Optimal. Leaf size=13 \[ -\frac{1}{12 \left (3 x^4+2\right )} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0025883, antiderivative size = 13, 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} \[ -\frac{1}{12 \left (3 x^4+2\right )} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 261
Rubi steps
\begin{align*} \int \frac{x^3}{\left (2+3 x^4\right )^2} \, dx &=-\frac{1}{12 \left (2+3 x^4\right )}\\ \end{align*}
Mathematica [A] time = 0.0030706, size = 13, normalized size = 1. \[ -\frac{1}{12 \left (3 x^4+2\right )} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 12, normalized size = 0.9 \begin{align*} -{\frac{1}{36\,{x}^{4}+24}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.25765, size = 15, normalized size = 1.15 \begin{align*} -\frac{1}{12 \,{\left (3 \, x^{4} + 2\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.62151, size = 26, normalized size = 2. \begin{align*} -\frac{1}{12 \,{\left (3 \, x^{4} + 2\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.135273, size = 8, normalized size = 0.62 \begin{align*} - \frac{1}{36 x^{4} + 24} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.13151, size = 15, normalized size = 1.15 \begin{align*} -\frac{1}{12 \,{\left (3 \, x^{4} + 2\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]