Optimal. Leaf size=53 \[ \frac{a^2 \left (a+b x^3\right )^6}{18 b^3}+\frac{\left (a+b x^3\right )^8}{24 b^3}-\frac{2 a \left (a+b x^3\right )^7}{21 b^3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.143505, antiderivative size = 53, 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 \[ \frac{a^2 \left (a+b x^3\right )^6}{18 b^3}+\frac{\left (a+b x^3\right )^8}{24 b^3}-\frac{2 a \left (a+b x^3\right )^7}{21 b^3} \]
Antiderivative was successfully verified.
[In] Int[x^8*(a + b*x^3)^5,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 13.5983, size = 46, normalized size = 0.87 \[ \frac{a^{2} \left (a + b x^{3}\right )^{6}}{18 b^{3}} - \frac{2 a \left (a + b x^{3}\right )^{7}}{21 b^{3}} + \frac{\left (a + b x^{3}\right )^{8}}{24 b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**8*(b*x**3+a)**5,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00372556, size = 69, normalized size = 1.3 \[ \frac{a^5 x^9}{9}+\frac{5}{12} a^4 b x^{12}+\frac{2}{3} a^3 b^2 x^{15}+\frac{5}{9} a^2 b^3 x^{18}+\frac{5}{21} a b^4 x^{21}+\frac{b^5 x^{24}}{24} \]
Antiderivative was successfully verified.
[In] Integrate[x^8*(a + b*x^3)^5,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 58, normalized size = 1.1 \[{\frac{{b}^{5}{x}^{24}}{24}}+{\frac{5\,a{b}^{4}{x}^{21}}{21}}+{\frac{5\,{a}^{2}{b}^{3}{x}^{18}}{9}}+{\frac{2\,{a}^{3}{b}^{2}{x}^{15}}{3}}+{\frac{5\,{a}^{4}b{x}^{12}}{12}}+{\frac{{a}^{5}{x}^{9}}{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^8*(b*x^3+a)^5,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.42127, size = 77, normalized size = 1.45 \[ \frac{1}{24} \, b^{5} x^{24} + \frac{5}{21} \, a b^{4} x^{21} + \frac{5}{9} \, a^{2} b^{3} x^{18} + \frac{2}{3} \, a^{3} b^{2} x^{15} + \frac{5}{12} \, a^{4} b x^{12} + \frac{1}{9} \, a^{5} x^{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5*x^8,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.189437, size = 1, normalized size = 0.02 \[ \frac{1}{24} x^{24} b^{5} + \frac{5}{21} x^{21} b^{4} a + \frac{5}{9} x^{18} b^{3} a^{2} + \frac{2}{3} x^{15} b^{2} a^{3} + \frac{5}{12} x^{12} b a^{4} + \frac{1}{9} x^{9} a^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5*x^8,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.124328, size = 66, normalized size = 1.25 \[ \frac{a^{5} x^{9}}{9} + \frac{5 a^{4} b x^{12}}{12} + \frac{2 a^{3} b^{2} x^{15}}{3} + \frac{5 a^{2} b^{3} x^{18}}{9} + \frac{5 a b^{4} x^{21}}{21} + \frac{b^{5} x^{24}}{24} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**8*(b*x**3+a)**5,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.215942, size = 77, normalized size = 1.45 \[ \frac{1}{24} \, b^{5} x^{24} + \frac{5}{21} \, a b^{4} x^{21} + \frac{5}{9} \, a^{2} b^{3} x^{18} + \frac{2}{3} \, a^{3} b^{2} x^{15} + \frac{5}{12} \, a^{4} b x^{12} + \frac{1}{9} \, a^{5} x^{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5*x^8,x, algorithm="giac")
[Out]