Integrand size = 14, antiderivative size = 16 \[ \int \frac {-4+5 x^2+x^3}{x^2} \, dx=\frac {4}{x}+5 x+\frac {x^2}{2} \]
[Out]
Time = 0.00 (sec) , antiderivative size = 16, 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 = {14} \[ \int \frac {-4+5 x^2+x^3}{x^2} \, dx=\frac {x^2}{2}+5 x+\frac {4}{x} \]
[In]
[Out]
Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (5-\frac {4}{x^2}+x\right ) \, dx \\ & = \frac {4}{x}+5 x+\frac {x^2}{2} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {-4+5 x^2+x^3}{x^2} \, dx=\frac {4}{x}+5 x+\frac {x^2}{2} \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94
method | result | size |
default | \(\frac {4}{x}+5 x +\frac {x^{2}}{2}\) | \(15\) |
risch | \(\frac {4}{x}+5 x +\frac {x^{2}}{2}\) | \(15\) |
gosper | \(\frac {x^{3}+10 x^{2}+8}{2 x}\) | \(16\) |
parallelrisch | \(\frac {x^{3}+10 x^{2}+8}{2 x}\) | \(16\) |
norman | \(\frac {\frac {1}{2} x^{3}+5 x^{2}+4}{x}\) | \(17\) |
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int \frac {-4+5 x^2+x^3}{x^2} \, dx=\frac {x^{3} + 10 \, x^{2} + 8}{2 \, x} \]
[In]
[Out]
Time = 0.03 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.62 \[ \int \frac {-4+5 x^2+x^3}{x^2} \, dx=\frac {x^{2}}{2} + 5 x + \frac {4}{x} \]
[In]
[Out]
none
Time = 0.20 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {-4+5 x^2+x^3}{x^2} \, dx=\frac {1}{2} \, x^{2} + 5 \, x + \frac {4}{x} \]
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {-4+5 x^2+x^3}{x^2} \, dx=\frac {1}{2} \, x^{2} + 5 \, x + \frac {4}{x} \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int \frac {-4+5 x^2+x^3}{x^2} \, dx=\frac {x^3+10\,x^2+8}{2\,x} \]
[In]
[Out]