Optimal. Leaf size=39 \[ -\frac {49}{3 (2+3 x)}-\frac {121}{5 (3+5 x)}+154 \log (2+3 x)-154 \log (3+5 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 39, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90}
\begin {gather*} -\frac {49}{3 (3 x+2)}-\frac {121}{5 (5 x+3)}+154 \log (3 x+2)-154 \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2}{(2+3 x)^2 (3+5 x)^2} \, dx &=\int \left (\frac {49}{(2+3 x)^2}+\frac {462}{2+3 x}+\frac {121}{(3+5 x)^2}-\frac {770}{3+5 x}\right ) \, dx\\ &=-\frac {49}{3 (2+3 x)}-\frac {121}{5 (3+5 x)}+154 \log (2+3 x)-154 \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 61, normalized size = 1.56 \begin {gather*} -\frac {1461+2314 x-2310 \left (6+19 x+15 x^2\right ) \log (5 (2+3 x))+2310 \left (6+19 x+15 x^2\right ) \log (3+5 x)}{15 (2+3 x) (3+5 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 36, normalized size = 0.92
method | result | size |
default | \(-\frac {49}{3 \left (2+3 x \right )}-\frac {121}{5 \left (3+5 x \right )}+154 \ln \left (2+3 x \right )-154 \ln \left (3+5 x \right )\) | \(36\) |
risch | \(\frac {-\frac {2314 x}{15}-\frac {487}{5}}{\left (2+3 x \right ) \left (3+5 x \right )}+154 \ln \left (2+3 x \right )-154 \ln \left (3+5 x \right )\) | \(39\) |
norman | \(\frac {\frac {487}{2} x^{2}+\frac {925}{6} x}{\left (2+3 x \right ) \left (3+5 x \right )}+154 \ln \left (2+3 x \right )-154 \ln \left (3+5 x \right )\) | \(42\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 36, normalized size = 0.92 \begin {gather*} -\frac {2314 \, x + 1461}{15 \, {\left (15 \, x^{2} + 19 \, x + 6\right )}} - 154 \, \log \left (5 \, x + 3\right ) + 154 \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.46, size = 55, normalized size = 1.41 \begin {gather*} -\frac {2310 \, {\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (5 \, x + 3\right ) - 2310 \, {\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (3 \, x + 2\right ) + 2314 \, x + 1461}{15 \, {\left (15 \, x^{2} + 19 \, x + 6\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 32, normalized size = 0.82 \begin {gather*} \frac {- 2314 x - 1461}{225 x^{2} + 285 x + 90} - 154 \log {\left (x + \frac {3}{5} \right )} + 154 \log {\left (x + \frac {2}{3} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.97, size = 38, normalized size = 0.97 \begin {gather*} -\frac {121}{5 \, {\left (5 \, x + 3\right )}} + \frac {245}{\frac {1}{5 \, x + 3} + 3} + 154 \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 26, normalized size = 0.67 \begin {gather*} 308\,\mathrm {atanh}\left (30\,x+19\right )-\frac {\frac {2314\,x}{225}+\frac {487}{75}}{x^2+\frac {19\,x}{15}+\frac {2}{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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