Optimal. Leaf size=40 \[ \frac{b \left (a+b x^2\right )^9}{180 a^2 x^{18}}-\frac{\left (a+b x^2\right )^9}{20 a x^{20}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0600336, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{b \left (a+b x^2\right )^9}{180 a^2 x^{18}}-\frac{\left (a+b x^2\right )^9}{20 a x^{20}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^8/x^21,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.56769, size = 32, normalized size = 0.8 \[ - \frac{\left (a + b x^{2}\right )^{9}}{20 a x^{20}} + \frac{b \left (a + b x^{2}\right )^{9}}{180 a^{2} x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**8/x**21,x)
[Out]
_______________________________________________________________________________________
Mathematica [B] time = 0.00772375, size = 106, normalized size = 2.65 \[ -\frac{a^8}{20 x^{20}}-\frac{4 a^7 b}{9 x^{18}}-\frac{7 a^6 b^2}{4 x^{16}}-\frac{4 a^5 b^3}{x^{14}}-\frac{35 a^4 b^4}{6 x^{12}}-\frac{28 a^3 b^5}{5 x^{10}}-\frac{7 a^2 b^6}{2 x^8}-\frac{4 a b^7}{3 x^6}-\frac{b^8}{4 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^8/x^21,x]
[Out]
_______________________________________________________________________________________
Maple [B] time = 0.009, size = 91, normalized size = 2.3 \[ -{\frac{35\,{a}^{4}{b}^{4}}{6\,{x}^{12}}}-{\frac{7\,{a}^{6}{b}^{2}}{4\,{x}^{16}}}-{\frac{{a}^{8}}{20\,{x}^{20}}}-{\frac{4\,a{b}^{7}}{3\,{x}^{6}}}-{\frac{{b}^{8}}{4\,{x}^{4}}}-{\frac{28\,{a}^{3}{b}^{5}}{5\,{x}^{10}}}-{\frac{7\,{a}^{2}{b}^{6}}{2\,{x}^{8}}}-4\,{\frac{{a}^{5}{b}^{3}}{{x}^{14}}}-{\frac{4\,{a}^{7}b}{9\,{x}^{18}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^8/x^21,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.35034, size = 124, normalized size = 3.1 \[ -\frac{45 \, b^{8} x^{16} + 240 \, a b^{7} x^{14} + 630 \, a^{2} b^{6} x^{12} + 1008 \, a^{3} b^{5} x^{10} + 1050 \, a^{4} b^{4} x^{8} + 720 \, a^{5} b^{3} x^{6} + 315 \, a^{6} b^{2} x^{4} + 80 \, a^{7} b x^{2} + 9 \, a^{8}}{180 \, x^{20}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^8/x^21,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.195605, size = 124, normalized size = 3.1 \[ -\frac{45 \, b^{8} x^{16} + 240 \, a b^{7} x^{14} + 630 \, a^{2} b^{6} x^{12} + 1008 \, a^{3} b^{5} x^{10} + 1050 \, a^{4} b^{4} x^{8} + 720 \, a^{5} b^{3} x^{6} + 315 \, a^{6} b^{2} x^{4} + 80 \, a^{7} b x^{2} + 9 \, a^{8}}{180 \, x^{20}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^8/x^21,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 4.20112, size = 99, normalized size = 2.48 \[ - \frac{9 a^{8} + 80 a^{7} b x^{2} + 315 a^{6} b^{2} x^{4} + 720 a^{5} b^{3} x^{6} + 1050 a^{4} b^{4} x^{8} + 1008 a^{3} b^{5} x^{10} + 630 a^{2} b^{6} x^{12} + 240 a b^{7} x^{14} + 45 b^{8} x^{16}}{180 x^{20}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**8/x**21,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.210059, size = 124, normalized size = 3.1 \[ -\frac{45 \, b^{8} x^{16} + 240 \, a b^{7} x^{14} + 630 \, a^{2} b^{6} x^{12} + 1008 \, a^{3} b^{5} x^{10} + 1050 \, a^{4} b^{4} x^{8} + 720 \, a^{5} b^{3} x^{6} + 315 \, a^{6} b^{2} x^{4} + 80 \, a^{7} b x^{2} + 9 \, a^{8}}{180 \, x^{20}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^8/x^21,x, algorithm="giac")
[Out]