Optimal. Leaf size=33 \[ \frac{x^2 \, _2F_1\left (2,\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right )}{2 a^2} \]
[Out]
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Rubi [A] time = 0.027139, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{x^2 \, _2F_1\left (2,\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right )}{2 a^2} \]
Antiderivative was successfully verified.
[In] Int[x/(a + b*x^n)^2,x]
[Out]
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Rubi in Sympy [A] time = 3.29808, size = 22, normalized size = 0.67 \[ \frac{x^{2}{{}_{2}F_{1}\left (\begin{matrix} 2, \frac{2}{n} \\ \frac{n + 2}{n} \end{matrix}\middle |{- \frac{b x^{n}}{a}} \right )}}{2 a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(a+b*x**n)**2,x)
[Out]
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Mathematica [A] time = 0.0520846, size = 53, normalized size = 1.61 \[ \frac{x^2 \left ((n-2) \, _2F_1\left (1,\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right )+\frac{2 a}{a+b x^n}\right )}{2 a^2 n} \]
Antiderivative was successfully verified.
[In] Integrate[x/(a + b*x^n)^2,x]
[Out]
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Maple [F] time = 0.074, size = 0, normalized size = 0. \[ \int{\frac{x}{ \left ( a+b{x}^{n} \right ) ^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(a+b*x^n)^2,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[{\left (n - 2\right )} \int \frac{x}{a b n x^{n} + a^{2} n}\,{d x} + \frac{x^{2}}{a b n x^{n} + a^{2} n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x^n + a)^2,x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{x}{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x^n + a)^2,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(x/(a+b*x**n)**2,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x}{{\left (b x^{n} + a\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x^n + a)^2,x, algorithm="giac")
[Out]