Integrand size = 5, antiderivative size = 9 \[ \int \frac {1}{\sqrt [3]{x}} \, dx=\frac {3 x^{2/3}}{2} \]
[Out]
Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {30} \[ \int \frac {1}{\sqrt [3]{x}} \, dx=\frac {3 x^{2/3}}{2} \]
[In]
[Out]
Rule 30
Rubi steps \begin{align*} \text {integral}& = \frac {3 x^{2/3}}{2} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int \frac {1}{\sqrt [3]{x}} \, dx=\frac {3 x^{2/3}}{2} \]
[In]
[Out]
Time = 0.01 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67
method | result | size |
gosper | \(\frac {3 x^{\frac {2}{3}}}{2}\) | \(6\) |
derivativedivides | \(\frac {3 x^{\frac {2}{3}}}{2}\) | \(6\) |
default | \(\frac {3 x^{\frac {2}{3}}}{2}\) | \(6\) |
trager | \(\frac {3 x^{\frac {2}{3}}}{2}\) | \(6\) |
risch | \(\frac {3 x^{\frac {2}{3}}}{2}\) | \(6\) |
[In]
[Out]
none
Time = 0.21 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.56 \[ \int \frac {1}{\sqrt [3]{x}} \, dx=\frac {3}{2} \, x^{\frac {2}{3}} \]
[In]
[Out]
Time = 0.05 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int \frac {1}{\sqrt [3]{x}} \, dx=\frac {3 x^{\frac {2}{3}}}{2} \]
[In]
[Out]
none
Time = 0.20 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.56 \[ \int \frac {1}{\sqrt [3]{x}} \, dx=\frac {3}{2} \, x^{\frac {2}{3}} \]
[In]
[Out]
none
Time = 0.42 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.56 \[ \int \frac {1}{\sqrt [3]{x}} \, dx=\frac {3}{2} \, x^{\frac {2}{3}} \]
[In]
[Out]
Time = 0.03 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.56 \[ \int \frac {1}{\sqrt [3]{x}} \, dx=\frac {3\,x^{2/3}}{2} \]
[In]
[Out]