Optimal. Leaf size=20 \[ \frac{x^{1-n}}{(1-n) (a+b)} \]
[Out]
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Rubi [A] time = 0.019008, 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 \[ \frac{x^{1-n}}{(1-n) (a+b)} \]
Antiderivative was successfully verified.
[In] Int[(a*x^n + b*x^n)^(-1),x]
[Out]
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Rubi in Sympy [A] time = 3.40945, size = 10, normalized size = 0.5 \[ \frac{x^{- n + 1}}{\left (a + b\right ) \left (- n + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a*x**n+b*x**n),x)
[Out]
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Mathematica [A] time = 0.00582209, size = 20, normalized size = 1. \[ \frac{x^{1-n}}{(1-n) (a+b)} \]
Antiderivative was successfully verified.
[In] Integrate[(a*x^n + b*x^n)^(-1),x]
[Out]
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Maple [A] time = 0.003, size = 19, normalized size = 1. \[ -{\frac{x}{ \left ( -1+n \right ){x}^{n} \left ( a+b \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a*x^n+b*x^n),x)
[Out]
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Maxima [A] time = 1.53807, size = 28, normalized size = 1.4 \[ -\frac{x x^{-n}}{a{\left (n - 1\right )} + b{\left (n - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a*x^n + b*x^n),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.238138, size = 30, normalized size = 1.5 \[ -\frac{x}{{\left ({\left (a + b\right )} n - a - b\right )} x^{n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a*x^n + b*x^n),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.93952, size = 32, normalized size = 1.6 \[ \begin{cases} - \frac{x}{a n x^{n} - a x^{n} + b n x^{n} - b x^{n}} & \text{for}\: n \neq 1 \\\frac{\log{\left (x \right )}}{a + b} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a*x**n+b*x**n),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{a x^{n} + b x^{n}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a*x^n + b*x^n),x, algorithm="giac")
[Out]