Optimal. Leaf size=19 \[ -\frac{\left (a+b x^2\right )^4}{8 a x^8} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0030151, antiderivative size = 19, 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 = {264} \[ -\frac{\left (a+b x^2\right )^4}{8 a x^8} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 264
Rubi steps
\begin{align*} \int \frac{\left (a+b x^2\right )^3}{x^9} \, dx &=-\frac{\left (a+b x^2\right )^4}{8 a x^8}\\ \end{align*}
Mathematica [B] time = 0.0062467, size = 43, normalized size = 2.26 \[ -\frac{a^2 b}{2 x^6}-\frac{a^3}{8 x^8}-\frac{3 a b^2}{4 x^4}-\frac{b^3}{2 x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] time = 0.004, size = 36, normalized size = 1.9 \begin{align*} -{\frac{{a}^{3}}{8\,{x}^{8}}}-{\frac{3\,a{b}^{2}}{4\,{x}^{4}}}-{\frac{{b}^{3}}{2\,{x}^{2}}}-{\frac{{a}^{2}b}{2\,{x}^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] time = 1.08615, size = 47, normalized size = 2.47 \begin{align*} -\frac{4 \, b^{3} x^{6} + 6 \, a b^{2} x^{4} + 4 \, a^{2} b x^{2} + a^{3}}{8 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.20025, size = 76, normalized size = 4. \begin{align*} -\frac{4 \, b^{3} x^{6} + 6 \, a b^{2} x^{4} + 4 \, a^{2} b x^{2} + a^{3}}{8 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 0.403944, size = 37, normalized size = 1.95 \begin{align*} - \frac{a^{3} + 4 a^{2} b x^{2} + 6 a b^{2} x^{4} + 4 b^{3} x^{6}}{8 x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] time = 2.64129, size = 47, normalized size = 2.47 \begin{align*} -\frac{4 \, b^{3} x^{6} + 6 \, a b^{2} x^{4} + 4 \, a^{2} b x^{2} + a^{3}}{8 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]