Optimal. Leaf size=46 \[ \frac {21}{2+3 x}-\frac {11}{2 (3+5 x)^2}+\frac {68}{3+5 x}-309 \log (2+3 x)+309 \log (3+5 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 46, 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 {21}{3 x+2}+\frac {68}{5 x+3}-\frac {11}{2 (5 x+3)^2}-309 \log (3 x+2)+309 \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)^2 (3+5 x)^3} \, dx &=\int \left (-\frac {63}{(2+3 x)^2}-\frac {927}{2+3 x}+\frac {55}{(3+5 x)^3}-\frac {340}{(3+5 x)^2}+\frac {1545}{3+5 x}\right ) \, dx\\ &=\frac {21}{2+3 x}-\frac {11}{2 (3+5 x)^2}+\frac {68}{3+5 x}-309 \log (2+3 x)+309 \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 48, normalized size = 1.04 \begin {gather*} \frac {21}{2+3 x}-\frac {11}{2 (3+5 x)^2}+\frac {68}{3+5 x}-309 \log (2+3 x)+309 \log (-3 (3+5 x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 45, normalized size = 0.98
method | result | size |
risch | \(\frac {1545 x^{2}+\frac {3811}{2} x +586}{\left (2+3 x \right ) \left (3+5 x \right )^{2}}-309 \ln \left (2+3 x \right )+309 \ln \left (3+5 x \right )\) | \(44\) |
default | \(\frac {21}{2+3 x}-\frac {11}{2 \left (3+5 x \right )^{2}}+\frac {68}{3+5 x}-309 \ln \left (2+3 x \right )+309 \ln \left (3+5 x \right )\) | \(45\) |
norman | \(\frac {-\frac {7325}{3} x^{3}-\frac {5561}{6} x -\frac {27115}{9} x^{2}}{\left (2+3 x \right ) \left (3+5 x \right )^{2}}-309 \ln \left (2+3 x \right )+309 \ln \left (3+5 x \right )\) | \(47\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 46, normalized size = 1.00 \begin {gather*} \frac {3090 \, x^{2} + 3811 \, x + 1172}{2 \, {\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} + 309 \, \log \left (5 \, x + 3\right ) - 309 \, \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 = 0.67, size = 75, normalized size = 1.63 \begin {gather*} \frac {3090 \, x^{2} + 618 \, {\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (5 \, x + 3\right ) - 618 \, {\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (3 \, x + 2\right ) + 3811 \, x + 1172}{2 \, {\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.15, size = 42, normalized size = 0.91 \begin {gather*} - \frac {- 3090 x^{2} - 3811 x - 1172}{150 x^{3} + 280 x^{2} + 174 x + 36} + 309 \log {\left (x + \frac {3}{5} \right )} - 309 \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 = 0.57, size = 49, normalized size = 1.07 \begin {gather*} \frac {21}{3 \, x + 2} - \frac {15 \, {\left (\frac {202}{3 \, x + 2} - 845\right )}}{2 \, {\left (\frac {1}{3 \, x + 2} - 5\right )}^{2}} + 309 \, \log \left ({\left | -\frac {1}{3 \, x + 2} + 5 \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 = 0.76 \begin {gather*} \frac {\frac {103\,x^2}{5}+\frac {3811\,x}{150}+\frac {586}{75}}{x^3+\frac {28\,x^2}{15}+\frac {29\,x}{25}+\frac {6}{25}}-618\,\mathrm {atanh}\left (30\,x+19\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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