Optimal. Leaf size=12 \[ -\frac{2 x}{\sqrt{b x^3}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0014569, antiderivative size = 12, 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} \[ -\frac{2 x}{\sqrt{b x^3}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{b x^3}} \, dx &=\frac{x^{3/2} \int \frac{1}{x^{3/2}} \, dx}{\sqrt{b x^3}}\\ &=-\frac{2 x}{\sqrt{b x^3}}\\ \end{align*}
Mathematica [A] time = 0.0011769, size = 12, normalized size = 1. \[ -\frac{2 x}{\sqrt{b x^3}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 11, normalized size = 0.9 \begin{align*} -2\,{\frac{x}{\sqrt{b{x}^{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.965119, size = 14, normalized size = 1.17 \begin{align*} -\frac{2 \, x}{\sqrt{b x^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.69723, size = 32, normalized size = 2.67 \begin{align*} -\frac{2 \, \sqrt{b x^{3}}}{b x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.523199, size = 15, normalized size = 1.25 \begin{align*} - \frac{2 x}{\sqrt{b} \sqrt{x^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.11946, size = 15, normalized size = 1.25 \begin{align*} -\frac{2}{\sqrt{b x} \mathrm{sgn}\left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]