Optimal. Leaf size=75 \[ -\frac{b^4 \log \left (a+b x^2\right )}{2 a^5}+\frac{b^4 \log (x)}{a^5}+\frac{b^3}{2 a^4 x^2}-\frac{b^2}{4 a^3 x^4}+\frac{b}{6 a^2 x^6}-\frac{1}{8 a x^8} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.103129, antiderivative size = 75, 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 \[ -\frac{b^4 \log \left (a+b x^2\right )}{2 a^5}+\frac{b^4 \log (x)}{a^5}+\frac{b^3}{2 a^4 x^2}-\frac{b^2}{4 a^3 x^4}+\frac{b}{6 a^2 x^6}-\frac{1}{8 a x^8} \]
Antiderivative was successfully verified.
[In] Int[1/(x^9*(a + b*x^2)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 16.4612, size = 71, normalized size = 0.95 \[ - \frac{1}{8 a x^{8}} + \frac{b}{6 a^{2} x^{6}} - \frac{b^{2}}{4 a^{3} x^{4}} + \frac{b^{3}}{2 a^{4} x^{2}} + \frac{b^{4} \log{\left (x^{2} \right )}}{2 a^{5}} - \frac{b^{4} \log{\left (a + b x^{2} \right )}}{2 a^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**9/(b*x**2+a),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0114208, size = 75, normalized size = 1. \[ -\frac{b^4 \log \left (a+b x^2\right )}{2 a^5}+\frac{b^4 \log (x)}{a^5}+\frac{b^3}{2 a^4 x^2}-\frac{b^2}{4 a^3 x^4}+\frac{b}{6 a^2 x^6}-\frac{1}{8 a x^8} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^9*(a + b*x^2)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 66, normalized size = 0.9 \[ -{\frac{1}{8\,a{x}^{8}}}+{\frac{b}{6\,{a}^{2}{x}^{6}}}-{\frac{{b}^{2}}{4\,{a}^{3}{x}^{4}}}+{\frac{{b}^{3}}{2\,{a}^{4}{x}^{2}}}+{\frac{{b}^{4}\ln \left ( x \right ) }{{a}^{5}}}-{\frac{{b}^{4}\ln \left ( b{x}^{2}+a \right ) }{2\,{a}^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^9/(b*x^2+a),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34439, size = 93, normalized size = 1.24 \[ -\frac{b^{4} \log \left (b x^{2} + a\right )}{2 \, a^{5}} + \frac{b^{4} \log \left (x^{2}\right )}{2 \, a^{5}} + \frac{12 \, b^{3} x^{6} - 6 \, a b^{2} x^{4} + 4 \, a^{2} b x^{2} - 3 \, a^{3}}{24 \, a^{4} x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2 + a)*x^9),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.202656, size = 93, normalized size = 1.24 \[ -\frac{12 \, b^{4} x^{8} \log \left (b x^{2} + a\right ) - 24 \, b^{4} x^{8} \log \left (x\right ) - 12 \, a b^{3} x^{6} + 6 \, a^{2} b^{2} x^{4} - 4 \, a^{3} b x^{2} + 3 \, a^{4}}{24 \, a^{5} x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2 + a)*x^9),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 2.91635, size = 68, normalized size = 0.91 \[ \frac{- 3 a^{3} + 4 a^{2} b x^{2} - 6 a b^{2} x^{4} + 12 b^{3} x^{6}}{24 a^{4} x^{8}} + \frac{b^{4} \log{\left (x \right )}}{a^{5}} - \frac{b^{4} \log{\left (\frac{a}{b} + x^{2} \right )}}{2 a^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**9/(b*x**2+a),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.212348, size = 109, normalized size = 1.45 \[ \frac{b^{4}{\rm ln}\left (x^{2}\right )}{2 \, a^{5}} - \frac{b^{4}{\rm ln}\left ({\left | b x^{2} + a \right |}\right )}{2 \, a^{5}} - \frac{25 \, b^{4} x^{8} - 12 \, a b^{3} x^{6} + 6 \, a^{2} b^{2} x^{4} - 4 \, a^{3} b x^{2} + 3 \, a^{4}}{24 \, a^{5} x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2 + a)*x^9),x, algorithm="giac")
[Out]