Optimal. Leaf size=16 \[ -\frac {\left (a+\frac {b}{x^2}\right )^3}{6 b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 16, 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 = {261} \[ -\frac {\left (a+\frac {b}{x^2}\right )^3}{6 b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 261
Rubi steps
\begin {align*} \int \frac {\left (a+\frac {b}{x^2}\right )^2}{x^3} \, dx &=-\frac {\left (a+\frac {b}{x^2}\right )^3}{6 b}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 30, normalized size = 1.88 \[ -\frac {a^2}{2 x^2}-\frac {a b}{2 x^4}-\frac {b^2}{6 x^6} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.74, size = 24, normalized size = 1.50 \[ -\frac {3 \, a^{2} x^{4} + 3 \, a b x^{2} + b^{2}}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 24, normalized size = 1.50 \[ -\frac {3 \, a^{2} x^{4} + 3 \, a b x^{2} + b^{2}}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 25, normalized size = 1.56 \[ -\frac {a^{2}}{2 x^{2}}-\frac {a b}{2 x^{4}}-\frac {b^{2}}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.83, size = 14, normalized size = 0.88 \[ -\frac {{\left (a + \frac {b}{x^{2}}\right )}^{3}}{6 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 26, normalized size = 1.62 \[ -\frac {\frac {a^2\,x^4}{2}+\frac {a\,b\,x^2}{2}+\frac {b^2}{6}}{x^6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.19, size = 26, normalized size = 1.62 \[ \frac {- 3 a^{2} x^{4} - 3 a b x^{2} - b^{2}}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________