Optimal. Leaf size=102 \[ -\frac{a^8}{7 x^7}-\frac{8 a^7 b}{5 x^5}-\frac{28 a^6 b^2}{3 x^3}-\frac{56 a^5 b^3}{x}+70 a^4 b^4 x+\frac{56}{3} a^3 b^5 x^3+\frac{28}{5} a^2 b^6 x^5+\frac{8}{7} a b^7 x^7+\frac{b^8 x^9}{9} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.104669, antiderivative size = 102, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{a^8}{7 x^7}-\frac{8 a^7 b}{5 x^5}-\frac{28 a^6 b^2}{3 x^3}-\frac{56 a^5 b^3}{x}+70 a^4 b^4 x+\frac{56}{3} a^3 b^5 x^3+\frac{28}{5} a^2 b^6 x^5+\frac{8}{7} a b^7 x^7+\frac{b^8 x^9}{9} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^8/x^8,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 19.4764, size = 100, normalized size = 0.98 \[ - \frac{a^{8}}{7 x^{7}} - \frac{8 a^{7} b}{5 x^{5}} - \frac{28 a^{6} b^{2}}{3 x^{3}} - \frac{56 a^{5} b^{3}}{x} + 70 a^{4} b^{4} x + \frac{56 a^{3} b^{5} x^{3}}{3} + \frac{28 a^{2} b^{6} x^{5}}{5} + \frac{8 a b^{7} x^{7}}{7} + \frac{b^{8} x^{9}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**8/x**8,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0110263, size = 102, normalized size = 1. \[ -\frac{a^8}{7 x^7}-\frac{8 a^7 b}{5 x^5}-\frac{28 a^6 b^2}{3 x^3}-\frac{56 a^5 b^3}{x}+70 a^4 b^4 x+\frac{56}{3} a^3 b^5 x^3+\frac{28}{5} a^2 b^6 x^5+\frac{8}{7} a b^7 x^7+\frac{b^8 x^9}{9} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^8/x^8,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.009, size = 89, normalized size = 0.9 \[ -{\frac{{a}^{8}}{7\,{x}^{7}}}-{\frac{8\,{a}^{7}b}{5\,{x}^{5}}}-{\frac{28\,{a}^{6}{b}^{2}}{3\,{x}^{3}}}-56\,{\frac{{a}^{5}{b}^{3}}{x}}+70\,{a}^{4}{b}^{4}x+{\frac{56\,{a}^{3}{b}^{5}{x}^{3}}{3}}+{\frac{28\,{a}^{2}{b}^{6}{x}^{5}}{5}}+{\frac{8\,a{b}^{7}{x}^{7}}{7}}+{\frac{{b}^{8}{x}^{9}}{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^8/x^8,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.35642, size = 123, normalized size = 1.21 \[ \frac{1}{9} \, b^{8} x^{9} + \frac{8}{7} \, a b^{7} x^{7} + \frac{28}{5} \, a^{2} b^{6} x^{5} + \frac{56}{3} \, a^{3} b^{5} x^{3} + 70 \, a^{4} b^{4} x - \frac{5880 \, a^{5} b^{3} x^{6} + 980 \, a^{6} b^{2} x^{4} + 168 \, a^{7} b x^{2} + 15 \, a^{8}}{105 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^8/x^8,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.196614, size = 124, normalized size = 1.22 \[ \frac{35 \, b^{8} x^{16} + 360 \, a b^{7} x^{14} + 1764 \, a^{2} b^{6} x^{12} + 5880 \, a^{3} b^{5} x^{10} + 22050 \, a^{4} b^{4} x^{8} - 17640 \, a^{5} b^{3} x^{6} - 2940 \, a^{6} b^{2} x^{4} - 504 \, a^{7} b x^{2} - 45 \, a^{8}}{315 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^8/x^8,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.90107, size = 100, normalized size = 0.98 \[ 70 a^{4} b^{4} x + \frac{56 a^{3} b^{5} x^{3}}{3} + \frac{28 a^{2} b^{6} x^{5}}{5} + \frac{8 a b^{7} x^{7}}{7} + \frac{b^{8} x^{9}}{9} - \frac{15 a^{8} + 168 a^{7} b x^{2} + 980 a^{6} b^{2} x^{4} + 5880 a^{5} b^{3} x^{6}}{105 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**8/x**8,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.209392, size = 123, normalized size = 1.21 \[ \frac{1}{9} \, b^{8} x^{9} + \frac{8}{7} \, a b^{7} x^{7} + \frac{28}{5} \, a^{2} b^{6} x^{5} + \frac{56}{3} \, a^{3} b^{5} x^{3} + 70 \, a^{4} b^{4} x - \frac{5880 \, a^{5} b^{3} x^{6} + 980 \, a^{6} b^{2} x^{4} + 168 \, a^{7} b x^{2} + 15 \, a^{8}}{105 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^8/x^8,x, algorithm="giac")
[Out]