Optimal. Leaf size=28 \[ \frac {2 \sqrt [4]{2} E\left (\left .\frac {1}{2} \sin ^{-1}\left (\sqrt {\frac {3}{2}} x\right )\right |2\right )}{\sqrt {3}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {228} \[ \frac {2 \sqrt [4]{2} E\left (\left .\frac {1}{2} \sin ^{-1}\left (\sqrt {\frac {3}{2}} x\right )\right |2\right )}{\sqrt {3}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 228
Rubi steps
\begin {align*} \int \frac {1}{\sqrt [4]{2-3 x^2}} \, dx &=\frac {2 \sqrt [4]{2} E\left (\left .\frac {1}{2} \sin ^{-1}\left (\sqrt {\frac {3}{2}} x\right )\right |2\right )}{\sqrt {3}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [C] time = 0.00, size = 24, normalized size = 0.86 \[ \frac {x \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};\frac {3 x^2}{2}\right )}{\sqrt [4]{2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [F] time = 0.90, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {{\left (-3 \, x^{2} + 2\right )}^{\frac {3}{4}}}{3 \, x^{2} - 2}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (-3 \, x^{2} + 2\right )}^{\frac {1}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [C] time = 0.28, size = 18, normalized size = 0.64 \[ \frac {2^{\frac {3}{4}} x \hypergeom \left (\left [\frac {1}{4}, \frac {1}{2}\right ], \left [\frac {3}{2}\right ], \frac {3 x^{2}}{2}\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (-3 \, x^{2} + 2\right )}^{\frac {1}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.09, size = 16, normalized size = 0.57 \[ \frac {2^{3/4}\,x\,{{}}_2{\mathrm {F}}_1\left (\frac {1}{4},\frac {1}{2};\ \frac {3}{2};\ \frac {3\,x^2}{2}\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [C] time = 0.69, size = 27, normalized size = 0.96 \[ \frac {2^{\frac {3}{4}} x {{}_{2}F_{1}\left (\begin {matrix} \frac {1}{4}, \frac {1}{2} \\ \frac {3}{2} \end {matrix}\middle | {\frac {3 x^{2} e^{2 i \pi }}{2}} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________