Optimal. Leaf size=46 \[ \frac {49}{2+3 x}-\frac {121}{10 (3+5 x)^2}+\frac {154}{3+5 x}-707 \log (2+3 x)+707 \log (3+5 x) \]
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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 = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90}
\begin {gather*} \frac {49}{3 x+2}+\frac {154}{5 x+3}-\frac {121}{10 (5 x+3)^2}-707 \log (3 x+2)+707 \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)^2}{(2+3 x)^2 (3+5 x)^3} \, dx &=\int \left (-\frac {147}{(2+3 x)^2}-\frac {2121}{2+3 x}+\frac {121}{(3+5 x)^3}-\frac {770}{(3+5 x)^2}+\frac {3535}{3+5 x}\right ) \, dx\\ &=\frac {49}{2+3 x}-\frac {121}{10 (3+5 x)^2}+\frac {154}{3+5 x}-707 \log (2+3 x)+707 \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 48, normalized size = 1.04 \begin {gather*} \frac {49}{2+3 x}-\frac {121}{10 (3+5 x)^2}+\frac {154}{3+5 x}-707 \log (5 (2+3 x))+707 \log (3+5 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 45, normalized size = 0.98
method | result | size |
risch | \(\frac {3535 x^{2}+\frac {43597}{10} x +\frac {6704}{5}}{\left (2+3 x \right ) \left (3+5 x \right )^{2}}-707 \ln \left (2+3 x \right )+707 \ln \left (3+5 x \right )\) | \(44\) |
default | \(\frac {49}{2+3 x}-\frac {121}{10 \left (3+5 x \right )^{2}}+\frac {154}{3+5 x}-707 \ln \left (2+3 x \right )+707 \ln \left (3+5 x \right )\) | \(45\) |
norman | \(\frac {-\frac {62041}{9} x^{2}-\frac {16760}{3} x^{3}-\frac {12725}{6} x}{\left (2+3 x \right ) \left (3+5 x \right )^{2}}-707 \ln \left (2+3 x \right )+707 \ln \left (3+5 x \right )\) | \(47\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 46, normalized size = 1.00 \begin {gather*} \frac {35350 \, x^{2} + 43597 \, x + 13408}{10 \, {\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} + 707 \, \log \left (5 \, x + 3\right ) - 707 \, \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 = 0.47, size = 75, normalized size = 1.63 \begin {gather*} \frac {35350 \, x^{2} + 7070 \, {\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (5 \, x + 3\right ) - 7070 \, {\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (3 \, x + 2\right ) + 43597 \, x + 13408}{10 \, {\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 = 0.16, size = 41, normalized size = 0.89 \begin {gather*} \frac {35350 x^{2} + 43597 x + 13408}{750 x^{3} + 1400 x^{2} + 870 x + 180} + 707 \log {\left (x + \frac {3}{5} \right )} - 707 \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 = 1.05, size = 49, normalized size = 1.07 \begin {gather*} \frac {49}{3 \, x + 2} - \frac {33 \, {\left (\frac {206}{3 \, x + 2} - 865\right )}}{2 \, {\left (\frac {1}{3 \, x + 2} - 5\right )}^{2}} + 707 \, \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 = 1.09, size = 35, normalized size = 0.76 \begin {gather*} \frac {\frac {707\,x^2}{15}+\frac {43597\,x}{750}+\frac {6704}{375}}{x^3+\frac {28\,x^2}{15}+\frac {29\,x}{25}+\frac {6}{25}}-1414\,\mathrm {atanh}\left (30\,x+19\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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