Optimal. Leaf size=13 \[ \frac{\sqrt{x^4+1}}{2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0024358, 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} \[ \frac{\sqrt{x^4+1}}{2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 261
Rubi steps
\begin{align*} \int \frac{x^3}{\sqrt{1+x^4}} \, dx &=\frac{\sqrt{1+x^4}}{2}\\ \end{align*}
Mathematica [A] time = 0.0018307, size = 13, normalized size = 1. \[ \frac{\sqrt{x^4+1}}{2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 10, normalized size = 0.8 \begin{align*}{\frac{1}{2}\sqrt{{x}^{4}+1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.03734, size = 12, normalized size = 0.92 \begin{align*} \frac{1}{2} \, \sqrt{x^{4} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.45237, size = 26, normalized size = 2. \begin{align*} \frac{1}{2} \, \sqrt{x^{4} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.175, size = 8, normalized size = 0.62 \begin{align*} \frac{\sqrt{x^{4} + 1}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.15676, size = 12, normalized size = 0.92 \begin{align*} \frac{1}{2} \, \sqrt{x^{4} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]