Optimal. Leaf size=19 \[ -\frac{\left (a+b x^3\right )^3}{9 a x^9} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0033423, 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} \[ -\frac{\left (a+b x^3\right )^3}{9 a x^9} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 264
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^2}{x^{10}} \, dx &=-\frac{\left (a+b x^3\right )^3}{9 a x^9}\\ \end{align*}
Mathematica [A] time = 0.0007634, size = 30, normalized size = 1.58 \[ -\frac{a^2}{9 x^9}-\frac{a b}{3 x^6}-\frac{b^2}{3 x^3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 25, normalized size = 1.3 \begin{align*} -{\frac{{b}^{2}}{3\,{x}^{3}}}-{\frac{ab}{3\,{x}^{6}}}-{\frac{{a}^{2}}{9\,{x}^{9}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.952874, size = 32, normalized size = 1.68 \begin{align*} -\frac{3 \, b^{2} x^{6} + 3 \, a b x^{3} + a^{2}}{9 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.82685, size = 54, normalized size = 2.84 \begin{align*} -\frac{3 \, b^{2} x^{6} + 3 \, a b x^{3} + a^{2}}{9 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.461835, size = 26, normalized size = 1.37 \begin{align*} - \frac{a^{2} + 3 a b x^{3} + 3 b^{2} x^{6}}{9 x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.11509, size = 32, normalized size = 1.68 \begin{align*} -\frac{3 \, b^{2} x^{6} + 3 \, a b x^{3} + a^{2}}{9 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]