Optimal. Leaf size=69 \[ -\frac{a^5}{27 x^{27}}-\frac{5 a^4 b}{24 x^{24}}-\frac{10 a^3 b^2}{21 x^{21}}-\frac{5 a^2 b^3}{9 x^{18}}-\frac{a b^4}{3 x^{15}}-\frac{b^5}{12 x^{12}} \]
[Out]
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Rubi [A] time = 0.0801097, antiderivative size = 69, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{a^5}{27 x^{27}}-\frac{5 a^4 b}{24 x^{24}}-\frac{10 a^3 b^2}{21 x^{21}}-\frac{5 a^2 b^3}{9 x^{18}}-\frac{a b^4}{3 x^{15}}-\frac{b^5}{12 x^{12}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^5/x^28,x]
[Out]
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Rubi in Sympy [A] time = 13.9344, size = 66, normalized size = 0.96 \[ - \frac{a^{5}}{27 x^{27}} - \frac{5 a^{4} b}{24 x^{24}} - \frac{10 a^{3} b^{2}}{21 x^{21}} - \frac{5 a^{2} b^{3}}{9 x^{18}} - \frac{a b^{4}}{3 x^{15}} - \frac{b^{5}}{12 x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**5/x**28,x)
[Out]
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Mathematica [A] time = 0.00780375, size = 69, normalized size = 1. \[ -\frac{a^5}{27 x^{27}}-\frac{5 a^4 b}{24 x^{24}}-\frac{10 a^3 b^2}{21 x^{21}}-\frac{5 a^2 b^3}{9 x^{18}}-\frac{a b^4}{3 x^{15}}-\frac{b^5}{12 x^{12}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^5/x^28,x]
[Out]
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Maple [A] time = 0.008, size = 58, normalized size = 0.8 \[ -{\frac{{a}^{5}}{27\,{x}^{27}}}-{\frac{5\,{a}^{4}b}{24\,{x}^{24}}}-{\frac{10\,{a}^{3}{b}^{2}}{21\,{x}^{21}}}-{\frac{5\,{a}^{2}{b}^{3}}{9\,{x}^{18}}}-{\frac{a{b}^{4}}{3\,{x}^{15}}}-{\frac{{b}^{5}}{12\,{x}^{12}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^5/x^28,x)
[Out]
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Maxima [A] time = 1.45702, size = 80, normalized size = 1.16 \[ -\frac{126 \, b^{5} x^{15} + 504 \, a b^{4} x^{12} + 840 \, a^{2} b^{3} x^{9} + 720 \, a^{3} b^{2} x^{6} + 315 \, a^{4} b x^{3} + 56 \, a^{5}}{1512 \, x^{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^28,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.202732, size = 80, normalized size = 1.16 \[ -\frac{126 \, b^{5} x^{15} + 504 \, a b^{4} x^{12} + 840 \, a^{2} b^{3} x^{9} + 720 \, a^{3} b^{2} x^{6} + 315 \, a^{4} b x^{3} + 56 \, a^{5}}{1512 \, x^{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^28,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.46091, size = 63, normalized size = 0.91 \[ - \frac{56 a^{5} + 315 a^{4} b x^{3} + 720 a^{3} b^{2} x^{6} + 840 a^{2} b^{3} x^{9} + 504 a b^{4} x^{12} + 126 b^{5} x^{15}}{1512 x^{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**5/x**28,x)
[Out]
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GIAC/XCAS [A] time = 0.218413, size = 80, normalized size = 1.16 \[ -\frac{126 \, b^{5} x^{15} + 504 \, a b^{4} x^{12} + 840 \, a^{2} b^{3} x^{9} + 720 \, a^{3} b^{2} x^{6} + 315 \, a^{4} b x^{3} + 56 \, a^{5}}{1512 \, x^{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^28,x, algorithm="giac")
[Out]