Optimal. Leaf size=15 \[ e^x \sqrt {1-x^2} \]
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Rubi [A]
time = 0.04, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {2326}
\begin {gather*} e^x \sqrt {1-x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
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*}
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Mathematica [A]
time = 0.18, size = 15, normalized size = 1.00 \begin {gather*} e^x \sqrt {1-x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 20, normalized size = 1.33
method | result | size |
gosper | \(-\frac {{\mathrm e}^{x} \left (1+x \right ) \left (-1+x \right )}{\sqrt {-x^{2}+1}}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.63, size = 21, normalized size = 1.40 \begin {gather*} -\frac {{\left (x^{2} - 1\right )} e^{x}}{\sqrt {x + 1} \sqrt {-x + 1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.50, size = 12, normalized size = 0.80 \begin {gather*} \sqrt {-x^{2} + 1} e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} - \int \left (- \frac {e^{x}}{\sqrt {1 - x^{2}}}\right )\, dx - \int \frac {x e^{x}}{\sqrt {1 - x^{2}}}\, dx - \int \frac {x^{2} e^{x}}{\sqrt {1 - x^{2}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.45, size = 12, normalized size = 0.80 \begin {gather*} {\mathrm {e}}^x\,\sqrt {1-x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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