Optimal. Leaf size=48 \[ -\frac {3 (37+47 x)}{5 \left (2+5 x+3 x^2\right )}+23 \log (1+x)+\frac {52}{25} \log (3+2 x)-\frac {627}{25} \log (2+3 x) \]
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Rubi [A]
time = 0.03, antiderivative size = 48, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {836, 814}
\begin {gather*} -\frac {3 (47 x+37)}{5 \left (3 x^2+5 x+2\right )}+23 \log (x+1)+\frac {52}{25} \log (2 x+3)-\frac {627}{25} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 814
Rule 836
Rubi steps
\begin {align*} \int \frac {5-x}{(3+2 x) \left (2+5 x+3 x^2\right )^2} \, dx &=-\frac {3 (37+47 x)}{5 \left (2+5 x+3 x^2\right )}-\frac {1}{5} \int \frac {397+282 x}{(3+2 x) \left (2+5 x+3 x^2\right )} \, dx\\ &=-\frac {3 (37+47 x)}{5 \left (2+5 x+3 x^2\right )}-\frac {1}{5} \int \left (-\frac {115}{1+x}-\frac {104}{5 (3+2 x)}+\frac {1881}{5 (2+3 x)}\right ) \, dx\\ &=-\frac {3 (37+47 x)}{5 \left (2+5 x+3 x^2\right )}+23 \log (1+x)+\frac {52}{25} \log (3+2 x)-\frac {627}{25} \log (2+3 x)\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 48, normalized size = 1.00 \begin {gather*} \frac {1}{25} \left (-\frac {15 (37+47 x)}{2+5 x+3 x^2}-627 \log (-4-6 x)+575 \log (-2 (1+x))+52 \log (3+2 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 40, normalized size = 0.83
method | result | size |
default | \(-\frac {6}{1+x}+23 \ln \left (1+x \right )+\frac {52 \ln \left (3+2 x \right )}{25}-\frac {51}{5 \left (2+3 x \right )}-\frac {627 \ln \left (2+3 x \right )}{25}\) | \(40\) |
risch | \(\frac {-\frac {47 x}{5}-\frac {37}{5}}{x^{2}+\frac {5}{3} x +\frac {2}{3}}+\frac {52 \ln \left (3+2 x \right )}{25}+23 \ln \left (1+x \right )-\frac {627 \ln \left (2+3 x \right )}{25}\) | \(40\) |
norman | \(\frac {\frac {333}{10} x^{2}+\frac {273}{10} x}{3 x^{2}+5 x +2}+\frac {52 \ln \left (3+2 x \right )}{25}+23 \ln \left (1+x \right )-\frac {627 \ln \left (2+3 x \right )}{25}\) | \(46\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 42, normalized size = 0.88 \begin {gather*} -\frac {3 \, {\left (47 \, x + 37\right )}}{5 \, {\left (3 \, x^{2} + 5 \, x + 2\right )}} - \frac {627}{25} \, \log \left (3 \, x + 2\right ) + \frac {52}{25} \, \log \left (2 \, x + 3\right ) + 23 \, \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 4.24, size = 71, normalized size = 1.48 \begin {gather*} -\frac {627 \, {\left (3 \, x^{2} + 5 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 52 \, {\left (3 \, x^{2} + 5 \, x + 2\right )} \log \left (2 \, x + 3\right ) - 575 \, {\left (3 \, x^{2} + 5 \, x + 2\right )} \log \left (x + 1\right ) + 705 \, x + 555}{25 \, {\left (3 \, x^{2} + 5 \, x + 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 41, normalized size = 0.85 \begin {gather*} - \frac {141 x + 111}{15 x^{2} + 25 x + 10} - \frac {627 \log {\left (x + \frac {2}{3} \right )}}{25} + 23 \log {\left (x + 1 \right )} + \frac {52 \log {\left (x + \frac {3}{2} \right )}}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.12, size = 45, normalized size = 0.94 \begin {gather*} -\frac {3 \, {\left (47 \, x + 37\right )}}{5 \, {\left (3 \, x + 2\right )} {\left (x + 1\right )}} - \frac {627}{25} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac {52}{25} \, \log \left ({\left | 2 \, x + 3 \right |}\right ) + 23 \, \log \left ({\left | x + 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 36, normalized size = 0.75 \begin {gather*} 23\,\ln \left (x+1\right )-\frac {627\,\ln \left (x+\frac {2}{3}\right )}{25}+\frac {52\,\ln \left (x+\frac {3}{2}\right )}{25}-\frac {\frac {47\,x}{5}+\frac {37}{5}}{x^2+\frac {5\,x}{3}+\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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