Optimal. Leaf size=75 \[ \frac {27}{14 (2+3 x)^2}+\frac {2889}{49 (2+3 x)}-\frac {125}{22 (3+5 x)^2}+\frac {12125}{121 (3+5 x)}-\frac {32 \log (1-2 x)}{456533}-\frac {204228}{343} \log (2+3 x)+\frac {792500 \log (3+5 x)}{1331} \]
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Rubi [A]
time = 0.02, antiderivative size = 75, 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 {2889}{49 (3 x+2)}+\frac {12125}{121 (5 x+3)}+\frac {27}{14 (3 x+2)^2}-\frac {125}{22 (5 x+3)^2}-\frac {32 \log (1-2 x)}{456533}-\frac {204228}{343} \log (3 x+2)+\frac {792500 \log (5 x+3)}{1331} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x) (2+3 x)^3 (3+5 x)^3} \, dx &=\int \left (-\frac {64}{456533 (-1+2 x)}-\frac {81}{7 (2+3 x)^3}-\frac {8667}{49 (2+3 x)^2}-\frac {612684}{343 (2+3 x)}+\frac {625}{11 (3+5 x)^3}-\frac {60625}{121 (3+5 x)^2}+\frac {3962500}{1331 (3+5 x)}\right ) \, dx\\ &=\frac {27}{14 (2+3 x)^2}+\frac {2889}{49 (2+3 x)}-\frac {125}{22 (3+5 x)^2}+\frac {12125}{121 (3+5 x)}-\frac {32 \log (1-2 x)}{456533}-\frac {204228}{343} \log (2+3 x)+\frac {792500 \log (3+5 x)}{1331}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 71, normalized size = 0.95 \begin {gather*} \frac {27}{14 (2+3 x)^2}-\frac {125}{22 (3+5 x)^2}+\frac {2889}{98+147 x}+\frac {12125}{363+605 x}-\frac {32 \log (1-2 x)}{456533}-\frac {204228}{343} \log (4+6 x)+\frac {792500 \log (6+10 x)}{1331} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 62, normalized size = 0.83
method | result | size |
risch | \(\frac {\frac {52953300}{5929} x^{3}+\frac {2053290}{121} x^{2}+\frac {63622288}{5929} x +\frac {26779805}{11858}}{\left (2+3 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {32 \ln \left (-1+2 x \right )}{456533}-\frac {204228 \ln \left (2+3 x \right )}{343}+\frac {792500 \ln \left (3+5 x \right )}{1331}\) | \(57\) |
norman | \(\frac {-\frac {127082567}{35574} x -\frac {669495125}{47432} x^{4}-\frac {38951875}{1452} x^{3}-\frac {7243867385}{426888} x^{2}}{\left (2+3 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {32 \ln \left (-1+2 x \right )}{456533}-\frac {204228 \ln \left (2+3 x \right )}{343}+\frac {792500 \ln \left (3+5 x \right )}{1331}\) | \(60\) |
default | \(-\frac {32 \ln \left (-1+2 x \right )}{456533}+\frac {27}{14 \left (2+3 x \right )^{2}}+\frac {2889}{49 \left (2+3 x \right )}-\frac {204228 \ln \left (2+3 x \right )}{343}-\frac {125}{22 \left (3+5 x \right )^{2}}+\frac {12125}{121 \left (3+5 x \right )}+\frac {792500 \ln \left (3+5 x \right )}{1331}\) | \(62\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 64, normalized size = 0.85 \begin {gather*} \frac {105906600 \, x^{3} + 201222420 \, x^{2} + 127244576 \, x + 26779805}{11858 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} + \frac {792500}{1331} \, \log \left (5 \, x + 3\right ) - \frac {204228}{343} \, \log \left (3 \, x + 2\right ) - \frac {32}{456533} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 123 vs.
\(2 (61) = 122\).
time = 0.75, size = 123, normalized size = 1.64 \begin {gather*} \frac {8154808200 \, x^{3} + 15494126340 \, x^{2} + 543655000 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (5 \, x + 3\right ) - 543654936 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (3 \, x + 2\right ) - 64 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (2 \, x - 1\right ) + 9797832352 \, x + 2062044985}{913066 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.15, size = 66, normalized size = 0.88 \begin {gather*} - \frac {- 105906600 x^{3} - 201222420 x^{2} - 127244576 x - 26779805}{2668050 x^{4} + 6759060 x^{3} + 6415178 x^{2} + 2703624 x + 426888} - \frac {32 \log {\left (x - \frac {1}{2} \right )}}{456533} + \frac {792500 \log {\left (x + \frac {3}{5} \right )}}{1331} - \frac {204228 \log {\left (x + \frac {2}{3} \right )}}{343} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.19, size = 59, normalized size = 0.79 \begin {gather*} \frac {105906600 \, x^{3} + 201222420 \, x^{2} + 127244576 \, x + 26779805}{11858 \, {\left (5 \, x + 3\right )}^{2} {\left (3 \, x + 2\right )}^{2}} + \frac {792500}{1331} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {204228}{343} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {32}{456533} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 55, normalized size = 0.73 \begin {gather*} \frac {792500\,\ln \left (x+\frac {3}{5}\right )}{1331}-\frac {204228\,\ln \left (x+\frac {2}{3}\right )}{343}-\frac {32\,\ln \left (x-\frac {1}{2}\right )}{456533}+\frac {\frac {235348\,x^3}{5929}+\frac {136886\,x^2}{1815}+\frac {63622288\,x}{1334025}+\frac {5355961}{533610}}{x^4+\frac {38\,x^3}{15}+\frac {541\,x^2}{225}+\frac {76\,x}{75}+\frac {4}{25}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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