Optimal. Leaf size=28 \[ -\frac{x^{n-1} (a+b x)^{1-n}}{a (1-n)} \]
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Rubi [A] time = 0.0027961, antiderivative size = 28, 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 = {37} \[ -\frac{x^{n-1} (a+b x)^{1-n}}{a (1-n)} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin{align*} \int x^{-2+n} (a+b x)^{-n} \, dx &=-\frac{x^{-1+n} (a+b x)^{1-n}}{a (1-n)}\\ \end{align*}
Mathematica [A] time = 0.0063209, size = 25, normalized size = 0.89 \[ \frac{x^{n-1} (a+b x)^{1-n}}{a (n-1)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 29, normalized size = 1. \begin{align*}{\frac{{x}^{-1+n} \left ( bx+a \right ) }{a \left ( -1+n \right ) \left ( bx+a \right ) ^{n}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{n - 2}}{{\left (b x + a\right )}^{n}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.6588, size = 66, normalized size = 2.36 \begin{align*} \frac{{\left (b x^{2} + a x\right )} x^{n - 2}}{{\left (a n - a\right )}{\left (b x + a\right )}^{n}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{n - 2}}{{\left (b x + a\right )}^{n}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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