Optimal. Leaf size=17 \[ \frac {x^2}{2}-x+2 \log (x+1) \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {697} \[ \frac {x^2}{2}-x+2 \log (x+1) \]
Antiderivative was successfully verified.
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Rule 697
Rubi steps
\begin {align*} \int \frac {1+x^2}{1+x} \, dx &=\int \left (-1+x+\frac {2}{1+x}\right ) \, dx\\ &=-x+\frac {x^2}{2}+2 \log (1+x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.06 \[ \frac {1}{2} \left (x^2-2 x+4 \log (x+1)-3\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 15, normalized size = 0.88 \[ \frac {1}{2} \, x^{2} - x + 2 \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 16, normalized size = 0.94 \[ \frac {1}{2} \, x^{2} - x + 2 \, \log \left ({\left | x + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 0.94 \[ \frac {x^{2}}{2}-x +2 \ln \left (x +1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.74, size = 15, normalized size = 0.88 \[ \frac {1}{2} \, x^{2} - x + 2 \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 15, normalized size = 0.88 \[ 2\,\ln \left (x+1\right )-x+\frac {x^2}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 12, normalized size = 0.71 \[ \frac {x^{2}}{2} - x + 2 \log {\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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