Optimal. Leaf size=35 \[ \frac{b \log \left (a+b x^8\right )}{8 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{8 a x^8} \]
[Out]
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Rubi [A] time = 0.0611305, antiderivative size = 35, 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 \[ \frac{b \log \left (a+b x^8\right )}{8 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{8 a x^8} \]
Antiderivative was successfully verified.
[In] Int[1/(x^9*(a + b*x^8)),x]
[Out]
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Rubi in Sympy [A] time = 8.37455, size = 34, normalized size = 0.97 \[ - \frac{1}{8 a x^{8}} - \frac{b \log{\left (x^{8} \right )}}{8 a^{2}} + \frac{b \log{\left (a + b x^{8} \right )}}{8 a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**9/(b*x**8+a),x)
[Out]
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Mathematica [A] time = 0.0123321, size = 35, normalized size = 1. \[ \frac{b \log \left (a+b x^8\right )}{8 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{8 a x^8} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^9*(a + b*x^8)),x]
[Out]
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Maple [A] time = 0.008, size = 32, normalized size = 0.9 \[ -{\frac{1}{8\,a{x}^{8}}}-{\frac{b\ln \left ( x \right ) }{{a}^{2}}}+{\frac{b\ln \left ( b{x}^{8}+a \right ) }{8\,{a}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^9/(b*x^8+a),x)
[Out]
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Maxima [A] time = 1.43521, size = 45, normalized size = 1.29 \[ \frac{b \log \left (b x^{8} + a\right )}{8 \, a^{2}} - \frac{b \log \left (x^{8}\right )}{8 \, a^{2}} - \frac{1}{8 \, a x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^8 + a)*x^9),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.224552, size = 45, normalized size = 1.29 \[ \frac{b x^{8} \log \left (b x^{8} + a\right ) - 8 \, b x^{8} \log \left (x\right ) - a}{8 \, a^{2} x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^8 + a)*x^9),x, algorithm="fricas")
[Out]
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Sympy [A] time = 26.8054, size = 31, normalized size = 0.89 \[ - \frac{1}{8 a x^{8}} - \frac{b \log{\left (x \right )}}{a^{2}} + \frac{b \log{\left (\frac{a}{b} + x^{8} \right )}}{8 a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**9/(b*x**8+a),x)
[Out]
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GIAC/XCAS [A] time = 0.228609, size = 58, normalized size = 1.66 \[ -\frac{b{\rm ln}\left (x^{8}\right )}{8 \, a^{2}} + \frac{b{\rm ln}\left ({\left | b x^{8} + a \right |}\right )}{8 \, a^{2}} + \frac{b x^{8} - a}{8 \, a^{2} x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^8 + a)*x^9),x, algorithm="giac")
[Out]