Optimal. Leaf size=15 \[ \frac{\log \left (a x^n+b\right )}{a n} \]
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Rubi [A] time = 0.0335621, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{\log \left (a x^n+b\right )}{a n} \]
Antiderivative was successfully verified.
[In] Int[1/(x*(a + b/x^n)),x]
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Rubi in Sympy [A] time = 4.10531, size = 10, normalized size = 0.67 \[ \frac{\log{\left (a x^{n} + b \right )}}{a n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(a+b/(x**n)),x)
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Mathematica [A] time = 0.00617183, size = 15, normalized size = 1. \[ \frac{\log \left (a x^n+b\right )}{a n} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*(a + b/x^n)),x]
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Maple [A] time = 0.003, size = 16, normalized size = 1.1 \[{\frac{\ln \left ( b+a{x}^{n} \right ) }{an}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(a+b/(x^n)),x)
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Maxima [A] time = 1.38408, size = 43, normalized size = 2.87 \[ \frac{\log \left (b x^{-n} + a\right )}{a n} - \frac{\log \left (x^{-n}\right )}{a n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^n)*x),x, algorithm="maxima")
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Fricas [A] time = 0.227582, size = 20, normalized size = 1.33 \[ \frac{\log \left (a x^{n} + b\right )}{a n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^n)*x),x, algorithm="fricas")
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Sympy [A] time = 2.37263, size = 39, normalized size = 2.6 \[ \begin{cases} \tilde{\infty } \log{\left (x \right )} & \text{for}\: a = 0 \wedge b = 0 \wedge n = 0 \\\frac{\log{\left (x \right )}}{a} & \text{for}\: b = 0 \\\frac{\log{\left (x \right )}}{a + b} & \text{for}\: n = 0 \\\frac{x^{n}}{b n} & \text{for}\: a = 0 \\\frac{\log{\left (x \right )}}{a} + \frac{\log{\left (\frac{a}{b} + x^{- n} \right )}}{a n} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(a+b/(x**n)),x)
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (a + \frac{b}{x^{n}}\right )} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^n)*x),x, algorithm="giac")
[Out]