Optimal. Leaf size=11 \[ -\frac{1}{4 \left (x^4+1\right )} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0028654, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125, Rules used = {28, 261} \[ -\frac{1}{4 \left (x^4+1\right )} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 28
Rule 261
Rubi steps
\begin{align*} \int \frac{x^3}{1+2 x^4+x^8} \, dx &=\int \frac{x^3}{\left (1+x^4\right )^2} \, dx\\ &=-\frac{1}{4 \left (1+x^4\right )}\\ \end{align*}
Mathematica [A] time = 0.0020691, size = 11, normalized size = 1. \[ -\frac{1}{4 \left (x^4+1\right )} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 10, normalized size = 0.9 \begin{align*} -{\frac{1}{4\,{x}^{4}+4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.959297, size = 12, normalized size = 1.09 \begin{align*} -\frac{1}{4 \,{\left (x^{4} + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.40466, size = 22, normalized size = 2. \begin{align*} -\frac{1}{4 \,{\left (x^{4} + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.099485, size = 8, normalized size = 0.73 \begin{align*} - \frac{1}{4 x^{4} + 4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.10829, size = 12, normalized size = 1.09 \begin{align*} -\frac{1}{4 \,{\left (x^{4} + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]