Optimal. Leaf size=23 \[ \frac{\log (x)}{a}-\frac{\log \left (a+b x^n\right )}{a n} \]
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Rubi [A] time = 0.0355037, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.308 \[ \frac{\log (x)}{a}-\frac{\log \left (a+b x^n\right )}{a n} \]
Antiderivative was successfully verified.
[In] Int[1/(x*(a + b*x^n)),x]
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Rubi in Sympy [A] time = 6.28034, size = 19, normalized size = 0.83 \[ \frac{\log{\left (x^{n} \right )}}{a n} - \frac{\log{\left (a + b x^{n} \right )}}{a n} \]
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 = 0.0172266, size = 22, normalized size = 0.96 \[ \frac{n \log (x)-\log \left (a+b x^n\right )}{a n} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*(a + b*x^n)),x]
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Maple [A] time = 0., size = 29, normalized size = 1.3 \[{\frac{\ln \left ({x}^{n} \right ) }{an}}-{\frac{\ln \left ( a+b{x}^{n} \right ) }{an}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(a+b*x^n),x)
[Out]
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Maxima [A] time = 1.38114, size = 38, normalized size = 1.65 \[ -\frac{\log \left (b x^{n} + a\right )}{a n} + \frac{\log \left (x^{n}\right )}{a n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^n + a)*x),x, algorithm="maxima")
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Fricas [A] time = 0.246484, size = 30, normalized size = 1.3 \[ \frac{n \log \left (x\right ) - \log \left (b x^{n} + a\right )}{a n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^n + a)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.1566, size = 41, normalized size = 1.78 \[ \begin{cases} \tilde{\infty } \log{\left (x \right )} & \text{for}\: a = 0 \wedge b = 0 \wedge n = 0 \\\frac{\log{\left (x \right )}}{a} & \text{for}\: b = 0 \\\frac{\log{\left (x \right )}}{a + b} & \text{for}\: n = 0 \\- \frac{x^{- n}}{b n} & \text{for}\: a = 0 \\\frac{\log{\left (x \right )}}{a} - \frac{\log{\left (\frac{a}{b} + x^{n} \right )}}{a n} & \text{otherwise} \end{cases} \]
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. \[ \int \frac{1}{{\left (b x^{n} + a\right )} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^n + a)*x),x, algorithm="giac")
[Out]