Optimal. Leaf size=17 \[ \log \left (a x^{1-n}+b\right )+n \log (x) \]
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Rubi [A] time = 0.124116, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 29, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.103 \[ \log \left (a x^{1-n}+b\right )+n \log (x) \]
Antiderivative was successfully verified.
[In] Int[(a + b*n*x^(-1 + n))/(x^n*(b + a*x^(1 - n))),x]
[Out]
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Rubi in Sympy [A] time = 8.12144, size = 20, normalized size = 1.18 \[ \frac{n \log{\left (x^{- n + 1} \right )}}{- n + 1} + \log{\left (a x^{- n + 1} + b \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*n*x**(-1+n))/(x**n)/(b+a*x**(1-n)),x)
[Out]
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Mathematica [A] time = 0.0125254, size = 10, normalized size = 0.59 \[ \log \left (a x+b x^n\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*n*x^(-1 + n))/(x^n*(b + a*x^(1 - n))),x]
[Out]
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Maple [A] time = 0.035, size = 13, normalized size = 0.8 \[ \ln \left ( ax+b{{\rm e}^{n\ln \left ( x \right ) }} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*n*x^(-1+n))/(x^n)/(b+a*x^(1-n)),x)
[Out]
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Maxima [A] time = 0.701296, size = 116, normalized size = 6.82 \[ b n{\left (\frac{\log \left (x\right )}{b} - \frac{n \log \left (x\right )}{b{\left (n - 1\right )}} + \frac{\log \left (\frac{a x + b x^{n}}{b}\right )}{b{\left (n - 1\right )}}\right )} + a{\left (\frac{n \log \left (x\right )}{a{\left (n - 1\right )}} - \frac{\log \left (\frac{a x + b x^{n}}{b}\right )}{a{\left (n - 1\right )}}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*n*x^(n - 1) + a)/((a*x^(-n + 1) + b)*x^n),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.275187, size = 14, normalized size = 0.82 \[ \log \left (a x + b x^{n}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*n*x^(n - 1) + a)/((a*x^(-n + 1) + b)*x^n),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*n*x**(-1+n))/(x**n)/(b+a*x**(1-n)),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{b n x^{n - 1} + a}{{\left (a x^{-n + 1} + b\right )} x^{n}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*n*x^(n - 1) + a)/((a*x^(-n + 1) + b)*x^n),x, algorithm="giac")
[Out]