Optimal. Leaf size=20 \[ \frac{x^{1-n}}{(1-n) (a+b)} \]
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Rubi [A] time = 0.0058103, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231, Rules used = {6, 12, 30} \[ \frac{x^{1-n}}{(1-n) (a+b)} \]
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{a x^n+b x^n} \, dx &=\int \frac{x^{-n}}{a+b} \, dx\\ &=\frac{\int x^{-n} \, dx}{a+b}\\ &=\frac{x^{1-n}}{(a+b) (1-n)}\\ \end{align*}
Mathematica [A] time = 0.0038062, size = 20, normalized size = 1. \[ \frac{x^{1-n}}{(1-n) (a+b)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 19, normalized size = 1. \begin{align*} -{\frac{x}{ \left ( -1+n \right ){x}^{n} \left ( a+b \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.07105, size = 28, normalized size = 1.4 \begin{align*} -\frac{x}{{\left (a{\left (n - 1\right )} + b{\left (n - 1\right )}\right )} x^{n}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.872954, size = 41, normalized size = 2.05 \begin{align*} -\frac{x}{{\left ({\left (a + b\right )} n - a - b\right )} x^{n}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.839191, size = 32, normalized size = 1.6 \begin{align*} \begin{cases} - \frac{x}{a n x^{n} - a x^{n} + b n x^{n} - b x^{n}} & \text{for}\: n \neq 1 \\\frac{\log{\left (x \right )}}{a + b} & \text{otherwise} \end{cases} \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{1}{a x^{n} + b x^{n}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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