Optimal. Leaf size=23 \[ \frac{3}{2 x+1}-\frac{3}{(2 x+1)^2}+\log (x+1) \]
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Rubi [A] time = 0.0263759, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {1620} \[ \frac{3}{2 x+1}-\frac{3}{(2 x+1)^2}+\log (x+1) \]
Antiderivative was successfully verified.
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Rule 1620
Rubi steps
\begin{align*} \int \frac{7+8 x^3}{(1+x) (1+2 x)^3} \, dx &=\int \left (\frac{1}{1+x}+\frac{12}{(1+2 x)^3}-\frac{6}{(1+2 x)^2}\right ) \, dx\\ &=-\frac{3}{(1+2 x)^2}+\frac{3}{1+2 x}+\log (1+x)\\ \end{align*}
Mathematica [A] time = 0.0092826, size = 24, normalized size = 1.04 \[ \frac{6 x+(2 x+1)^2 \log (x+1)}{(2 x+1)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 24, normalized size = 1. \begin{align*} -3\, \left ( 1+2\,x \right ) ^{-2}+3\, \left ( 1+2\,x \right ) ^{-1}+\ln \left ( 1+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.938688, size = 27, normalized size = 1.17 \begin{align*} \frac{6 \, x}{4 \, x^{2} + 4 \, x + 1} + \log \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.74517, size = 76, normalized size = 3.3 \begin{align*} \frac{{\left (4 \, x^{2} + 4 \, x + 1\right )} \log \left (x + 1\right ) + 6 \, x}{4 \, x^{2} + 4 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.104271, size = 17, normalized size = 0.74 \begin{align*} \frac{6 x}{4 x^{2} + 4 x + 1} + \log{\left (x + 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15593, size = 22, normalized size = 0.96 \begin{align*} \frac{6 \, x}{{\left (2 \, x + 1\right )}^{2}} + \log \left ({\left | x + 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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