Optimal. Leaf size=14 \[ \frac {x}{2 \sqrt [3]{\frac {b}{x^3}}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {15, 30} \[ \frac {x}{2 \sqrt [3]{\frac {b}{x^3}}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{\sqrt [3]{\frac {b}{x^3}}} \, dx &=\frac {\int x \, dx}{\sqrt [3]{\frac {b}{x^3}} x}\\ &=\frac {x}{2 \sqrt [3]{\frac {b}{x^3}}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \[ \frac {x}{2 \sqrt [3]{\frac {b}{x^3}}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.84, size = 15, normalized size = 1.07 \[ \frac {x^{4} \left (\frac {b}{x^{3}}\right )^{\frac {2}{3}}}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (\frac {b}{x^{3}}\right )^{\frac {1}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 11, normalized size = 0.79 \[ \frac {x}{2 \left (\frac {b}{x^{3}}\right )^{\frac {1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.31, size = 10, normalized size = 0.71 \[ \frac {x}{2 \, \left (\frac {b}{x^{3}}\right )^{\frac {1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.94, size = 15, normalized size = 1.07 \[ \frac {x^4\,{\left (\frac {b}{x^3}\right )}^{2/3}}{2\,b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.45, size = 15, normalized size = 1.07 \[ \frac {x}{2 \sqrt [3]{b} \sqrt [3]{\frac {1}{x^{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________