Optimal. Leaf size=40 \[ \frac{b \left (a+b x^3\right )^6}{126 a^2 x^{18}}-\frac{\left (a+b x^3\right )^6}{21 a x^{21}} \]
[Out]
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Rubi [A] time = 0.0521835, 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 \[ \frac{b \left (a+b x^3\right )^6}{126 a^2 x^{18}}-\frac{\left (a+b x^3\right )^6}{21 a x^{21}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^5/x^22,x]
[Out]
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Rubi in Sympy [A] time = 5.79237, size = 32, normalized size = 0.8 \[ - \frac{\left (a + b x^{3}\right )^{6}}{21 a x^{21}} + \frac{b \left (a + b x^{3}\right )^{6}}{126 a^{2} x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**5/x**22,x)
[Out]
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Mathematica [A] time = 0.00747992, size = 69, normalized size = 1.72 \[ -\frac{a^5}{21 x^{21}}-\frac{5 a^4 b}{18 x^{18}}-\frac{2 a^3 b^2}{3 x^{15}}-\frac{5 a^2 b^3}{6 x^{12}}-\frac{5 a b^4}{9 x^9}-\frac{b^5}{6 x^6} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^5/x^22,x]
[Out]
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Maple [A] time = 0.008, size = 58, normalized size = 1.5 \[ -{\frac{5\,{a}^{2}{b}^{3}}{6\,{x}^{12}}}-{\frac{2\,{a}^{3}{b}^{2}}{3\,{x}^{15}}}-{\frac{5\,{a}^{4}b}{18\,{x}^{18}}}-{\frac{{b}^{5}}{6\,{x}^{6}}}-{\frac{{a}^{5}}{21\,{x}^{21}}}-{\frac{5\,a{b}^{4}}{9\,{x}^{9}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^5/x^22,x)
[Out]
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Maxima [A] time = 1.44937, size = 80, normalized size = 2. \[ -\frac{21 \, b^{5} x^{15} + 70 \, a b^{4} x^{12} + 105 \, a^{2} b^{3} x^{9} + 84 \, a^{3} b^{2} x^{6} + 35 \, a^{4} b x^{3} + 6 \, a^{5}}{126 \, x^{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^22,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.209432, size = 80, normalized size = 2. \[ -\frac{21 \, b^{5} x^{15} + 70 \, a b^{4} x^{12} + 105 \, a^{2} b^{3} x^{9} + 84 \, a^{3} b^{2} x^{6} + 35 \, a^{4} b x^{3} + 6 \, a^{5}}{126 \, x^{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^22,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.07306, size = 63, normalized size = 1.58 \[ - \frac{6 a^{5} + 35 a^{4} b x^{3} + 84 a^{3} b^{2} x^{6} + 105 a^{2} b^{3} x^{9} + 70 a b^{4} x^{12} + 21 b^{5} x^{15}}{126 x^{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**5/x**22,x)
[Out]
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GIAC/XCAS [A] time = 0.225787, size = 80, normalized size = 2. \[ -\frac{21 \, b^{5} x^{15} + 70 \, a b^{4} x^{12} + 105 \, a^{2} b^{3} x^{9} + 84 \, a^{3} b^{2} x^{6} + 35 \, a^{4} b x^{3} + 6 \, a^{5}}{126 \, x^{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^22,x, algorithm="giac")
[Out]