Optimal. Leaf size=33 \[ -\frac {11}{250 (3+5 x)^2}-\frac {31}{125 (3+5 x)}-\frac {6}{125} \log (3+5 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 33, 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 = {78}
\begin {gather*} -\frac {31}{125 (5 x+3)}-\frac {11}{250 (5 x+3)^2}-\frac {6}{125} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {(1-2 x) (2+3 x)}{(3+5 x)^3} \, dx &=\int \left (\frac {11}{25 (3+5 x)^3}+\frac {31}{25 (3+5 x)^2}-\frac {6}{25 (3+5 x)}\right ) \, dx\\ &=-\frac {11}{250 (3+5 x)^2}-\frac {31}{125 (3+5 x)}-\frac {6}{125} \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 33, normalized size = 1.00 \begin {gather*} -\frac {11}{250 (3+5 x)^2}-\frac {31}{125 (3+5 x)}-\frac {6}{125} \log (3+5 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 28, normalized size = 0.85
method | result | size |
risch | \(\frac {-\frac {31 x}{25}-\frac {197}{250}}{\left (3+5 x \right )^{2}}-\frac {6 \ln \left (3+5 x \right )}{125}\) | \(24\) |
norman | \(\frac {\frac {104}{75} x +\frac {197}{90} x^{2}}{\left (3+5 x \right )^{2}}-\frac {6 \ln \left (3+5 x \right )}{125}\) | \(27\) |
default | \(-\frac {11}{250 \left (3+5 x \right )^{2}}-\frac {31}{125 \left (3+5 x \right )}-\frac {6 \ln \left (3+5 x \right )}{125}\) | \(28\) |
meijerg | \(\frac {x \left (\frac {5 x}{3}+2\right )}{27 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {x^{2}}{54 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {x \left (15 x +6\right )}{75 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {6 \ln \left (1+\frac {5 x}{3}\right )}{125}\) | \(52\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 28, normalized size = 0.85 \begin {gather*} -\frac {310 \, x + 197}{250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} - \frac {6}{125} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.11, size = 37, normalized size = 1.12 \begin {gather*} -\frac {12 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 310 \, x + 197}{250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 26, normalized size = 0.79 \begin {gather*} - \frac {310 x + 197}{6250 x^{2} + 7500 x + 2250} - \frac {6 \log {\left (5 x + 3 \right )}}{125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.58, size = 24, normalized size = 0.73 \begin {gather*} -\frac {310 \, x + 197}{250 \, {\left (5 \, x + 3\right )}^{2}} - \frac {6}{125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.11, size = 24, normalized size = 0.73 \begin {gather*} -\frac {6\,\ln \left (x+\frac {3}{5}\right )}{125}-\frac {\frac {31\,x}{625}+\frac {197}{6250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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