Optimal. Leaf size=15 \[ -\frac{1}{2} \sqrt{1-x^4} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0029978, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {261} \[ -\frac{1}{2} \sqrt{1-x^4} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 261
Rubi steps
\begin{align*} \int \frac{x^3}{\sqrt{1-x^4}} \, dx &=-\frac{1}{2} \sqrt{1-x^4}\\ \end{align*}
Mathematica [A] time = 0.0019959, size = 15, normalized size = 1. \[ -\frac{1}{2} \sqrt{1-x^4} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 23, normalized size = 1.5 \begin{align*}{\frac{ \left ( -1+x \right ) \left ( 1+x \right ) \left ({x}^{2}+1 \right ) }{2}{\frac{1}{\sqrt{-{x}^{4}+1}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.953804, size = 15, normalized size = 1. \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 = 1.81672, size = 28, normalized size = 1.87 \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 = 0.22111, size = 10, normalized size = 0.67 \begin{align*} - \frac{\sqrt{1 - x^{4}}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.14395, size = 15, normalized size = 1. \begin{align*} -\frac{1}{2} \, \sqrt{-x^{4} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]