Integrand size = 22, antiderivative size = 56 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^2 \, dx=\frac {49 (2+3 x)^5}{1215}-\frac {259}{729} (2+3 x)^6+\frac {503}{567} (2+3 x)^7-\frac {185}{486} (2+3 x)^8+\frac {100 (2+3 x)^9}{2187} \]
[Out]
Time = 0.02 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^2 \, dx=\frac {100 (3 x+2)^9}{2187}-\frac {185}{486} (3 x+2)^8+\frac {503}{567} (3 x+2)^7-\frac {259}{729} (3 x+2)^6+\frac {49 (3 x+2)^5}{1215} \]
[In]
[Out]
Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {49}{81} (2+3 x)^4-\frac {518}{81} (2+3 x)^5+\frac {503}{27} (2+3 x)^6-\frac {740}{81} (2+3 x)^7+\frac {100}{81} (2+3 x)^8\right ) \, dx \\ & = \frac {49 (2+3 x)^5}{1215}-\frac {259}{729} (2+3 x)^6+\frac {503}{567} (2+3 x)^7-\frac {185}{486} (2+3 x)^8+\frac {100 (2+3 x)^9}{2187} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.93 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^2 \, dx=144 x+384 x^2+\frac {424 x^3}{3}-1174 x^4-\frac {9791 x^5}{5}+115 x^6+\frac {21141 x^7}{7}+\frac {5805 x^8}{2}+900 x^9 \]
[In]
[Out]
Time = 0.74 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.79
method | result | size |
gosper | \(\frac {x \left (189000 x^{8}+609525 x^{7}+634230 x^{6}+24150 x^{5}-411222 x^{4}-246540 x^{3}+29680 x^{2}+80640 x +30240\right )}{210}\) | \(44\) |
default | \(900 x^{9}+\frac {5805}{2} x^{8}+\frac {21141}{7} x^{7}+115 x^{6}-\frac {9791}{5} x^{5}-1174 x^{4}+\frac {424}{3} x^{3}+384 x^{2}+144 x\) | \(45\) |
norman | \(900 x^{9}+\frac {5805}{2} x^{8}+\frac {21141}{7} x^{7}+115 x^{6}-\frac {9791}{5} x^{5}-1174 x^{4}+\frac {424}{3} x^{3}+384 x^{2}+144 x\) | \(45\) |
risch | \(900 x^{9}+\frac {5805}{2} x^{8}+\frac {21141}{7} x^{7}+115 x^{6}-\frac {9791}{5} x^{5}-1174 x^{4}+\frac {424}{3} x^{3}+384 x^{2}+144 x\) | \(45\) |
parallelrisch | \(900 x^{9}+\frac {5805}{2} x^{8}+\frac {21141}{7} x^{7}+115 x^{6}-\frac {9791}{5} x^{5}-1174 x^{4}+\frac {424}{3} x^{3}+384 x^{2}+144 x\) | \(45\) |
[In]
[Out]
none
Time = 0.22 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.79 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^2 \, dx=900 \, x^{9} + \frac {5805}{2} \, x^{8} + \frac {21141}{7} \, x^{7} + 115 \, x^{6} - \frac {9791}{5} \, x^{5} - 1174 \, x^{4} + \frac {424}{3} \, x^{3} + 384 \, x^{2} + 144 \, x \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^2 \, dx=900 x^{9} + \frac {5805 x^{8}}{2} + \frac {21141 x^{7}}{7} + 115 x^{6} - \frac {9791 x^{5}}{5} - 1174 x^{4} + \frac {424 x^{3}}{3} + 384 x^{2} + 144 x \]
[In]
[Out]
none
Time = 0.20 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.79 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^2 \, dx=900 \, x^{9} + \frac {5805}{2} \, x^{8} + \frac {21141}{7} \, x^{7} + 115 \, x^{6} - \frac {9791}{5} \, x^{5} - 1174 \, x^{4} + \frac {424}{3} \, x^{3} + 384 \, x^{2} + 144 \, x \]
[In]
[Out]
none
Time = 0.31 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.79 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^2 \, dx=900 \, x^{9} + \frac {5805}{2} \, x^{8} + \frac {21141}{7} \, x^{7} + 115 \, x^{6} - \frac {9791}{5} \, x^{5} - 1174 \, x^{4} + \frac {424}{3} \, x^{3} + 384 \, x^{2} + 144 \, x \]
[In]
[Out]
Time = 0.04 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.79 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^2 \, dx=900\,x^9+\frac {5805\,x^8}{2}+\frac {21141\,x^7}{7}+115\,x^6-\frac {9791\,x^5}{5}-1174\,x^4+\frac {424\,x^3}{3}+384\,x^2+144\,x \]
[In]
[Out]