Optimal. Leaf size=52 \[ -\frac{(c x)^{n-2} \, _2F_1\left (1,-\frac{2-n}{n};2 \left (1-\frac{1}{n}\right );-\frac{b x^n}{a}\right )}{a c (2-n)} \]
[Out]
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Rubi [A] time = 0.0509951, antiderivative size = 52, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ -\frac{(c x)^{n-2} \, _2F_1\left (1,-\frac{2-n}{n};2 \left (1-\frac{1}{n}\right );-\frac{b x^n}{a}\right )}{a c (2-n)} \]
Antiderivative was successfully verified.
[In] Int[(c*x)^(-3 + n)/(a + b*x^n),x]
[Out]
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Rubi in Sympy [A] time = 4.98069, size = 31, normalized size = 0.6 \[ - \frac{\left (c x\right )^{n - 2}{{}_{2}F_{1}\left (\begin{matrix} 1, \frac{n - 2}{n} \\ 2 - \frac{2}{n} \end{matrix}\middle |{- \frac{b x^{n}}{a}} \right )}}{a c \left (- n + 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x)**(-3+n)/(a+b*x**n),x)
[Out]
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Mathematica [A] time = 0.0340331, size = 47, normalized size = 0.9 \[ \frac{x^{-n-2} (c x)^n \left (\, _2F_1\left (1,-\frac{2}{n};\frac{n-2}{n};-\frac{b x^n}{a}\right )-1\right )}{2 b c^3} \]
Antiderivative was successfully verified.
[In] Integrate[(c*x)^(-3 + n)/(a + b*x^n),x]
[Out]
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Maple [F] time = 0.096, size = 0, normalized size = 0. \[ \int{\frac{ \left ( cx \right ) ^{-3+n}}{a+b{x}^{n}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x)^(-3+n)/(a+b*x^n),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ -a c^{n} \int \frac{1}{b^{2} c^{3} x^{3} x^{n} + a b c^{3} x^{3}}\,{d x} - \frac{c^{n - 3}}{2 \, b x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x)^(n - 3)/(b*x^n + a),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{\left (c x\right )^{n - 3}}{b x^{n} + a}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x)^(n - 3)/(b*x^n + a),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x)**(-3+n)/(a+b*x**n),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (c x\right )^{n - 3}}{b x^{n} + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x)^(n - 3)/(b*x^n + a),x, algorithm="giac")
[Out]