Integrand size = 14, antiderivative size = 32 \[ \int x^4 \left (3-4 x+x^2\right )^2 \, dx=\frac {9 x^5}{5}-4 x^6+\frac {22 x^7}{7}-x^8+\frac {x^9}{9} \]
[Out]
Time = 0.01 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {712} \[ \int x^4 \left (3-4 x+x^2\right )^2 \, dx=\frac {x^9}{9}-x^8+\frac {22 x^7}{7}-4 x^6+\frac {9 x^5}{5} \]
[In]
[Out]
Rule 712
Rubi steps \begin{align*} \text {integral}& = \int \left (9 x^4-24 x^5+22 x^6-8 x^7+x^8\right ) \, dx \\ & = \frac {9 x^5}{5}-4 x^6+\frac {22 x^7}{7}-x^8+\frac {x^9}{9} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00 \[ \int x^4 \left (3-4 x+x^2\right )^2 \, dx=\frac {9 x^5}{5}-4 x^6+\frac {22 x^7}{7}-x^8+\frac {x^9}{9} \]
[In]
[Out]
Time = 9.66 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.81
method | result | size |
gosper | \(\frac {x^{5} \left (35 x^{4}-315 x^{3}+990 x^{2}-1260 x +567\right )}{315}\) | \(26\) |
default | \(\frac {9}{5} x^{5}-4 x^{6}+\frac {22}{7} x^{7}-x^{8}+\frac {1}{9} x^{9}\) | \(27\) |
norman | \(\frac {9}{5} x^{5}-4 x^{6}+\frac {22}{7} x^{7}-x^{8}+\frac {1}{9} x^{9}\) | \(27\) |
risch | \(\frac {9}{5} x^{5}-4 x^{6}+\frac {22}{7} x^{7}-x^{8}+\frac {1}{9} x^{9}\) | \(27\) |
parallelrisch | \(\frac {9}{5} x^{5}-4 x^{6}+\frac {22}{7} x^{7}-x^{8}+\frac {1}{9} x^{9}\) | \(27\) |
[In]
[Out]
none
Time = 0.34 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.81 \[ \int x^4 \left (3-4 x+x^2\right )^2 \, dx=\frac {1}{9} \, x^{9} - x^{8} + \frac {22}{7} \, x^{7} - 4 \, x^{6} + \frac {9}{5} \, x^{5} \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.81 \[ \int x^4 \left (3-4 x+x^2\right )^2 \, dx=\frac {x^{9}}{9} - x^{8} + \frac {22 x^{7}}{7} - 4 x^{6} + \frac {9 x^{5}}{5} \]
[In]
[Out]
none
Time = 0.20 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.81 \[ \int x^4 \left (3-4 x+x^2\right )^2 \, dx=\frac {1}{9} \, x^{9} - x^{8} + \frac {22}{7} \, x^{7} - 4 \, x^{6} + \frac {9}{5} \, x^{5} \]
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.81 \[ \int x^4 \left (3-4 x+x^2\right )^2 \, dx=\frac {1}{9} \, x^{9} - x^{8} + \frac {22}{7} \, x^{7} - 4 \, x^{6} + \frac {9}{5} \, x^{5} \]
[In]
[Out]
Time = 0.03 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.81 \[ \int x^4 \left (3-4 x+x^2\right )^2 \, dx=\frac {x^9}{9}-x^8+\frac {22\,x^7}{7}-4\,x^6+\frac {9\,x^5}{5} \]
[In]
[Out]