Optimal. Leaf size=15 \[ e^x \sqrt{1-x^2} \]
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Rubi [A] time = 0.0569821, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.04, Rules used = {2288} \[ e^x \sqrt{1-x^2} \]
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin{align*} \int \frac{e^x \left (1-x-x^2\right )}{\sqrt{1-x^2}} \, dx &=e^x \sqrt{1-x^2}\\ \end{align*}
Mathematica [A] time = 0.0257325, size = 15, normalized size = 1. \[ e^x \sqrt{1-x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 20, normalized size = 1.3 \begin{align*} -{{{\rm e}^{x}} \left ( 1+x \right ) \left ( -1+x \right ){\frac{1}{\sqrt{-{x}^{2}+1}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.09179, size = 28, normalized size = 1.87 \begin{align*} -\frac{{\left (x^{2} - 1\right )} e^{x}}{\sqrt{x + 1} \sqrt{-x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.07677, size = 27, normalized size = 1.8 \begin{align*} \sqrt{-x^{2} + 1} e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} - \int - \frac{e^{x}}{\sqrt{1 - x^{2}}}\, dx - \int \frac{x e^{x}}{\sqrt{1 - x^{2}}}\, dx - \int \frac{x^{2} e^{x}}{\sqrt{1 - x^{2}}}\, dx \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 -\frac{{\left (x^{2} + x - 1\right )} e^{x}}{\sqrt{-x^{2} + 1}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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