Optimal. Leaf size=50 \[ \frac {343}{81 (2+3 x)^3}+\frac {1421}{54 (2+3 x)^2}+\frac {7189}{27 (2+3 x)}-1331 \log (2+3 x)+1331 \log (3+5 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 50, 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 {7189}{27 (3 x+2)}+\frac {1421}{54 (3 x+2)^2}+\frac {343}{81 (3 x+2)^3}-1331 \log (3 x+2)+1331 \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)^3}{(2+3 x)^4 (3+5 x)} \, dx &=\int \left (-\frac {343}{9 (2+3 x)^4}-\frac {1421}{9 (2+3 x)^3}-\frac {7189}{9 (2+3 x)^2}-\frac {3993}{2+3 x}+\frac {6655}{3+5 x}\right ) \, dx\\ &=\frac {343}{81 (2+3 x)^3}+\frac {1421}{54 (2+3 x)^2}+\frac {7189}{27 (2+3 x)}-1331 \log (2+3 x)+1331 \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 40, normalized size = 0.80 \begin {gather*} \frac {7 \left (25964+75771 x+55458 x^2\right )}{162 (2+3 x)^3}-1331 \log (5 (2+3 x))+1331 \log (3+5 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 45, normalized size = 0.90
method | result | size |
risch | \(\frac {\frac {7189}{3} x^{2}+\frac {58933}{18} x +\frac {90874}{81}}{\left (2+3 x \right )^{3}}-1331 \ln \left (2+3 x \right )+1331 \ln \left (3+5 x \right )\) | \(37\) |
norman | \(\frac {-\frac {10353}{2} x^{2}-\frac {3549}{2} x -\frac {45437}{12} x^{3}}{\left (2+3 x \right )^{3}}-1331 \ln \left (2+3 x \right )+1331 \ln \left (3+5 x \right )\) | \(40\) |
default | \(\frac {343}{81 \left (2+3 x \right )^{3}}+\frac {1421}{54 \left (2+3 x \right )^{2}}+\frac {7189}{27 \left (2+3 x \right )}-1331 \ln \left (2+3 x \right )+1331 \ln \left (3+5 x \right )\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 46, normalized size = 0.92 \begin {gather*} \frac {7 \, {\left (55458 \, x^{2} + 75771 \, x + 25964\right )}}{162 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + 1331 \, \log \left (5 \, x + 3\right ) - 1331 \, \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 = 0.43, size = 75, normalized size = 1.50 \begin {gather*} \frac {388206 \, x^{2} + 215622 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (5 \, x + 3\right ) - 215622 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 530397 \, x + 181748}{162 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.16, size = 42, normalized size = 0.84 \begin {gather*} - \frac {- 388206 x^{2} - 530397 x - 181748}{4374 x^{3} + 8748 x^{2} + 5832 x + 1296} + 1331 \log {\left (x + \frac {3}{5} \right )} - 1331 \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 = 0.77, size = 38, normalized size = 0.76 \begin {gather*} \frac {7 \, {\left (55458 \, x^{2} + 75771 \, x + 25964\right )}}{162 \, {\left (3 \, x + 2\right )}^{3}} + 1331 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 1331 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.12, size = 35, normalized size = 0.70 \begin {gather*} \frac {\frac {7189\,x^2}{81}+\frac {58933\,x}{486}+\frac {90874}{2187}}{x^3+2\,x^2+\frac {4\,x}{3}+\frac {8}{27}}-2662\,\mathrm {atanh}\left (30\,x+19\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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