Optimal. Leaf size=68 \[ -\frac {49}{12 (2+3 x)^4}-\frac {154}{3 (2+3 x)^3}-\frac {1133}{2 (2+3 x)^2}-\frac {7480}{2+3 x}-\frac {3025}{3+5 x}+46475 \log (2+3 x)-46475 \log (3+5 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 68, 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 {7480}{3 x+2}-\frac {3025}{5 x+3}-\frac {1133}{2 (3 x+2)^2}-\frac {154}{3 (3 x+2)^3}-\frac {49}{12 (3 x+2)^4}+46475 \log (3 x+2)-46475 \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)^5 (3+5 x)^2} \, dx &=\int \left (\frac {49}{(2+3 x)^5}+\frac {462}{(2+3 x)^4}+\frac {3399}{(2+3 x)^3}+\frac {22440}{(2+3 x)^2}+\frac {139425}{2+3 x}+\frac {15125}{(3+5 x)^2}-\frac {232375}{3+5 x}\right ) \, dx\\ &=-\frac {49}{12 (2+3 x)^4}-\frac {154}{3 (2+3 x)^3}-\frac {1133}{2 (2+3 x)^2}-\frac {7480}{2+3 x}-\frac {3025}{3+5 x}+46475 \log (2+3 x)-46475 \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.07, size = 57, normalized size = 0.84 \begin {gather*} -\frac {940153+5720639 x+13046462 x^2+13217490 x^3+5019300 x^4}{4 (2+3 x)^4 (3+5 x)}+46475 \log (5 (2+3 x))-46475 \log (3+5 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 63, normalized size = 0.93
method | result | size |
risch | \(\frac {-1254825 x^{4}-\frac {6608745}{2} x^{3}-\frac {6523231}{2} x^{2}-\frac {5720639}{4} x -\frac {940153}{4}}{\left (2+3 x \right )^{4} \left (3+5 x \right )}+46475 \ln \left (2+3 x \right )-46475 \ln \left (3+5 x \right )\) | \(54\) |
norman | \(\frac {\frac {10314009}{2} x^{3}+\frac {2230801}{6} x +\frac {18094267}{8} x^{2}+\frac {126920655}{64} x^{5}+\frac {334298673}{64} x^{4}}{\left (2+3 x \right )^{4} \left (3+5 x \right )}+46475 \ln \left (2+3 x \right )-46475 \ln \left (3+5 x \right )\) | \(57\) |
default | \(-\frac {49}{12 \left (2+3 x \right )^{4}}-\frac {154}{3 \left (2+3 x \right )^{3}}-\frac {1133}{2 \left (2+3 x \right )^{2}}-\frac {7480}{2+3 x}-\frac {3025}{3+5 x}+46475 \ln \left (2+3 x \right )-46475 \ln \left (3+5 x \right )\) | \(63\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 66, normalized size = 0.97 \begin {gather*} -\frac {5019300 \, x^{4} + 13217490 \, x^{3} + 13046462 \, x^{2} + 5720639 \, x + 940153}{4 \, {\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )}} - 46475 \, \log \left (5 \, x + 3\right ) + 46475 \, \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 = 0.38, size = 115, normalized size = 1.69 \begin {gather*} -\frac {5019300 \, x^{4} + 13217490 \, x^{3} + 13046462 \, x^{2} + 185900 \, {\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )} \log \left (5 \, x + 3\right ) - 185900 \, {\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )} \log \left (3 \, x + 2\right ) + 5720639 \, x + 940153}{4 \, {\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 63, normalized size = 0.93 \begin {gather*} \frac {- 5019300 x^{4} - 13217490 x^{3} - 13046462 x^{2} - 5720639 x - 940153}{1620 x^{5} + 5292 x^{4} + 6912 x^{3} + 4512 x^{2} + 1472 x + 192} - 46475 \log {\left (x + \frac {3}{5} \right )} + 46475 \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 = 1.10, size = 67, normalized size = 0.99 \begin {gather*} -\frac {3025}{5 \, x + 3} + \frac {25 \, {\left (\frac {884412}{5 \, x + 3} + \frac {341028}{{\left (5 \, x + 3\right )}^{2}} + \frac {45688}{{\left (5 \, x + 3\right )}^{3}} + 784485\right )}}{4 \, {\left (\frac {1}{5 \, x + 3} + 3\right )}^{4}} + 46475 \, \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 = 0.05, size = 56, normalized size = 0.82 \begin {gather*} 92950\,\mathrm {atanh}\left (30\,x+19\right )-\frac {\frac {9295\,x^4}{3}+\frac {146861\,x^3}{18}+\frac {6523231\,x^2}{810}+\frac {5720639\,x}{1620}+\frac {940153}{1620}}{x^5+\frac {49\,x^4}{15}+\frac {64\,x^3}{15}+\frac {376\,x^2}{135}+\frac {368\,x}{405}+\frac {16}{135}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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