Optimal. Leaf size=12 \[ \log (x+1)-\frac{2}{3 x^3} \]
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Rubi [A] time = 0.0320389, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {1593, 1620} \[ \log (x+1)-\frac{2}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 1593
Rule 1620
Rubi steps
\begin{align*} \int \frac{2+2 x+x^4}{x^4+x^5} \, dx &=\int \frac{2+2 x+x^4}{x^4 (1+x)} \, dx\\ &=\int \left (\frac{2}{x^4}+\frac{1}{1+x}\right ) \, dx\\ &=-\frac{2}{3 x^3}+\log (1+x)\\ \end{align*}
Mathematica [A] time = 0.0039845, size = 12, normalized size = 1. \[ \log (x+1)-\frac{2}{3 x^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 11, normalized size = 0.9 \begin{align*} -{\frac{2}{3\,{x}^{3}}}+\ln \left ( 1+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.989715, size = 14, normalized size = 1.17 \begin{align*} -\frac{2}{3 \, x^{3}} + \log \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.51519, size = 43, normalized size = 3.58 \begin{align*} \frac{3 \, x^{3} \log \left (x + 1\right ) - 2}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.090996, size = 10, normalized size = 0.83 \begin{align*} \log{\left (x + 1 \right )} - \frac{2}{3 x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13153, size = 15, normalized size = 1.25 \begin{align*} -\frac{2}{3 \, x^{3}} + \log \left ({\left | x + 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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