Optimal. Leaf size=19 \[ \frac{3 x}{(3-n) \sqrt [3]{b x^n}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0055366, antiderivative size = 19, normalized size of antiderivative = 1., 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} \[ \frac{3 x}{(3-n) \sqrt [3]{b x^n}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{\sqrt [3]{b x^n}} \, dx &=\frac{x^{n/3} \int x^{-n/3} \, dx}{\sqrt [3]{b x^n}}\\ &=\frac{3 x}{(3-n) \sqrt [3]{b x^n}}\\ \end{align*}
Mathematica [A] time = 0.0042143, size = 17, normalized size = 0.89 \[ -\frac{3 x}{(n-3) \sqrt [3]{b x^n}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 16, normalized size = 0.8 \begin{align*} -3\,{\frac{x}{ \left ( -3+n \right ) \sqrt [3]{b{x}^{n}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\left (b x^{n}\right )^{\frac{1}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]