Optimal. Leaf size=19 \[ \frac{2 x^4}{11 b \sqrt{\frac{b}{x^3}}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0020722, 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} \[ \frac{2 x^4}{11 b \sqrt{\frac{b}{x^3}}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{\left (\frac{b}{x^3}\right )^{3/2}} \, dx &=\frac{\int x^{9/2} \, dx}{b \sqrt{\frac{b}{x^3}} x^{3/2}}\\ &=\frac{2 x^4}{11 b \sqrt{\frac{b}{x^3}}}\\ \end{align*}
Mathematica [A] time = 0.0016997, size = 14, normalized size = 0.74 \[ \frac{2 x}{11 \left (\frac{b}{x^3}\right )^{3/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 11, normalized size = 0.6 \begin{align*}{\frac{2\,x}{11} \left ({\frac{b}{{x}^{3}}} \right ) ^{-{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.990229, size = 14, normalized size = 0.74 \begin{align*} \frac{2 \, x}{11 \, \left (\frac{b}{x^{3}}\right )^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.70442, size = 35, normalized size = 1.84 \begin{align*} \frac{2 \, x^{7} \sqrt{\frac{b}{x^{3}}}}{11 \, b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.658073, size = 17, normalized size = 0.89 \begin{align*} \frac{2 x}{11 b^{\frac{3}{2}} \left (\frac{1}{x^{3}}\right )^{\frac{3}{2}}} \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 (\frac{b}{x^{3}}\right )^{\frac{3}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]