Optimal. Leaf size=57 \[ \frac {49}{2 (2+3 x)^2}+\frac {707}{2+3 x}-\frac {121}{2 (3+5 x)^2}+\frac {1133}{3+5 x}-6934 \log (2+3 x)+6934 \log (3+5 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 57, 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 {707}{3 x+2}+\frac {1133}{5 x+3}+\frac {49}{2 (3 x+2)^2}-\frac {121}{2 (5 x+3)^2}-6934 \log (3 x+2)+6934 \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)^3 (3+5 x)^3} \, dx &=\int \left (-\frac {147}{(2+3 x)^3}-\frac {2121}{(2+3 x)^2}-\frac {20802}{2+3 x}+\frac {605}{(3+5 x)^3}-\frac {5665}{(3+5 x)^2}+\frac {34670}{3+5 x}\right ) \, dx\\ &=\frac {49}{2 (2+3 x)^2}+\frac {707}{2+3 x}-\frac {121}{2 (3+5 x)^2}+\frac {1133}{3+5 x}-6934 \log (2+3 x)+6934 \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 59, normalized size = 1.04 \begin {gather*} \frac {49}{2 (2+3 x)^2}+\frac {707}{2+3 x}-\frac {121}{2 (3+5 x)^2}+\frac {1133}{3+5 x}-6934 \log (5 (2+3 x))+6934 \log (3+5 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 54, normalized size = 0.95
method | result | size |
risch | \(\frac {104010 x^{3}+197619 x^{2}+124966 x +\frac {52601}{2}}{\left (2+3 x \right )^{2} \left (3+5 x \right )^{2}}-6934 \ln \left (2+3 x \right )+6934 \ln \left (3+5 x \right )\) | \(49\) |
norman | \(\frac {-\frac {14228573}{72} x^{2}-\frac {3748975}{12} x^{3}-\frac {1315025}{8} x^{4}-\frac {249623}{6} x}{\left (2+3 x \right )^{2} \left (3+5 x \right )^{2}}-6934 \ln \left (2+3 x \right )+6934 \ln \left (3+5 x \right )\) | \(52\) |
default | \(\frac {49}{2 \left (2+3 x \right )^{2}}+\frac {707}{2+3 x}-\frac {121}{2 \left (3+5 x \right )^{2}}+\frac {1133}{3+5 x}-6934 \ln \left (2+3 x \right )+6934 \ln \left (3+5 x \right )\) | \(54\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 56, normalized size = 0.98 \begin {gather*} \frac {208020 \, x^{3} + 395238 \, x^{2} + 249932 \, x + 52601}{2 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} + 6934 \, \log \left (5 \, x + 3\right ) - 6934 \, \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 = 95, normalized size = 1.67 \begin {gather*} \frac {208020 \, x^{3} + 395238 \, x^{2} + 13868 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (5 \, x + 3\right ) - 13868 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (3 \, x + 2\right ) + 249932 \, x + 52601}{2 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.18, size = 51, normalized size = 0.89 \begin {gather*} \frac {208020 x^{3} + 395238 x^{2} + 249932 x + 52601}{450 x^{4} + 1140 x^{3} + 1082 x^{2} + 456 x + 72} + 6934 \log {\left (x + \frac {3}{5} \right )} - 6934 \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 = 1.20, size = 48, normalized size = 0.84 \begin {gather*} \frac {208020 \, x^{3} + 395238 \, x^{2} + 249932 \, x + 52601}{2 \, {\left (15 \, x^{2} + 19 \, x + 6\right )}^{2}} + 6934 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 6934 \, \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 = 45, normalized size = 0.79 \begin {gather*} \frac {\frac {6934\,x^3}{15}+\frac {65873\,x^2}{75}+\frac {124966\,x}{225}+\frac {52601}{450}}{x^4+\frac {38\,x^3}{15}+\frac {541\,x^2}{225}+\frac {76\,x}{75}+\frac {4}{25}}-13868\,\mathrm {atanh}\left (30\,x+19\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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