Optimal. Leaf size=23 \[ \frac {3}{x+1}-\frac {5}{3 (x+1)^3}+2 \log (x+1) \]
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Rubi [A] time = 0.02, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {1850} \[ \frac {3}{x+1}-\frac {5}{3 (x+1)^3}+2 \log (x+1) \]
Antiderivative was successfully verified.
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Rule 1850
Rubi steps
\begin {align*} \int \frac {4+3 x^2+2 x^3}{(1+x)^4} \, dx &=\int \left (\frac {5}{(1+x)^4}-\frac {3}{(1+x)^2}+\frac {2}{1+x}\right ) \, dx\\ &=-\frac {5}{3 (1+x)^3}+\frac {3}{1+x}+2 \log (1+x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 1.00 \[ \frac {3}{x+1}-\frac {5}{3 (x+1)^3}+2 \log (x+1) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.56, size = 46, normalized size = 2.00 \[ \frac {9 \, x^{2} + 6 \, {\left (x^{3} + 3 \, x^{2} + 3 \, x + 1\right )} \log \left (x + 1\right ) + 18 \, x + 4}{3 \, {\left (x^{3} + 3 \, x^{2} + 3 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.37, size = 25, normalized size = 1.09 \[ \frac {9 \, x^{2} + 18 \, x + 4}{3 \, {\left (x + 1\right )}^{3}} + 2 \, \log \left ({\left | x + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 22, normalized size = 0.96 \[ 2 \ln \left (x +1\right )-\frac {5}{3 \left (x +1\right )^{3}}+\frac {3}{x +1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.74, size = 34, normalized size = 1.48 \[ \frac {9 \, x^{2} + 18 \, x + 4}{3 \, {\left (x^{3} + 3 \, x^{2} + 3 \, x + 1\right )}} + 2 \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 23, normalized size = 1.00 \[ 2\,\ln \left (x+1\right )+\frac {3\,x^2+6\,x+\frac {4}{3}}{{\left (x+1\right )}^3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 31, normalized size = 1.35 \[ \frac {9 x^{2} + 18 x + 4}{3 x^{3} + 9 x^{2} + 9 x + 3} + 2 \log {\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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