Optimal. Leaf size=17 \[ -\frac{1}{b n \left (a+b x^n\right )} \]
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Rubi [A] time = 0.0045928, antiderivative size = 17, 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 = {261} \[ -\frac{1}{b n \left (a+b x^n\right )} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x^{-1+n}}{\left (a+b x^n\right )^2} \, dx &=-\frac{1}{b n \left (a+b x^n\right )}\\ \end{align*}
Mathematica [A] time = 0.0052548, size = 17, normalized size = 1. \[ -\frac{1}{b n \left (a+b x^n\right )} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.016, size = 24, normalized size = 1.4 \begin{align*}{\frac{{{\rm e}^{n\ln \left ( x \right ) }}}{an \left ( a+b{{\rm e}^{n\ln \left ( x \right ) }} \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.985065, size = 23, normalized size = 1.35 \begin{align*} -\frac{1}{{\left (b x^{n} + a\right )} b n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.967611, size = 32, normalized size = 1.88 \begin{align*} -\frac{1}{b^{2} n x^{n} + a b n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 9.18444, size = 51, normalized size = 3. \begin{align*} \begin{cases} \tilde{\infty } \log{\left (x \right )} & \text{for}\: a = 0 \wedge b = 0 \wedge n = 0 \\- \frac{x^{- n}}{b^{2} n} & \text{for}\: a = 0 \\\frac{\tilde{\infty } x^{n}}{n} & \text{for}\: b = - a x^{- n} \\\frac{\log{\left (x \right )}}{\left (a + b\right )^{2}} & \text{for}\: n = 0 \\\frac{x^{n}}{a^{2} n + a b n x^{n}} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12172, size = 23, normalized size = 1.35 \begin{align*} -\frac{1}{{\left (b x^{n} + a\right )} b n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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