Optimal. Leaf size=16 \[ \frac{3}{2} \sqrt [3]{x^2+2 x-3} \]
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Rubi [A] time = 0.0039318, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {629} \[ \frac{3}{2} \sqrt [3]{x^2+2 x-3} \]
Antiderivative was successfully verified.
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Rule 629
Rubi steps
\begin{align*} \int \frac{1+x}{\left (-3+2 x+x^2\right )^{2/3}} \, dx &=\frac{3}{2} \sqrt [3]{-3+2 x+x^2}\\ \end{align*}
Mathematica [A] time = 0.0038345, size = 16, normalized size = 1. \[ \frac{3}{2} \sqrt [3]{x^2+2 x-3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.04, size = 19, normalized size = 1.2 \begin{align*}{\frac{ \left ( 9+3\,x \right ) \left ( -1+x \right ) }{2} \left ({x}^{2}+2\,x-3 \right ) ^{-{\frac{2}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.17557, size = 16, normalized size = 1. \begin{align*} \frac{3}{2} \,{\left (x^{2} + 2 \, x - 3\right )}^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.02086, size = 36, normalized size = 2.25 \begin{align*} \frac{3}{2} \,{\left (x^{2} + 2 \, x - 3\right )}^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.15836, size = 14, normalized size = 0.88 \begin{align*} \frac{3 \sqrt [3]{x^{2} + 2 x - 3}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.21356, size = 16, normalized size = 1. \begin{align*} \frac{3}{2} \,{\left (x^{2} + 2 \, x - 3\right )}^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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