Optimal. Leaf size=15 \[ \frac{\log \left (2 x^n+3\right )}{2 n} \]
[Out]
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Rubi [A] time = 0.0153048, 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 \[ \frac{\log \left (2 x^n+3\right )}{2 n} \]
Antiderivative was successfully verified.
[In] Int[(2*x + 3*x^(1 - n))^(-1),x]
[Out]
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Rubi in Sympy [A] time = 2.72339, size = 10, normalized size = 0.67 \[ \frac{\log{\left (2 x^{n} + 3 \right )}}{2 n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(2*x+3*x**(1-n)),x)
[Out]
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Mathematica [A] time = 0.00513285, size = 15, normalized size = 1. \[ \frac{\log \left (2 x^n+3\right )}{2 n} \]
Antiderivative was successfully verified.
[In] Integrate[(2*x + 3*x^(1 - n))^(-1),x]
[Out]
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Maple [B] time = 0.016, size = 34, normalized size = 2.3 \[ -{\frac{\ln \left ( x \right ) }{2\,n}}+{\frac{\ln \left ( x \right ) }{2}}+{\frac{\ln \left ( 2\,x+3\,{{\rm e}^{ \left ( 1-n \right ) \ln \left ( x \right ) }} \right ) }{2\,n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(2*x+3*x^(1-n)),x)
[Out]
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Maxima [A] time = 1.37878, size = 15, normalized size = 1. \[ \frac{\log \left (x^{n} + \frac{3}{2}\right )}{2 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(3*x^(-n + 1) + 2*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.23396, size = 35, normalized size = 2.33 \[ \frac{{\left (n - 1\right )} \log \left (x\right ) + \log \left (3 \, x^{-n + 1} + 2 \, x\right )}{2 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(3*x^(-n + 1) + 2*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.03032, size = 22, normalized size = 1.47 \[ \begin{cases} \frac{\log{\left (x \right )}}{2} + \frac{\log{\left (\frac{2}{3} + x^{- n} \right )}}{2 n} & \text{for}\: n \neq 0 \\\frac{\log{\left (x \right )}}{5} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(2*x+3*x**(1-n)),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{3 \, x^{-n + 1} + 2 \, x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(3*x^(-n + 1) + 2*x),x, algorithm="giac")
[Out]