Integrand size = 22, antiderivative size = 79 \[ \int \frac {(2+3 x)^7 (3+5 x)^3}{1-2 x} \, dx=-\frac {1092596789 x}{1024}-\frac {1065169973 x^2}{1024}-\frac {969544757 x^3}{768}-\frac {772025397 x^4}{512}-\frac {504354357 x^5}{320}-\frac {85228263 x^6}{64}-\frac {95297877 x^7}{112}-\frac {24381405 x^8}{64}-\frac {423225 x^9}{4}-\frac {54675 x^{10}}{4}-\frac {1096135733 \log (1-2 x)}{2048} \]
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Time = 0.03 (sec) , antiderivative size = 79, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int \frac {(2+3 x)^7 (3+5 x)^3}{1-2 x} \, dx=-\frac {54675 x^{10}}{4}-\frac {423225 x^9}{4}-\frac {24381405 x^8}{64}-\frac {95297877 x^7}{112}-\frac {85228263 x^6}{64}-\frac {504354357 x^5}{320}-\frac {772025397 x^4}{512}-\frac {969544757 x^3}{768}-\frac {1065169973 x^2}{1024}-\frac {1092596789 x}{1024}-\frac {1096135733 \log (1-2 x)}{2048} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {1092596789}{1024}-\frac {1065169973 x}{512}-\frac {969544757 x^2}{256}-\frac {772025397 x^3}{128}-\frac {504354357 x^4}{64}-\frac {255684789 x^5}{32}-\frac {95297877 x^6}{16}-\frac {24381405 x^7}{8}-\frac {3809025 x^8}{4}-\frac {273375 x^9}{2}-\frac {1096135733}{1024 (-1+2 x)}\right ) \, dx \\ & = -\frac {1092596789 x}{1024}-\frac {1065169973 x^2}{1024}-\frac {969544757 x^3}{768}-\frac {772025397 x^4}{512}-\frac {504354357 x^5}{320}-\frac {85228263 x^6}{64}-\frac {95297877 x^7}{112}-\frac {24381405 x^8}{64}-\frac {423225 x^9}{4}-\frac {54675 x^{10}}{4}-\frac {1096135733 \log (1-2 x)}{2048} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 82, normalized size of antiderivative = 1.04 \[ \int \frac {(2+3 x)^7 (3+5 x)^3}{1-2 x} \, dx=\frac {1933652224451}{1720320}-\frac {1092596789 x}{1024}-\frac {1065169973 x^2}{1024}-\frac {969544757 x^3}{768}-\frac {772025397 x^4}{512}-\frac {504354357 x^5}{320}-\frac {85228263 x^6}{64}-\frac {95297877 x^7}{112}-\frac {24381405 x^8}{64}-\frac {423225 x^9}{4}-\frac {54675 x^{10}}{4}-\frac {1096135733 \log (1-2 x)}{2048} \]
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Time = 2.53 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.71
method | result | size |
parallelrisch | \(-\frac {54675 x^{10}}{4}-\frac {423225 x^{9}}{4}-\frac {24381405 x^{8}}{64}-\frac {95297877 x^{7}}{112}-\frac {85228263 x^{6}}{64}-\frac {504354357 x^{5}}{320}-\frac {772025397 x^{4}}{512}-\frac {969544757 x^{3}}{768}-\frac {1065169973 x^{2}}{1024}-\frac {1092596789 x}{1024}-\frac {1096135733 \ln \left (x -\frac {1}{2}\right )}{2048}\) | \(56\) |
default | \(-\frac {54675 x^{10}}{4}-\frac {423225 x^{9}}{4}-\frac {24381405 x^{8}}{64}-\frac {95297877 x^{7}}{112}-\frac {85228263 x^{6}}{64}-\frac {504354357 x^{5}}{320}-\frac {772025397 x^{4}}{512}-\frac {969544757 x^{3}}{768}-\frac {1065169973 x^{2}}{1024}-\frac {1092596789 x}{1024}-\frac {1096135733 \ln \left (-1+2 x \right )}{2048}\) | \(58\) |
norman | \(-\frac {54675 x^{10}}{4}-\frac {423225 x^{9}}{4}-\frac {24381405 x^{8}}{64}-\frac {95297877 x^{7}}{112}-\frac {85228263 x^{6}}{64}-\frac {504354357 x^{5}}{320}-\frac {772025397 x^{4}}{512}-\frac {969544757 x^{3}}{768}-\frac {1065169973 x^{2}}{1024}-\frac {1092596789 x}{1024}-\frac {1096135733 \ln \left (-1+2 x \right )}{2048}\) | \(58\) |
risch | \(-\frac {54675 x^{10}}{4}-\frac {423225 x^{9}}{4}-\frac {24381405 x^{8}}{64}-\frac {95297877 x^{7}}{112}-\frac {85228263 x^{6}}{64}-\frac {504354357 x^{5}}{320}-\frac {772025397 x^{4}}{512}-\frac {969544757 x^{3}}{768}-\frac {1065169973 x^{2}}{1024}-\frac {1092596789 x}{1024}-\frac {1096135733 \ln \left (-1+2 x \right )}{2048}\) | \(58\) |
meijerg | \(-\frac {1096135733 \ln \left (1-2 x \right )}{2048}-\frac {34853 x \left (120 x^{3}+80 x^{2}+60 x +60\right )}{8}-26784 x -\frac {114291 x \left (40320 x^{7}+23040 x^{6}+13440 x^{5}+8064 x^{4}+5040 x^{3}+3360 x^{2}+2520 x +2520\right )}{14336}-\frac {39285 x \left (71680 x^{8}+40320 x^{7}+23040 x^{6}+13440 x^{5}+8064 x^{4}+5040 x^{3}+3360 x^{2}+2520 x +2520\right )}{28672}-\frac {6075 x \left (1419264 x^{9}+788480 x^{8}+443520 x^{7}+253440 x^{6}+147840 x^{5}+88704 x^{4}+55440 x^{3}+36960 x^{2}+27720 x +27720\right )}{630784}-\frac {647577 x \left (192 x^{4}+120 x^{3}+80 x^{2}+60 x +60\right )}{160}-\frac {238671 x \left (2240 x^{5}+1344 x^{4}+840 x^{3}+560 x^{2}+420 x +420\right )}{640}-\frac {2954853 x \left (7680 x^{6}+4480 x^{5}+2688 x^{4}+1680 x^{3}+1120 x^{2}+840 x +840\right )}{35840}-15564 x \left (6 x +6\right )-\frac {96445 x \left (16 x^{2}+12 x +12\right )}{6}\) | \(265\) |
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Time = 0.22 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^7 (3+5 x)^3}{1-2 x} \, dx=-\frac {54675}{4} \, x^{10} - \frac {423225}{4} \, x^{9} - \frac {24381405}{64} \, x^{8} - \frac {95297877}{112} \, x^{7} - \frac {85228263}{64} \, x^{6} - \frac {504354357}{320} \, x^{5} - \frac {772025397}{512} \, x^{4} - \frac {969544757}{768} \, x^{3} - \frac {1065169973}{1024} \, x^{2} - \frac {1092596789}{1024} \, x - \frac {1096135733}{2048} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.06 (sec) , antiderivative size = 76, normalized size of antiderivative = 0.96 \[ \int \frac {(2+3 x)^7 (3+5 x)^3}{1-2 x} \, dx=- \frac {54675 x^{10}}{4} - \frac {423225 x^{9}}{4} - \frac {24381405 x^{8}}{64} - \frac {95297877 x^{7}}{112} - \frac {85228263 x^{6}}{64} - \frac {504354357 x^{5}}{320} - \frac {772025397 x^{4}}{512} - \frac {969544757 x^{3}}{768} - \frac {1065169973 x^{2}}{1024} - \frac {1092596789 x}{1024} - \frac {1096135733 \log {\left (2 x - 1 \right )}}{2048} \]
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Time = 0.20 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^7 (3+5 x)^3}{1-2 x} \, dx=-\frac {54675}{4} \, x^{10} - \frac {423225}{4} \, x^{9} - \frac {24381405}{64} \, x^{8} - \frac {95297877}{112} \, x^{7} - \frac {85228263}{64} \, x^{6} - \frac {504354357}{320} \, x^{5} - \frac {772025397}{512} \, x^{4} - \frac {969544757}{768} \, x^{3} - \frac {1065169973}{1024} \, x^{2} - \frac {1092596789}{1024} \, x - \frac {1096135733}{2048} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.26 (sec) , antiderivative size = 58, normalized size of antiderivative = 0.73 \[ \int \frac {(2+3 x)^7 (3+5 x)^3}{1-2 x} \, dx=-\frac {54675}{4} \, x^{10} - \frac {423225}{4} \, x^{9} - \frac {24381405}{64} \, x^{8} - \frac {95297877}{112} \, x^{7} - \frac {85228263}{64} \, x^{6} - \frac {504354357}{320} \, x^{5} - \frac {772025397}{512} \, x^{4} - \frac {969544757}{768} \, x^{3} - \frac {1065169973}{1024} \, x^{2} - \frac {1092596789}{1024} \, x - \frac {1096135733}{2048} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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Time = 0.06 (sec) , antiderivative size = 55, normalized size of antiderivative = 0.70 \[ \int \frac {(2+3 x)^7 (3+5 x)^3}{1-2 x} \, dx=-\frac {1092596789\,x}{1024}-\frac {1096135733\,\ln \left (x-\frac {1}{2}\right )}{2048}-\frac {1065169973\,x^2}{1024}-\frac {969544757\,x^3}{768}-\frac {772025397\,x^4}{512}-\frac {504354357\,x^5}{320}-\frac {85228263\,x^6}{64}-\frac {95297877\,x^7}{112}-\frac {24381405\,x^8}{64}-\frac {423225\,x^9}{4}-\frac {54675\,x^{10}}{4} \]
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