Optimal. Leaf size=10 \[ \frac {1}{x+1}+\log (x+1) \]
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Rubi [A] time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {43} \[ \frac {1}{x+1}+\log (x+1) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {x}{(1+x)^2} \, dx &=\int \left (-\frac {1}{(1+x)^2}+\frac {1}{1+x}\right ) \, dx\\ &=\frac {1}{1+x}+\log (1+x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 1.00 \[ \frac {1}{x+1}+\log (x+1) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 16, normalized size = 1.60 \[ \frac {{\left (x + 1\right )} \log \left (x + 1\right ) + 1}{x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 11, normalized size = 1.10 \[ \frac {1}{x + 1} + \log \left ({\left | x + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 11, normalized size = 1.10 \[ \ln \left (x +1\right )+\frac {1}{x +1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 10, normalized size = 1.00 \[ \frac {1}{x + 1} + \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 10, normalized size = 1.00 \[ \ln \left (x+1\right )+\frac {1}{x+1} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 8, normalized size = 0.80 \[ \log {\left (x + 1 \right )} + \frac {1}{x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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