Optimal. Leaf size=28 \[ \frac{1}{45} b \log \left (b x^5+3\right )-\frac{1}{9} b \log (x)-\frac{1}{15 x^5} \]
[Out]
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Rubi [A] time = 0.0447055, antiderivative size = 28, 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 \[ \frac{1}{45} b \log \left (b x^5+3\right )-\frac{1}{9} b \log (x)-\frac{1}{15 x^5} \]
Antiderivative was successfully verified.
[In] Int[1/(x^6*(3 + b*x^5)),x]
[Out]
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Rubi in Sympy [A] time = 6.23248, size = 26, normalized size = 0.93 \[ - \frac{b \log{\left (x^{5} \right )}}{45} + \frac{b \log{\left (b x^{5} + 3 \right )}}{45} - \frac{1}{15 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**6/(b*x**5+3),x)
[Out]
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Mathematica [A] time = 0.0083346, size = 28, normalized size = 1. \[ \frac{1}{45} b \log \left (b x^5+3\right )-\frac{1}{9} b \log (x)-\frac{1}{15 x^5} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^6*(3 + b*x^5)),x]
[Out]
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Maple [A] time = 0.009, size = 23, normalized size = 0.8 \[ -{\frac{1}{15\,{x}^{5}}}-{\frac{b\ln \left ( x \right ) }{9}}+{\frac{b\ln \left ( b{x}^{5}+3 \right ) }{45}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^6/(b*x^5+3),x)
[Out]
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Maxima [A] time = 1.43884, size = 32, normalized size = 1.14 \[ \frac{1}{45} \, b \log \left (b x^{5} + 3\right ) - \frac{1}{45} \, b \log \left (x^{5}\right ) - \frac{1}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^5 + 3)*x^6),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214911, size = 38, normalized size = 1.36 \[ \frac{b x^{5} \log \left (b x^{5} + 3\right ) - 5 \, b x^{5} \log \left (x\right ) - 3}{45 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^5 + 3)*x^6),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.72954, size = 24, normalized size = 0.86 \[ - \frac{b \log{\left (x \right )}}{9} + \frac{b \log{\left (x^{5} + \frac{3}{b} \right )}}{45} - \frac{1}{15 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**6/(b*x**5+3),x)
[Out]
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GIAC/XCAS [A] time = 0.284526, size = 42, normalized size = 1.5 \[ \frac{1}{45} \, b{\rm ln}\left ({\left | b x^{5} + 3 \right |}\right ) - \frac{1}{9} \, b{\rm ln}\left ({\left | x \right |}\right ) + \frac{b x^{5} - 3}{45 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^5 + 3)*x^6),x, algorithm="giac")
[Out]