Optimal. Leaf size=35 \[ \frac{b \log \left (a+b x^5\right )}{5 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{5 a x^5} \]
[Out]
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Rubi [A] time = 0.0538295, 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 \[ \frac{b \log \left (a+b x^5\right )}{5 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{5 a x^5} \]
Antiderivative was successfully verified.
[In] Int[1/(x^6*(a + b*x^5)),x]
[Out]
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Rubi in Sympy [A] time = 8.0728, size = 34, normalized size = 0.97 \[ - \frac{1}{5 a x^{5}} - \frac{b \log{\left (x^{5} \right )}}{5 a^{2}} + \frac{b \log{\left (a + b x^{5} \right )}}{5 a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**6/(b*x**5+a),x)
[Out]
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Mathematica [A] time = 0.0113012, size = 35, normalized size = 1. \[ \frac{b \log \left (a+b x^5\right )}{5 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{5 a x^5} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^6*(a + b*x^5)),x]
[Out]
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Maple [A] time = 0.009, size = 32, normalized size = 0.9 \[ -{\frac{1}{5\,a{x}^{5}}}-{\frac{b\ln \left ( x \right ) }{{a}^{2}}}+{\frac{b\ln \left ( b{x}^{5}+a \right ) }{5\,{a}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^6/(b*x^5+a),x)
[Out]
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Maxima [A] time = 1.43319, size = 45, normalized size = 1.29 \[ \frac{b \log \left (b x^{5} + a\right )}{5 \, a^{2}} - \frac{b \log \left (x^{5}\right )}{5 \, a^{2}} - \frac{1}{5 \, a x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^5 + a)*x^6),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219342, size = 45, normalized size = 1.29 \[ \frac{b x^{5} \log \left (b x^{5} + a\right ) - 5 \, b x^{5} \log \left (x\right ) - a}{5 \, a^{2} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^5 + a)*x^6),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.9688, size = 31, normalized size = 0.89 \[ - \frac{1}{5 a x^{5}} - \frac{b \log{\left (x \right )}}{a^{2}} + \frac{b \log{\left (\frac{a}{b} + x^{5} \right )}}{5 a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**6/(b*x**5+a),x)
[Out]
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GIAC/XCAS [A] time = 0.231607, size = 57, normalized size = 1.63 \[ \frac{b{\rm ln}\left ({\left | b x^{5} + a \right |}\right )}{5 \, a^{2}} - \frac{b{\rm ln}\left ({\left | x \right |}\right )}{a^{2}} + \frac{b x^{5} - a}{5 \, a^{2} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^5 + a)*x^6),x, algorithm="giac")
[Out]