Integrand size = 17, antiderivative size = 20 \[ \int \frac {x^2}{\sqrt {-b+a x^3}} \, dx=\frac {2 \sqrt {-b+a x^3}}{3 a} \]
[Out]
Time = 0.00 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {267} \[ \int \frac {x^2}{\sqrt {-b+a x^3}} \, dx=\frac {2 \sqrt {a x^3-b}}{3 a} \]
[In]
[Out]
Rule 267
Rubi steps \begin{align*} \text {integral}& = \frac {2 \sqrt {-b+a x^3}}{3 a} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {x^2}{\sqrt {-b+a x^3}} \, dx=\frac {2 \sqrt {-b+a x^3}}{3 a} \]
[In]
[Out]
Time = 3.61 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85
method | result | size |
gosper | \(\frac {2 \sqrt {a \,x^{3}-b}}{3 a}\) | \(17\) |
derivativedivides | \(\frac {2 \sqrt {a \,x^{3}-b}}{3 a}\) | \(17\) |
default | \(\frac {2 \sqrt {a \,x^{3}-b}}{3 a}\) | \(17\) |
trager | \(\frac {2 \sqrt {a \,x^{3}-b}}{3 a}\) | \(17\) |
risch | \(\frac {2 \sqrt {a \,x^{3}-b}}{3 a}\) | \(17\) |
elliptic | \(\frac {2 \sqrt {a \,x^{3}-b}}{3 a}\) | \(17\) |
pseudoelliptic | \(\frac {2 \sqrt {a \,x^{3}-b}}{3 a}\) | \(17\) |
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {x^2}{\sqrt {-b+a x^3}} \, dx=\frac {2 \, \sqrt {a x^{3} - b}}{3 \, a} \]
[In]
[Out]
Time = 0.08 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.30 \[ \int \frac {x^2}{\sqrt {-b+a x^3}} \, dx=\begin {cases} \frac {2 \sqrt {a x^{3} - b}}{3 a} & \text {for}\: a \neq 0 \\\frac {x^{3}}{3 \sqrt {- b}} & \text {otherwise} \end {cases} \]
[In]
[Out]
none
Time = 0.18 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {x^2}{\sqrt {-b+a x^3}} \, dx=\frac {2 \, \sqrt {a x^{3} - b}}{3 \, a} \]
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {x^2}{\sqrt {-b+a x^3}} \, dx=\frac {2 \, \sqrt {a x^{3} - b}}{3 \, a} \]
[In]
[Out]
Time = 5.21 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {x^2}{\sqrt {-b+a x^3}} \, dx=\frac {2\,\sqrt {a\,x^3-b}}{3\,a} \]
[In]
[Out]