Optimal. Leaf size=9 \[ \frac {e^x}{x+1} \]
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Rubi [A] time = 0.03, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2197} \[ \frac {e^x}{x+1} \]
Antiderivative was successfully verified.
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Rule 2197
Rubi steps
\begin {align*} \int \frac {e^x x}{(1+x)^2} \, dx &=\frac {e^x}{1+x}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 9, normalized size = 1.00 \[ \frac {e^x}{x+1} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 8, normalized size = 0.89 \[ \frac {e^{x}}{x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.92, size = 30, normalized size = 3.33 \[ -\frac {e^{\left (-{\left (x + 1\right )} {\left (\frac {1}{x + 1} - 1\right )}\right )}}{{\left (x + 1\right )} {\left (\frac {1}{x + 1} - 1\right )} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 9, normalized size = 1.00 \[ \frac {{\mathrm e}^{x}}{x +1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 8, normalized size = 0.89 \[ \frac {e^{x}}{x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 8, normalized size = 0.89 \[ \frac {{\mathrm {e}}^x}{x+1} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 5, normalized size = 0.56 \[ \frac {e^{x}}{x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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