Optimal. Leaf size=15 \[ -\frac{\log \left (a+\frac{b}{x^2}\right )}{2 b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0036942, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {260} \[ -\frac{\log \left (a+\frac{b}{x^2}\right )}{2 b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 260
Rubi steps
\begin{align*} \int \frac{1}{\left (a+\frac{b}{x^2}\right ) x^3} \, dx &=-\frac{\log \left (a+\frac{b}{x^2}\right )}{2 b}\\ \end{align*}
Mathematica [A] time = 0.004896, size = 22, normalized size = 1.47 \[ \frac{\log (x)}{b}-\frac{\log \left (a x^2+b\right )}{2 b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 21, normalized size = 1.4 \begin{align*} -{\frac{\ln \left ( a{x}^{2}+b \right ) }{2\,b}}+{\frac{\ln \left ( x \right ) }{b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.02235, size = 18, normalized size = 1.2 \begin{align*} -\frac{\log \left (a + \frac{b}{x^{2}}\right )}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.66191, size = 49, normalized size = 3.27 \begin{align*} -\frac{\log \left (a x^{2} + b\right ) - 2 \, \log \left (x\right )}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.202757, size = 15, normalized size = 1. \begin{align*} \frac{\log{\left (x \right )}}{b} - \frac{\log{\left (x^{2} + \frac{b}{a} \right )}}{2 b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.14458, size = 32, normalized size = 2.13 \begin{align*} \frac{\log \left (x^{2}\right )}{2 \, b} - \frac{\log \left ({\left | a x^{2} + b \right |}\right )}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]