Optimal. Leaf size=66 \[ -\frac{a^5}{9 x^9}-\frac{5 a^4 b}{6 x^6}-\frac{10 a^3 b^2}{3 x^3}+10 a^2 b^3 \log (x)+\frac{5}{3} a b^4 x^3+\frac{b^5 x^6}{6} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0822964, antiderivative size = 66, 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 \[ -\frac{a^5}{9 x^9}-\frac{5 a^4 b}{6 x^6}-\frac{10 a^3 b^2}{3 x^3}+10 a^2 b^3 \log (x)+\frac{5}{3} a b^4 x^3+\frac{b^5 x^6}{6} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^5/x^10,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{5}}{9 x^{9}} - \frac{5 a^{4} b}{6 x^{6}} - \frac{10 a^{3} b^{2}}{3 x^{3}} + \frac{10 a^{2} b^{3} \log{\left (x^{3} \right )}}{3} + \frac{5 a b^{4} x^{3}}{3} + \frac{b^{5} \int ^{x^{3}} x\, dx}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**5/x**10,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0116637, size = 66, normalized size = 1. \[ -\frac{a^5}{9 x^9}-\frac{5 a^4 b}{6 x^6}-\frac{10 a^3 b^2}{3 x^3}+10 a^2 b^3 \log (x)+\frac{5}{3} a b^4 x^3+\frac{b^5 x^6}{6} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^5/x^10,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.009, size = 57, normalized size = 0.9 \[ -{\frac{{a}^{5}}{9\,{x}^{9}}}-{\frac{5\,{a}^{4}b}{6\,{x}^{6}}}-{\frac{10\,{a}^{3}{b}^{2}}{3\,{x}^{3}}}+{\frac{5\,a{b}^{4}{x}^{3}}{3}}+{\frac{{b}^{5}{x}^{6}}{6}}+10\,{a}^{2}{b}^{3}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^5/x^10,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.44055, size = 82, normalized size = 1.24 \[ \frac{1}{6} \, b^{5} x^{6} + \frac{5}{3} \, a b^{4} x^{3} + \frac{10}{3} \, a^{2} b^{3} \log \left (x^{3}\right ) - \frac{60 \, a^{3} b^{2} x^{6} + 15 \, a^{4} b x^{3} + 2 \, a^{5}}{18 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^10,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.213293, size = 82, normalized size = 1.24 \[ \frac{3 \, b^{5} x^{15} + 30 \, a b^{4} x^{12} + 180 \, a^{2} b^{3} x^{9} \log \left (x\right ) - 60 \, a^{3} b^{2} x^{6} - 15 \, a^{4} b x^{3} - 2 \, a^{5}}{18 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^10,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.88879, size = 63, normalized size = 0.95 \[ 10 a^{2} b^{3} \log{\left (x \right )} + \frac{5 a b^{4} x^{3}}{3} + \frac{b^{5} x^{6}}{6} - \frac{2 a^{5} + 15 a^{4} b x^{3} + 60 a^{3} b^{2} x^{6}}{18 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**5/x**10,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.225811, size = 96, normalized size = 1.45 \[ \frac{1}{6} \, b^{5} x^{6} + \frac{5}{3} \, a b^{4} x^{3} + 10 \, a^{2} b^{3}{\rm ln}\left ({\left | x \right |}\right ) - \frac{110 \, a^{2} b^{3} x^{9} + 60 \, a^{3} b^{2} x^{6} + 15 \, a^{4} b x^{3} + 2 \, a^{5}}{18 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^10,x, algorithm="giac")
[Out]