Optimal. Leaf size=62 \[ -\frac{b^2 \left (a+b x^3\right )^6}{504 a^3 x^{18}}+\frac{b \left (a+b x^3\right )^6}{84 a^2 x^{21}}-\frac{\left (a+b x^3\right )^6}{24 a x^{24}} \]
[Out]
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Rubi [A] time = 0.077408, antiderivative size = 62, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ -\frac{b^2 \left (a+b x^3\right )^6}{504 a^3 x^{18}}+\frac{b \left (a+b x^3\right )^6}{84 a^2 x^{21}}-\frac{\left (a+b x^3\right )^6}{24 a x^{24}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^5/x^25,x]
[Out]
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Rubi in Sympy [A] time = 14.0305, size = 68, normalized size = 1.1 \[ - \frac{a^{5}}{24 x^{24}} - \frac{5 a^{4} b}{21 x^{21}} - \frac{5 a^{3} b^{2}}{9 x^{18}} - \frac{2 a^{2} b^{3}}{3 x^{15}} - \frac{5 a b^{4}}{12 x^{12}} - \frac{b^{5}}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**5/x**25,x)
[Out]
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Mathematica [A] time = 0.0128134, size = 69, normalized size = 1.11 \[ -\frac{a^5}{24 x^{24}}-\frac{5 a^4 b}{21 x^{21}}-\frac{5 a^3 b^2}{9 x^{18}}-\frac{2 a^2 b^3}{3 x^{15}}-\frac{5 a b^4}{12 x^{12}}-\frac{b^5}{9 x^9} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^5/x^25,x]
[Out]
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Maple [A] time = 0.009, size = 58, normalized size = 0.9 \[ -{\frac{5\,{a}^{3}{b}^{2}}{9\,{x}^{18}}}-{\frac{5\,a{b}^{4}}{12\,{x}^{12}}}-{\frac{2\,{a}^{2}{b}^{3}}{3\,{x}^{15}}}-{\frac{{a}^{5}}{24\,{x}^{24}}}-{\frac{{b}^{5}}{9\,{x}^{9}}}-{\frac{5\,{a}^{4}b}{21\,{x}^{21}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^5/x^25,x)
[Out]
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Maxima [A] time = 1.44933, size = 80, normalized size = 1.29 \[ -\frac{56 \, b^{5} x^{15} + 210 \, a b^{4} x^{12} + 336 \, a^{2} b^{3} x^{9} + 280 \, a^{3} b^{2} x^{6} + 120 \, a^{4} b x^{3} + 21 \, a^{5}}{504 \, x^{24}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^25,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207343, size = 80, normalized size = 1.29 \[ -\frac{56 \, b^{5} x^{15} + 210 \, a b^{4} x^{12} + 336 \, a^{2} b^{3} x^{9} + 280 \, a^{3} b^{2} x^{6} + 120 \, a^{4} b x^{3} + 21 \, a^{5}}{504 \, x^{24}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^25,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.23828, size = 63, normalized size = 1.02 \[ - \frac{21 a^{5} + 120 a^{4} b x^{3} + 280 a^{3} b^{2} x^{6} + 336 a^{2} b^{3} x^{9} + 210 a b^{4} x^{12} + 56 b^{5} x^{15}}{504 x^{24}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**5/x**25,x)
[Out]
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GIAC/XCAS [A] time = 0.222404, size = 80, normalized size = 1.29 \[ -\frac{56 \, b^{5} x^{15} + 210 \, a b^{4} x^{12} + 336 \, a^{2} b^{3} x^{9} + 280 \, a^{3} b^{2} x^{6} + 120 \, a^{4} b x^{3} + 21 \, a^{5}}{504 \, x^{24}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^25,x, algorithm="giac")
[Out]