Optimal. Leaf size=24 \[ \frac{x \, _2F_1\left (1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right )}{a} \]
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Rubi [A] time = 0.0195887, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{x \, _2F_1\left (1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right )}{a} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^n)^(-1),x]
[Out]
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Rubi in Sympy [A] time = 1.77875, size = 17, normalized size = 0.71 \[ \frac{x{{}_{2}F_{1}\left (\begin{matrix} 1, \frac{1}{n} \\ 1 + \frac{1}{n} \end{matrix}\middle |{- \frac{b x^{n}}{a}} \right )}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b*x**n),x)
[Out]
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Mathematica [A] time = 0.00778167, size = 24, normalized size = 1. \[ \frac{x \, _2F_1\left (1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right )}{a} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^n)^(-1),x]
[Out]
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Maple [F] time = 0.046, size = 0, normalized size = 0. \[ \int \left ( a+b{x}^{n} \right ) ^{-1}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b*x^n),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{b x^{n} + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x^n + a),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{b x^{n} + a}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x^n + a),x, algorithm="fricas")
[Out]
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b*x**n),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{b x^{n} + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x^n + a),x, algorithm="giac")
[Out]