Integrand size = 20, antiderivative size = 56 \[ \int (1-2 x) (2+3 x)^6 (3+5 x)^3 \, dx=-\frac {1}{243} (2+3 x)^7+\frac {107 (2+3 x)^8}{1944}-\frac {185}{729} (2+3 x)^9+\frac {205}{486} (2+3 x)^{10}-\frac {250 (2+3 x)^{11}}{2673} \]
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Time = 0.02 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \[ \int (1-2 x) (2+3 x)^6 (3+5 x)^3 \, dx=-\frac {250 (3 x+2)^{11}}{2673}+\frac {205}{486} (3 x+2)^{10}-\frac {185}{729} (3 x+2)^9+\frac {107 (3 x+2)^8}{1944}-\frac {1}{243} (3 x+2)^7 \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {7}{81} (2+3 x)^6+\frac {107}{81} (2+3 x)^7-\frac {185}{27} (2+3 x)^8+\frac {1025}{81} (2+3 x)^9-\frac {250}{81} (2+3 x)^{10}\right ) \, dx \\ & = -\frac {1}{243} (2+3 x)^7+\frac {107 (2+3 x)^8}{1944}-\frac {185}{729} (2+3 x)^9+\frac {205}{486} (2+3 x)^{10}-\frac {250 (2+3 x)^{11}}{2673} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.07 \[ \int (1-2 x) (2+3 x)^6 (3+5 x)^3 \, dx=1728 x+10368 x^2+34032 x^3+61220 x^4+36148 x^5-94668 x^6-272403 x^7-\frac {2731671 x^8}{8}-243945 x^9-\frac {193185 x^{10}}{2}-\frac {182250 x^{11}}{11} \]
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Time = 2.17 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.96
method | result | size |
gosper | \(-\frac {x \left (1458000 x^{10}+8500140 x^{9}+21467160 x^{8}+30048381 x^{7}+23971464 x^{6}+8330784 x^{5}-3181024 x^{4}-5387360 x^{3}-2994816 x^{2}-912384 x -152064\right )}{88}\) | \(54\) |
default | \(-\frac {182250}{11} x^{11}-\frac {193185}{2} x^{10}-243945 x^{9}-\frac {2731671}{8} x^{8}-272403 x^{7}-94668 x^{6}+36148 x^{5}+61220 x^{4}+34032 x^{3}+10368 x^{2}+1728 x\) | \(55\) |
norman | \(-\frac {182250}{11} x^{11}-\frac {193185}{2} x^{10}-243945 x^{9}-\frac {2731671}{8} x^{8}-272403 x^{7}-94668 x^{6}+36148 x^{5}+61220 x^{4}+34032 x^{3}+10368 x^{2}+1728 x\) | \(55\) |
risch | \(-\frac {182250}{11} x^{11}-\frac {193185}{2} x^{10}-243945 x^{9}-\frac {2731671}{8} x^{8}-272403 x^{7}-94668 x^{6}+36148 x^{5}+61220 x^{4}+34032 x^{3}+10368 x^{2}+1728 x\) | \(55\) |
parallelrisch | \(-\frac {182250}{11} x^{11}-\frac {193185}{2} x^{10}-243945 x^{9}-\frac {2731671}{8} x^{8}-272403 x^{7}-94668 x^{6}+36148 x^{5}+61220 x^{4}+34032 x^{3}+10368 x^{2}+1728 x\) | \(55\) |
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Time = 0.21 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.96 \[ \int (1-2 x) (2+3 x)^6 (3+5 x)^3 \, dx=-\frac {182250}{11} \, x^{11} - \frac {193185}{2} \, x^{10} - 243945 \, x^{9} - \frac {2731671}{8} \, x^{8} - 272403 \, x^{7} - 94668 \, x^{6} + 36148 \, x^{5} + 61220 \, x^{4} + 34032 \, x^{3} + 10368 \, x^{2} + 1728 \, x \]
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Time = 0.03 (sec) , antiderivative size = 58, normalized size of antiderivative = 1.04 \[ \int (1-2 x) (2+3 x)^6 (3+5 x)^3 \, dx=- \frac {182250 x^{11}}{11} - \frac {193185 x^{10}}{2} - 243945 x^{9} - \frac {2731671 x^{8}}{8} - 272403 x^{7} - 94668 x^{6} + 36148 x^{5} + 61220 x^{4} + 34032 x^{3} + 10368 x^{2} + 1728 x \]
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Time = 0.20 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.96 \[ \int (1-2 x) (2+3 x)^6 (3+5 x)^3 \, dx=-\frac {182250}{11} \, x^{11} - \frac {193185}{2} \, x^{10} - 243945 \, x^{9} - \frac {2731671}{8} \, x^{8} - 272403 \, x^{7} - 94668 \, x^{6} + 36148 \, x^{5} + 61220 \, x^{4} + 34032 \, x^{3} + 10368 \, x^{2} + 1728 \, x \]
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Time = 0.28 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.96 \[ \int (1-2 x) (2+3 x)^6 (3+5 x)^3 \, dx=-\frac {182250}{11} \, x^{11} - \frac {193185}{2} \, x^{10} - 243945 \, x^{9} - \frac {2731671}{8} \, x^{8} - 272403 \, x^{7} - 94668 \, x^{6} + 36148 \, x^{5} + 61220 \, x^{4} + 34032 \, x^{3} + 10368 \, x^{2} + 1728 \, x \]
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Time = 0.07 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.96 \[ \int (1-2 x) (2+3 x)^6 (3+5 x)^3 \, dx=-\frac {182250\,x^{11}}{11}-\frac {193185\,x^{10}}{2}-243945\,x^9-\frac {2731671\,x^8}{8}-272403\,x^7-94668\,x^6+36148\,x^5+61220\,x^4+34032\,x^3+10368\,x^2+1728\,x \]
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