \, b^{3} x^{9} + 20 \, a b^{2} x^{6} + 15 \, a^{2} b x^{3} + 4 \, a^{3}}{60 \, x^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^16,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.96989, size = 39, normalized size = 0.98 \[ - \frac{4 a^{3} + 15 a^{2} b x^{3} + 20 a b^{2} x^{6} + 10 b^{3} x^{9}}{60 x^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**3/x**16,x)
[Out]
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GIAC/XCAS [A] time = 0.214195, size = 50, normalized size = 1.25 \[ -\frac{10 \, b^{3} x^{9} + 20 \, a b^{2} x^{6} + 15 \, a^{2} b x^{3} + 4 \, a^{3}}{60 \, x^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^16,x, algorithm="giac")
[Out]