Optimal. Leaf size=33 \[ \frac{3}{5} 2^{n-1} (x+1)^{10/3} \, _2F_1\left (\frac{10}{3},-n;\frac{13}{3};\frac{x+1}{2}\right ) \]
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Rubi [A] time = 0.007115, antiderivative size = 33, 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, Rules used = {69} \[ \frac{3}{5} 2^{n-1} (x+1)^{10/3} \, _2F_1\left (\frac{10}{3},-n;\frac{13}{3};\frac{x+1}{2}\right ) \]
Antiderivative was successfully verified.
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Rule 69
Rubi steps
\begin{align*} \int (1-x)^n (1+x)^{7/3} \, dx &=\frac{3}{5} 2^{-1+n} (1+x)^{10/3} \, _2F_1\left (\frac{10}{3},-n;\frac{13}{3};\frac{1+x}{2}\right )\\ \end{align*}
Mathematica [A] time = 0.0119043, size = 33, normalized size = 1. \[ \frac{3}{5} 2^{n-1} (x+1)^{10/3} \, _2F_1\left (\frac{10}{3},-n;\frac{13}{3};\frac{x+1}{2}\right ) \]
Antiderivative was successfully verified.
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Maple [F] time = 0.029, size = 0, normalized size = 0. \begin{align*} \int \left ( 1-x \right ) ^{n} \left ( 1+x \right ) ^{{\frac{7}{3}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (x + 1\right )}^{\frac{7}{3}}{\left (-x + 1\right )}^{n}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left ({\left (x^{2} + 2 \, x + 1\right )}{\left (x + 1\right )}^{\frac{1}{3}}{\left (-x + 1\right )}^{n}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (x + 1\right )}^{\frac{7}{3}}{\left (-x + 1\right )}^{n}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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