Optimal. Leaf size=75 \[ -\frac {34371}{343 (3 x+2)}-\frac {625}{11 (5 x+3)}-\frac {324}{49 (3 x+2)^2}-\frac {3}{7 (3 x+2)^3}-\frac {32 \log (1-2 x)}{290521}+\frac {1612242 \log (3 x+2)}{2401}-\frac {81250}{121} \log (5 x+3) \]
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Rubi [A] time = 0.03, 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 = {88} \[ -\frac {34371}{343 (3 x+2)}-\frac {625}{11 (5 x+3)}-\frac {324}{49 (3 x+2)^2}-\frac {3}{7 (3 x+2)^3}-\frac {32 \log (1-2 x)}{290521}+\frac {1612242 \log (3 x+2)}{2401}-\frac {81250}{121} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x) (2+3 x)^4 (3+5 x)^2} \, dx &=\int \left (-\frac {64}{290521 (-1+2 x)}+\frac {27}{7 (2+3 x)^4}+\frac {1944}{49 (2+3 x)^3}+\frac {103113}{343 (2+3 x)^2}+\frac {4836726}{2401 (2+3 x)}+\frac {3125}{11 (3+5 x)^2}-\frac {406250}{121 (3+5 x)}\right ) \, dx\\ &=-\frac {3}{7 (2+3 x)^3}-\frac {324}{49 (2+3 x)^2}-\frac {34371}{343 (2+3 x)}-\frac {625}{11 (3+5 x)}-\frac {32 \log (1-2 x)}{290521}+\frac {1612242 \log (2+3 x)}{2401}-\frac {81250}{121} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.12, size = 62, normalized size = 0.83 \[ \frac {2 \left (-\frac {77 \left (22801770 x^3+44843517 x^2+29372133 x+6406511\right )}{2 (3 x+2)^3 (5 x+3)}-16 \log (1-2 x)+97540641 \log (6 x+4)-97540625 \log (10 x+6)\right )}{290521} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.96, size = 123, normalized size = 1.64 \[ -\frac {1755736290 \, x^{3} + 3452950809 \, x^{2} + 195081250 \, {\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (5 \, x + 3\right ) - 195081282 \, {\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (3 \, x + 2\right ) + 32 \, {\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (2 \, x - 1\right ) + 2261654241 \, x + 493301347}{290521 \, {\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.98, size = 73, normalized size = 0.97 \[ -\frac {625}{11 \, {\left (5 \, x + 3\right )}} + \frac {135 \, {\left (\frac {37929}{5 \, x + 3} + \frac {7564}{{\left (5 \, x + 3\right )}^{2}} + 49386\right )}}{343 \, {\left (\frac {1}{5 \, x + 3} + 3\right )}^{3}} + \frac {1612242}{2401} \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) - \frac {32}{290521} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 62, normalized size = 0.83 \[ -\frac {32 \ln \left (2 x -1\right )}{290521}+\frac {1612242 \ln \left (3 x +2\right )}{2401}-\frac {81250 \ln \left (5 x +3\right )}{121}-\frac {625}{11 \left (5 x +3\right )}-\frac {3}{7 \left (3 x +2\right )^{3}}-\frac {324}{49 \left (3 x +2\right )^{2}}-\frac {34371}{343 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 64, normalized size = 0.85 \[ -\frac {22801770 \, x^{3} + 44843517 \, x^{2} + 29372133 \, x + 6406511}{3773 \, {\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )}} - \frac {81250}{121} \, \log \left (5 \, x + 3\right ) + \frac {1612242}{2401} \, \log \left (3 \, x + 2\right ) - \frac {32}{290521} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.17, size = 56, normalized size = 0.75 \[ \frac {1612242\,\ln \left (x+\frac {2}{3}\right )}{2401}-\frac {32\,\ln \left (x-\frac {1}{2}\right )}{290521}-\frac {81250\,\ln \left (x+\frac {3}{5}\right )}{121}-\frac {\frac {168902\,x^3}{3773}+\frac {1660871\,x^2}{18865}+\frac {1398673\,x}{24255}+\frac {6406511}{509355}}{x^4+\frac {13\,x^3}{5}+\frac {38\,x^2}{15}+\frac {148\,x}{135}+\frac {8}{45}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.24, size = 65, normalized size = 0.87 \[ - \frac {22801770 x^{3} + 44843517 x^{2} + 29372133 x + 6406511}{509355 x^{4} + 1324323 x^{3} + 1290366 x^{2} + 558404 x + 90552} - \frac {32 \log {\left (x - \frac {1}{2} \right )}}{290521} - \frac {81250 \log {\left (x + \frac {3}{5} \right )}}{121} + \frac {1612242 \log {\left (x + \frac {2}{3} \right )}}{2401} \]
Verification of antiderivative is not currently implemented for this CAS.
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