Optimal. Leaf size=66 \[ \frac {7}{(2+3 x)^3}+\frac {309}{2 (2+3 x)^2}+\frac {3060}{2+3 x}-\frac {275}{2 (3+5 x)^2}+\frac {3350}{3+5 x}-25350 \log (2+3 x)+25350 \log (3+5 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 66, 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 {3060}{3 x+2}+\frac {3350}{5 x+3}+\frac {309}{2 (3 x+2)^2}-\frac {275}{2 (5 x+3)^2}+\frac {7}{(3 x+2)^3}-25350 \log (3 x+2)+25350 \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)^3} \, dx &=\int \left (-\frac {63}{(2+3 x)^4}-\frac {927}{(2+3 x)^3}-\frac {9180}{(2+3 x)^2}-\frac {76050}{2+3 x}+\frac {1375}{(3+5 x)^3}-\frac {16750}{(3+5 x)^2}+\frac {126750}{3+5 x}\right ) \, dx\\ &=\frac {7}{(2+3 x)^3}+\frac {309}{2 (2+3 x)^2}+\frac {3060}{2+3 x}-\frac {275}{2 (3+5 x)^2}+\frac {3350}{3+5 x}-25350 \log (2+3 x)+25350 \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 68, normalized size = 1.03 \begin {gather*} \frac {7}{(2+3 x)^3}+\frac {309}{2 (2+3 x)^2}+\frac {3060}{2+3 x}-\frac {275}{2 (3+5 x)^2}+\frac {3350}{3+5 x}-25350 \log (2+3 x)+25350 \log (-3 (3+5 x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 63, normalized size = 0.95
method | result | size |
risch | \(\frac {1140750 x^{4}+2927925 x^{3}+2815540 x^{2}+\frac {2404363}{2} x +192304}{\left (2+3 x \right )^{3} \left (3+5 x \right )^{2}}-25350 \ln \left (2+3 x \right )+25350 \ln \left (3+5 x \right )\) | \(54\) |
norman | \(\frac {-4628370 x^{4}-4451741 x^{3}-1802850 x^{5}-\frac {17111248}{9} x^{2}-\frac {1825199}{6} x}{\left (2+3 x \right )^{3} \left (3+5 x \right )^{2}}-25350 \ln \left (2+3 x \right )+25350 \ln \left (3+5 x \right )\) | \(57\) |
default | \(\frac {7}{\left (2+3 x \right )^{3}}+\frac {309}{2 \left (2+3 x \right )^{2}}+\frac {3060}{2+3 x}-\frac {275}{2 \left (3+5 x \right )^{2}}+\frac {3350}{3+5 x}-25350 \ln \left (2+3 x \right )+25350 \ln \left (3+5 x \right )\) | \(63\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 66, normalized size = 1.00 \begin {gather*} \frac {2281500 \, x^{4} + 5855850 \, x^{3} + 5631080 \, x^{2} + 2404363 \, x + 384608}{2 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} + 25350 \, \log \left (5 \, x + 3\right ) - 25350 \, \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 = 0.73, size = 115, normalized size = 1.74 \begin {gather*} \frac {2281500 \, x^{4} + 5855850 \, x^{3} + 5631080 \, x^{2} + 50700 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (5 \, x + 3\right ) - 50700 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (3 \, x + 2\right ) + 2404363 \, x + 384608}{2 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 63, normalized size = 0.95 \begin {gather*} - \frac {- 2281500 x^{4} - 5855850 x^{3} - 5631080 x^{2} - 2404363 x - 384608}{1350 x^{5} + 4320 x^{4} + 5526 x^{3} + 3532 x^{2} + 1128 x + 144} + 25350 \log {\left (x + \frac {3}{5} \right )} - 25350 \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 = 0.60, size = 55, normalized size = 0.83 \begin {gather*} \frac {2281500 \, x^{4} + 5855850 \, x^{3} + 5631080 \, x^{2} + 2404363 \, x + 384608}{2 \, {\left (5 \, x + 3\right )}^{2} {\left (3 \, x + 2\right )}^{3}} + 25350 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 25350 \, \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 = 55, normalized size = 0.83 \begin {gather*} \frac {1690\,x^4+\frac {13013\,x^3}{3}+\frac {563108\,x^2}{135}+\frac {2404363\,x}{1350}+\frac {192304}{675}}{x^5+\frac {16\,x^4}{5}+\frac {307\,x^3}{75}+\frac {1766\,x^2}{675}+\frac {188\,x}{225}+\frac {8}{75}}-50700\,\mathrm {atanh}\left (30\,x+19\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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