Optimal. Leaf size=13 \[ -\frac {\log \left (a+\frac {b}{x}\right )}{b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, 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} \[ -\frac {\log \left (a+\frac {b}{x}\right )}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 260
Rubi steps
\begin {align*} \int \frac {1}{\left (a+\frac {b}{x}\right ) x^2} \, dx &=-\frac {\log \left (a+\frac {b}{x}\right )}{b}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 18, normalized size = 1.38 \[ \frac {\log (x)}{b}-\frac {\log (a x+b)}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.96, size = 16, normalized size = 1.23 \[ -\frac {\log \left (a x + b\right ) - \log \relax (x)}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.23, size = 14, normalized size = 1.08 \[ -\frac {\log \left ({\left | a + \frac {b}{x} \right |}\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 19, normalized size = 1.46 \[ \frac {\ln \relax (x )}{b}-\frac {\ln \left (a x +b \right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.10, size = 13, normalized size = 1.00 \[ -\frac {\log \left (a + \frac {b}{x}\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 15, normalized size = 1.15 \[ -\frac {2\,\mathrm {atanh}\left (\frac {2\,a\,x}{b}+1\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.15, size = 10, normalized size = 0.77 \[ \frac {\log {\relax (x )} - \log {\left (x + \frac {b}{a} \right )}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________