Optimal. Leaf size=15 \[ e^x \sqrt {1-x^2} \]
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Rubi [A] time = 0.06, 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 = {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*}
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Mathematica [A] time = 0.03, size = 15, normalized size = 1.00 \[ e^x \sqrt {1-x^2} \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {e^x \left (1-x-x^2\right )}{\sqrt {1-x^2}} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 1.05, size = 12, normalized size = 0.80 \[ \sqrt {-x^{2} + 1} e^{x} \]
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 \[ \int -\frac {{\left (x^{2} + x - 1\right )} e^{x}}{\sqrt {-x^{2} + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.30, 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 = 0.65, size = 21, normalized size = 1.40 \[ -\frac {{\left (x^{2} - 1\right )} e^{x}}{\sqrt {x + 1} \sqrt {-x + 1}} \]
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 \[ {\mathrm {e}}^x\,\sqrt {1-x^2} \]
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 \[ - \int \left (- \frac {e^{x}}{\sqrt {1 - x^{2}}}\right )\, dx - \int \frac {x e^{x}}{\sqrt {1 - x^{2}}}\, dx - \int \frac {x^{2} e^{x}}{\sqrt {1 - x^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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