Integrand size = 20, antiderivative size = 30 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right ) \, dx=8 x+12 x^2+\frac {8 x^3}{3}-\frac {15 x^4}{4}+\frac {8 x^5}{5} \]
[Out]
Time = 0.00 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right ) \, dx=\frac {8 x^5}{5}-\frac {15 x^4}{4}+\frac {8 x^3}{3}+12 x^2+8 x \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = 8 x+12 x^2+\frac {8 x^3}{3}-\frac {15 x^4}{4}+\frac {8 x^5}{5} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right ) \, dx=8 x+12 x^2+\frac {8 x^3}{3}-\frac {15 x^4}{4}+\frac {8 x^5}{5} \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.83
method | result | size |
gosper | \(8 x +12 x^{2}+\frac {8}{3} x^{3}-\frac {15}{4} x^{4}+\frac {8}{5} x^{5}\) | \(25\) |
default | \(8 x +12 x^{2}+\frac {8}{3} x^{3}-\frac {15}{4} x^{4}+\frac {8}{5} x^{5}\) | \(25\) |
norman | \(8 x +12 x^{2}+\frac {8}{3} x^{3}-\frac {15}{4} x^{4}+\frac {8}{5} x^{5}\) | \(25\) |
risch | \(8 x +12 x^{2}+\frac {8}{3} x^{3}-\frac {15}{4} x^{4}+\frac {8}{5} x^{5}\) | \(25\) |
parallelrisch | \(8 x +12 x^{2}+\frac {8}{3} x^{3}-\frac {15}{4} x^{4}+\frac {8}{5} x^{5}\) | \(25\) |
parts | \(8 x +12 x^{2}+\frac {8}{3} x^{3}-\frac {15}{4} x^{4}+\frac {8}{5} x^{5}\) | \(25\) |
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.80 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right ) \, dx=\frac {8}{5} \, x^{5} - \frac {15}{4} \, x^{4} + \frac {8}{3} \, x^{3} + 12 \, x^{2} + 8 \, x \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.90 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right ) \, dx=\frac {8 x^{5}}{5} - \frac {15 x^{4}}{4} + \frac {8 x^{3}}{3} + 12 x^{2} + 8 x \]
[In]
[Out]
none
Time = 0.20 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.80 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right ) \, dx=\frac {8}{5} \, x^{5} - \frac {15}{4} \, x^{4} + \frac {8}{3} \, x^{3} + 12 \, x^{2} + 8 \, x \]
[In]
[Out]
none
Time = 0.29 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.80 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right ) \, dx=\frac {8}{5} \, x^{5} - \frac {15}{4} \, x^{4} + \frac {8}{3} \, x^{3} + 12 \, x^{2} + 8 \, x \]
[In]
[Out]
Time = 0.01 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.80 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right ) \, dx=\frac {8\,x^5}{5}-\frac {15\,x^4}{4}+\frac {8\,x^3}{3}+12\,x^2+8\,x \]
[In]
[Out]