Integrand size = 17, antiderivative size = 54 \[ \int \left (8+8 x-x^3+8 x^4\right )^2 \, dx=64 x+64 x^2+\frac {64 x^3}{3}-4 x^4+\frac {112 x^5}{5}+\frac {64 x^6}{3}+\frac {x^7}{7}-2 x^8+\frac {64 x^9}{9} \]
[Out]
Time = 0.01 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {2086} \[ \int \left (8+8 x-x^3+8 x^4\right )^2 \, dx=\frac {64 x^9}{9}-2 x^8+\frac {x^7}{7}+\frac {64 x^6}{3}+\frac {112 x^5}{5}-4 x^4+\frac {64 x^3}{3}+64 x^2+64 x \]
[In]
[Out]
Rule 2086
Rubi steps \begin{align*} \text {integral}& = \int \left (64+128 x+64 x^2-16 x^3+112 x^4+128 x^5+x^6-16 x^7+64 x^8\right ) \, dx \\ & = 64 x+64 x^2+\frac {64 x^3}{3}-4 x^4+\frac {112 x^5}{5}+\frac {64 x^6}{3}+\frac {x^7}{7}-2 x^8+\frac {64 x^9}{9} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.00 \[ \int \left (8+8 x-x^3+8 x^4\right )^2 \, dx=64 x+64 x^2+\frac {64 x^3}{3}-4 x^4+\frac {112 x^5}{5}+\frac {64 x^6}{3}+\frac {x^7}{7}-2 x^8+\frac {64 x^9}{9} \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 45, normalized size of antiderivative = 0.83
method | result | size |
gosper | \(64 x +64 x^{2}+\frac {64}{3} x^{3}-4 x^{4}+\frac {112}{5} x^{5}+\frac {64}{3} x^{6}+\frac {1}{7} x^{7}-2 x^{8}+\frac {64}{9} x^{9}\) | \(45\) |
default | \(64 x +64 x^{2}+\frac {64}{3} x^{3}-4 x^{4}+\frac {112}{5} x^{5}+\frac {64}{3} x^{6}+\frac {1}{7} x^{7}-2 x^{8}+\frac {64}{9} x^{9}\) | \(45\) |
norman | \(64 x +64 x^{2}+\frac {64}{3} x^{3}-4 x^{4}+\frac {112}{5} x^{5}+\frac {64}{3} x^{6}+\frac {1}{7} x^{7}-2 x^{8}+\frac {64}{9} x^{9}\) | \(45\) |
risch | \(64 x +64 x^{2}+\frac {64}{3} x^{3}-4 x^{4}+\frac {112}{5} x^{5}+\frac {64}{3} x^{6}+\frac {1}{7} x^{7}-2 x^{8}+\frac {64}{9} x^{9}\) | \(45\) |
parallelrisch | \(64 x +64 x^{2}+\frac {64}{3} x^{3}-4 x^{4}+\frac {112}{5} x^{5}+\frac {64}{3} x^{6}+\frac {1}{7} x^{7}-2 x^{8}+\frac {64}{9} x^{9}\) | \(45\) |
[In]
[Out]
none
Time = 0.31 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.81 \[ \int \left (8+8 x-x^3+8 x^4\right )^2 \, dx=\frac {64}{9} \, x^{9} - 2 \, x^{8} + \frac {1}{7} \, x^{7} + \frac {64}{3} \, x^{6} + \frac {112}{5} \, x^{5} - 4 \, x^{4} + \frac {64}{3} \, x^{3} + 64 \, x^{2} + 64 \, x \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.91 \[ \int \left (8+8 x-x^3+8 x^4\right )^2 \, dx=\frac {64 x^{9}}{9} - 2 x^{8} + \frac {x^{7}}{7} + \frac {64 x^{6}}{3} + \frac {112 x^{5}}{5} - 4 x^{4} + \frac {64 x^{3}}{3} + 64 x^{2} + 64 x \]
[In]
[Out]
none
Time = 0.19 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.81 \[ \int \left (8+8 x-x^3+8 x^4\right )^2 \, dx=\frac {64}{9} \, x^{9} - 2 \, x^{8} + \frac {1}{7} \, x^{7} + \frac {64}{3} \, x^{6} + \frac {112}{5} \, x^{5} - 4 \, x^{4} + \frac {64}{3} \, x^{3} + 64 \, x^{2} + 64 \, x \]
[In]
[Out]
none
Time = 0.34 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.81 \[ \int \left (8+8 x-x^3+8 x^4\right )^2 \, dx=\frac {64}{9} \, x^{9} - 2 \, x^{8} + \frac {1}{7} \, x^{7} + \frac {64}{3} \, x^{6} + \frac {112}{5} \, x^{5} - 4 \, x^{4} + \frac {64}{3} \, x^{3} + 64 \, x^{2} + 64 \, x \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.81 \[ \int \left (8+8 x-x^3+8 x^4\right )^2 \, dx=\frac {64\,x^9}{9}-2\,x^8+\frac {x^7}{7}+\frac {64\,x^6}{3}+\frac {112\,x^5}{5}-4\,x^4+\frac {64\,x^3}{3}+64\,x^2+64\,x \]
[In]
[Out]