Optimal. Leaf size=14 \[ \frac {1}{x (-3-\log (1+x))} \]
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Rubi [A] time = 0.17, antiderivative size = 13, normalized size of antiderivative = 0.93, number of steps used = 2, number of rules used = 2, integrand size = 57, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.035, Rules used = {6688, 6687} \begin {gather*} -\frac {1}{x (\log (x+1)+3)} \end {gather*}
Antiderivative was successfully verified.
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Rule 6687
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3+4 x+(1+x) \log (1+x)}{x^2 (1+x) (3+\log (1+x))^2} \, dx\\ &=-\frac {1}{x (3+\log (1+x))}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 13, normalized size = 0.93 \begin {gather*} -\frac {1}{x (3+\log (1+x))} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 14, normalized size = 1.00 \begin {gather*} -\frac {1}{x \log \left (x + 1\right ) + 3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 14, normalized size = 1.00 \begin {gather*} -\frac {1}{x \log \left (x + 1\right ) + 3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 14, normalized size = 1.00
method | result | size |
norman | \(-\frac {1}{x \left (3+\ln \left (x +1\right )\right )}\) | \(14\) |
risch | \(-\frac {1}{x \left (3+\ln \left (x +1\right )\right )}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 14, normalized size = 1.00 \begin {gather*} -\frac {1}{x \log \left (x + 1\right ) + 3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.88, size = 77, normalized size = 5.50 \begin {gather*} \frac {\frac {2\,x\,\ln \left (x+1\right )}{3}+\frac {4\,x^2\,\ln \left (x+1\right )}{3}+\frac {2\,x^3\,\ln \left (x+1\right )}{3}+3\,x^2+2\,x^3-1}{3\,x+x\,\ln \left (x+1\right )+2\,x^2\,\ln \left (x+1\right )+x^3\,\ln \left (x+1\right )+6\,x^2+3\,x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 12, normalized size = 0.86 \begin {gather*} - \frac {1}{x \log {\left (x + 1 \right )} + 3 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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