Optimal. Leaf size=110 \[ \frac {7}{(2+3 x)^7}+\frac {707}{6 (2+3 x)^6}+\frac {6934}{5 (2+3 x)^5}+\frac {28555}{2 (2+3 x)^4}+\frac {424975}{3 (2+3 x)^3}+\frac {2958125}{2 (2+3 x)^2}+\frac {19637500}{2+3 x}-\frac {378125}{2 (3+5 x)^2}+\frac {9212500}{3+5 x}-125825000 \log (2+3 x)+125825000 \log (3+5 x) \]
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Rubi [A]
time = 0.04, antiderivative size = 110, 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 {19637500}{3 x+2}+\frac {9212500}{5 x+3}+\frac {2958125}{2 (3 x+2)^2}-\frac {378125}{2 (5 x+3)^2}+\frac {424975}{3 (3 x+2)^3}+\frac {28555}{2 (3 x+2)^4}+\frac {6934}{5 (3 x+2)^5}+\frac {707}{6 (3 x+2)^6}+\frac {7}{(3 x+2)^7}-125825000 \log (3 x+2)+125825000 \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)^8 (3+5 x)^3} \, dx &=\int \left (-\frac {147}{(2+3 x)^8}-\frac {2121}{(2+3 x)^7}-\frac {20802}{(2+3 x)^6}-\frac {171330}{(2+3 x)^5}-\frac {1274925}{(2+3 x)^4}-\frac {8874375}{(2+3 x)^3}-\frac {58912500}{(2+3 x)^2}-\frac {377475000}{2+3 x}+\frac {1890625}{(3+5 x)^3}-\frac {46062500}{(3+5 x)^2}+\frac {629125000}{3+5 x}\right ) \, dx\\ &=\frac {7}{(2+3 x)^7}+\frac {707}{6 (2+3 x)^6}+\frac {6934}{5 (2+3 x)^5}+\frac {28555}{2 (2+3 x)^4}+\frac {424975}{3 (2+3 x)^3}+\frac {2958125}{2 (2+3 x)^2}+\frac {19637500}{2+3 x}-\frac {378125}{2 (3+5 x)^2}+\frac {9212500}{3+5 x}-125825000 \log (2+3 x)+125825000 \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.08, size = 112, normalized size = 1.02 \begin {gather*} \frac {7}{(2+3 x)^7}+\frac {707}{6 (2+3 x)^6}+\frac {6934}{5 (2+3 x)^5}+\frac {28555}{2 (2+3 x)^4}+\frac {424975}{3 (2+3 x)^3}+\frac {2958125}{2 (2+3 x)^2}+\frac {19637500}{2+3 x}-\frac {378125}{2 (3+5 x)^2}+\frac {9212500}{3+5 x}-125825000 \log (5 (2+3 x))+125825000 \log (3+5 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 99, normalized size = 0.90
method | result | size |
risch | \(\frac {458632125000 x^{8}+2400174787500 x^{7}+5494073130000 x^{6}+7184568494250 x^{5}+5870529249480 x^{4}+3069174545346 x^{3}+\frac {5013039895644}{5} x^{2}+\frac {1871049429619}{10} x +\frac {76360244444}{5}}{\left (2+3 x \right )^{7} \left (3+5 x \right )^{2}}-125825000 \ln \left (2+3 x \right )+125825000 \ln \left (3+5 x \right )\) | \(74\) |
norman | \(\frac {-\frac {1389572341639677}{160} x^{7}-\frac {908671535442153}{80} x^{6}-\frac {371281638742833}{40} x^{5}-\frac {23194424249865}{32} x^{9}-\frac {19413250318497}{4} x^{4}-\frac {15174715949901}{4} x^{8}-\frac {9513712133317}{6} x^{3}-\frac {2663463599995}{9} x^{2}-\frac {144950399999}{6} x}{\left (2+3 x \right )^{7} \left (3+5 x \right )^{2}}-125825000 \ln \left (2+3 x \right )+125825000 \ln \left (3+5 x \right )\) | \(77\) |
default | \(\frac {7}{\left (2+3 x \right )^{7}}+\frac {707}{6 \left (2+3 x \right )^{6}}+\frac {6934}{5 \left (2+3 x \right )^{5}}+\frac {28555}{2 \left (2+3 x \right )^{4}}+\frac {424975}{3 \left (2+3 x \right )^{3}}+\frac {2958125}{2 \left (2+3 x \right )^{2}}+\frac {19637500}{2+3 x}-\frac {378125}{2 \left (3+5 x \right )^{2}}+\frac {9212500}{3+5 x}-125825000 \ln \left (2+3 x \right )+125825000 \ln \left (3+5 x \right )\) | \(99\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 106, normalized size = 0.96 \begin {gather*} \frac {4586321250000 \, x^{8} + 24001747875000 \, x^{7} + 54940731300000 \, x^{6} + 71845684942500 \, x^{5} + 58705292494800 \, x^{4} + 30691745453460 \, x^{3} + 10026079791288 \, x^{2} + 1871049429619 \, x + 152720488888}{10 \, {\left (54675 \, x^{9} + 320760 \, x^{8} + 836163 \, x^{7} + 1271214 \, x^{6} + 1242108 \, x^{5} + 808920 \, x^{4} + 351120 \, x^{3} + 97952 \, x^{2} + 15936 \, x + 1152\right )}} + 125825000 \, \log \left (5 \, x + 3\right ) - 125825000 \, \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 = 0.40, size = 195, normalized size = 1.77 \begin {gather*} \frac {4586321250000 \, x^{8} + 24001747875000 \, x^{7} + 54940731300000 \, x^{6} + 71845684942500 \, x^{5} + 58705292494800 \, x^{4} + 30691745453460 \, x^{3} + 10026079791288 \, x^{2} + 1258250000 \, {\left (54675 \, x^{9} + 320760 \, x^{8} + 836163 \, x^{7} + 1271214 \, x^{6} + 1242108 \, x^{5} + 808920 \, x^{4} + 351120 \, x^{3} + 97952 \, x^{2} + 15936 \, x + 1152\right )} \log \left (5 \, x + 3\right ) - 1258250000 \, {\left (54675 \, x^{9} + 320760 \, x^{8} + 836163 \, x^{7} + 1271214 \, x^{6} + 1242108 \, x^{5} + 808920 \, x^{4} + 351120 \, x^{3} + 97952 \, x^{2} + 15936 \, x + 1152\right )} \log \left (3 \, x + 2\right ) + 1871049429619 \, x + 152720488888}{10 \, {\left (54675 \, x^{9} + 320760 \, x^{8} + 836163 \, x^{7} + 1271214 \, x^{6} + 1242108 \, x^{5} + 808920 \, x^{4} + 351120 \, x^{3} + 97952 \, x^{2} + 15936 \, x + 1152\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 102, normalized size = 0.93 \begin {gather*} \frac {4586321250000 x^{8} + 24001747875000 x^{7} + 54940731300000 x^{6} + 71845684942500 x^{5} + 58705292494800 x^{4} + 30691745453460 x^{3} + 10026079791288 x^{2} + 1871049429619 x + 152720488888}{546750 x^{9} + 3207600 x^{8} + 8361630 x^{7} + 12712140 x^{6} + 12421080 x^{5} + 8089200 x^{4} + 3511200 x^{3} + 979520 x^{2} + 159360 x + 11520} + 125825000 \log {\left (x + \frac {3}{5} \right )} - 125825000 \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 = 1.02, size = 75, normalized size = 0.68 \begin {gather*} \frac {4586321250000 \, x^{8} + 24001747875000 \, x^{7} + 54940731300000 \, x^{6} + 71845684942500 \, x^{5} + 58705292494800 \, x^{4} + 30691745453460 \, x^{3} + 10026079791288 \, x^{2} + 1871049429619 \, x + 152720488888}{10 \, {\left (5 \, x + 3\right )}^{2} {\left (3 \, x + 2\right )}^{7}} + 125825000 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 125825000 \, \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 = 0.05, size = 95, normalized size = 0.86 \begin {gather*} \frac {\frac {25165000\,x^8}{3}+\frac {395090500\,x^7}{9}+\frac {8139367600\,x^6}{81}+\frac {31931415530\,x^5}{243}+\frac {43485401848\,x^4}{405}+\frac {1023058181782\,x^3}{18225}+\frac {1671013298548\,x^2}{91125}+\frac {1871049429619\,x}{546750}+\frac {76360244444}{273375}}{x^9+\frac {88\,x^8}{15}+\frac {1147\,x^7}{75}+\frac {15694\,x^6}{675}+\frac {46004\,x^5}{2025}+\frac {5992\,x^4}{405}+\frac {23408\,x^3}{3645}+\frac {97952\,x^2}{54675}+\frac {5312\,x}{18225}+\frac {128}{6075}}-251650000\,\mathrm {atanh}\left (30\,x+19\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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