Optimal. Leaf size=16 \[ -\frac{\left (a+\frac{b}{x^2}\right )^4}{8 b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0037042, antiderivative size = 16, 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 = {261} \[ -\frac{\left (a+\frac{b}{x^2}\right )^4}{8 b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 261
Rubi steps
\begin{align*} \int \frac{\left (a+\frac{b}{x^2}\right )^3}{x^3} \, dx &=-\frac{\left (a+\frac{b}{x^2}\right )^4}{8 b}\\ \end{align*}
Mathematica [B] time = 0.0063126, size = 43, normalized size = 2.69 \[ -\frac{3 a^2 b}{4 x^4}-\frac{a^3}{2 x^2}-\frac{a b^2}{2 x^6}-\frac{b^3}{8 x^8} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] time = 0.004, size = 36, normalized size = 2.3 \begin{align*} -{\frac{3\,{a}^{2}b}{4\,{x}^{4}}}-{\frac{{a}^{3}}{2\,{x}^{2}}}-{\frac{{b}^{3}}{8\,{x}^{8}}}-{\frac{{b}^{2}a}{2\,{x}^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.941985, size = 19, normalized size = 1.19 \begin{align*} -\frac{{\left (a + \frac{b}{x^{2}}\right )}^{4}}{8 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.38565, size = 76, normalized size = 4.75 \begin{align*} -\frac{4 \, a^{3} x^{6} + 6 \, a^{2} b x^{4} + 4 \, a b^{2} x^{2} + b^{3}}{8 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 0.403389, size = 37, normalized size = 2.31 \begin{align*} - \frac{4 a^{3} x^{6} + 6 a^{2} b x^{4} + 4 a b^{2} x^{2} + b^{3}}{8 x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] time = 1.17921, size = 47, normalized size = 2.94 \begin{align*} -\frac{4 \, a^{3} x^{6} + 6 \, a^{2} b x^{4} + 4 \, a b^{2} x^{2} + b^{3}}{8 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]