Optimal. Leaf size=38 \[ -\frac{2^{-n} (1-x)^{n+1} \, _2F_1\left (n,n+1;n+2;\frac{1-x}{2}\right )}{n+1} \]
[Out]
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Rubi [A] time = 0.0223566, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{2^{-n} (1-x)^{n+1} \, _2F_1\left (n,n+1;n+2;\frac{1-x}{2}\right )}{n+1} \]
Antiderivative was successfully verified.
[In] Int[(1 - x)^n/(1 + x)^n,x]
[Out]
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Rubi in Sympy [A] time = 3.48828, size = 26, normalized size = 0.68 \[ - \frac{2^{- n} \left (- x + 1\right )^{n + 1}{{}_{2}F_{1}\left (\begin{matrix} n, n + 1 \\ n + 2 \end{matrix}\middle |{- \frac{x}{2} + \frac{1}{2}} \right )}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-x)**n/((1+x)**n),x)
[Out]
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Mathematica [A] time = 0.028162, size = 40, normalized size = 1.05 \[ -\frac{2^n (x+1)^{1-n} \, _2F_1\left (1-n,-n;2-n;\frac{x+1}{2}\right )}{n-1} \]
Antiderivative was successfully verified.
[In] Integrate[(1 - x)^n/(1 + x)^n,x]
[Out]
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Maple [F] time = 0.088, size = 0, normalized size = 0. \[ \int{\frac{ \left ( 1-x \right ) ^{n}}{ \left ( 1+x \right ) ^{n}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-x)^n/((1+x)^n),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (x + 1\right )}^{-n}{\left (-x + 1\right )}^{n}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x + 1)^n/(x + 1)^n,x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{{\left (-x + 1\right )}^{n}}{{\left (x + 1\right )}^{n}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x + 1)^n/(x + 1)^n,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((1-x)**n/((1+x)**n),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (-x + 1\right )}^{n}}{{\left (x + 1\right )}^{n}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x + 1)^n/(x + 1)^n,x, algorithm="giac")
[Out]