Optimal. Leaf size=15 \[ \frac{\log \left (b x^n+2\right )}{b n} \]
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Rubi [A] time = 0.0049866, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {260} \[ \frac{\log \left (b x^n+2\right )}{b n} \]
Antiderivative was successfully verified.
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Rule 260
Rubi steps
\begin{align*} \int \frac{x^{-1+n}}{2+b x^n} \, dx &=\frac{\log \left (2+b x^n\right )}{b n}\\ \end{align*}
Mathematica [A] time = 0.0021038, size = 15, normalized size = 1. \[ \frac{\log \left (b x^n+2\right )}{b n} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.012, size = 18, normalized size = 1.2 \begin{align*}{\frac{\ln \left ( 2+b{{\rm e}^{n\ln \left ( x \right ) }} \right ) }{bn}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.940252, size = 20, normalized size = 1.33 \begin{align*} \frac{\log \left (b x^{n} + 2\right )}{b n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.02488, size = 30, normalized size = 2. \begin{align*} \frac{\log \left (b x^{n} + 2\right )}{b n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.29555, size = 27, normalized size = 1.8 \begin{align*} \begin{cases} \frac{\log{\left (x \right )}}{2} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left (x \right )}}{b + 2} & \text{for}\: n = 0 \\\frac{x^{n}}{2 n} & \text{for}\: b = 0 \\\frac{\log{\left (x^{n} + \frac{2}{b} \right )}}{b n} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11453, size = 22, normalized size = 1.47 \begin{align*} \frac{\log \left ({\left | b x^{n} + 2 \right |}\right )}{b n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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