Optimal. Leaf size=16 \[ -\frac{\sqrt{b x^2}}{2 x^3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0014777, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {15, 30} \[ -\frac{\sqrt{b x^2}}{2 x^3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{\sqrt{b x^2}}{x^4} \, dx &=\frac{\sqrt{b x^2} \int \frac{1}{x^3} \, dx}{x}\\ &=-\frac{\sqrt{b x^2}}{2 x^3}\\ \end{align*}
Mathematica [A] time = 0.0009968, size = 16, normalized size = 1. \[ -\frac{\sqrt{b x^2}}{2 x^3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 13, normalized size = 0.8 \begin{align*} -{\frac{1}{2\,{x}^{3}}\sqrt{b{x}^{2}}} \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: RuntimeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.23177, size = 30, normalized size = 1.88 \begin{align*} -\frac{\sqrt{b x^{2}}}{2 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.642912, size = 17, normalized size = 1.06 \begin{align*} - \frac{\sqrt{b} \sqrt{x^{2}}}{2 x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.21879, size = 14, normalized size = 0.88 \begin{align*} -\frac{\sqrt{b} \mathrm{sgn}\left (x\right )}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]