Optimal. Leaf size=48 \[ \frac {7}{9 (2+3 x)^3}+\frac {11}{2 (2+3 x)^2}+\frac {55}{2+3 x}-275 \log (2+3 x)+275 \log (3+5 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 48, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78}
\begin {gather*} \frac {55}{3 x+2}+\frac {11}{2 (3 x+2)^2}+\frac {7}{9 (3 x+2)^3}-275 \log (3 x+2)+275 \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {1-2 x}{(2+3 x)^4 (3+5 x)} \, dx &=\int \left (-\frac {7}{(2+3 x)^4}-\frac {33}{(2+3 x)^3}-\frac {165}{(2+3 x)^2}-\frac {825}{2+3 x}+\frac {1375}{3+5 x}\right ) \, dx\\ &=\frac {7}{9 (2+3 x)^3}+\frac {11}{2 (2+3 x)^2}+\frac {55}{2+3 x}-275 \log (2+3 x)+275 \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 40, normalized size = 0.83 \begin {gather*} \frac {4172+12177 x+8910 x^2}{18 (2+3 x)^3}-275 \log (2+3 x)+275 \log (-3 (3+5 x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 45, normalized size = 0.94
method | result | size |
risch | \(\frac {495 x^{2}+\frac {1353}{2} x +\frac {2086}{9}}{\left (2+3 x \right )^{3}}-275 \ln \left (2+3 x \right )+275 \ln \left (3+5 x \right )\) | \(37\) |
norman | \(\frac {-\frac {733}{2} x -\frac {2139}{2} x^{2}-\frac {3129}{4} x^{3}}{\left (2+3 x \right )^{3}}-275 \ln \left (2+3 x \right )+275 \ln \left (3+5 x \right )\) | \(40\) |
default | \(\frac {7}{9 \left (2+3 x \right )^{3}}+\frac {11}{2 \left (2+3 x \right )^{2}}+\frac {55}{2+3 x}-275 \ln \left (2+3 x \right )+275 \ln \left (3+5 x \right )\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 46, normalized size = 0.96 \begin {gather*} \frac {8910 \, x^{2} + 12177 \, x + 4172}{18 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + 275 \, \log \left (5 \, x + 3\right ) - 275 \, \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 = 1.04, size = 75, normalized size = 1.56 \begin {gather*} \frac {8910 \, x^{2} + 4950 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (5 \, x + 3\right ) - 4950 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 12177 \, x + 4172}{18 \, {\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 = 0.06, size = 42, normalized size = 0.88 \begin {gather*} - \frac {- 8910 x^{2} - 12177 x - 4172}{486 x^{3} + 972 x^{2} + 648 x + 144} + 275 \log {\left (x + \frac {3}{5} \right )} - 275 \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 = 0.85, size = 38, normalized size = 0.79 \begin {gather*} \frac {8910 \, x^{2} + 12177 \, x + 4172}{18 \, {\left (3 \, x + 2\right )}^{3}} + 275 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 275 \, \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 = 0.04, size = 35, normalized size = 0.73 \begin {gather*} \frac {\frac {55\,x^2}{3}+\frac {451\,x}{18}+\frac {2086}{243}}{x^3+2\,x^2+\frac {4\,x}{3}+\frac {8}{27}}-550\,\mathrm {atanh}\left (30\,x+19\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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