Optimal. Leaf size=13 \[ \frac {2}{3} \left (1+x^2\right )^{3/4} \]
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Rubi [A]
time = 0.00, antiderivative size = 13, 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 = {267}
\begin {gather*} \frac {2}{3} \left (x^2+1\right )^{3/4} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
Rubi steps
\begin {align*} \int \frac {x}{\sqrt [4]{1+x^2}} \, dx &=\frac {2}{3} \left (1+x^2\right )^{3/4}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {2}{3} \left (1+x^2\right )^{3/4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.26, size = 10, normalized size = 0.77
method | result | size |
gosper | \(\frac {2 \left (x^{2}+1\right )^{\frac {3}{4}}}{3}\) | \(10\) |
derivativedivides | \(\frac {2 \left (x^{2}+1\right )^{\frac {3}{4}}}{3}\) | \(10\) |
default | \(\frac {2 \left (x^{2}+1\right )^{\frac {3}{4}}}{3}\) | \(10\) |
trager | \(\frac {2 \left (x^{2}+1\right )^{\frac {3}{4}}}{3}\) | \(10\) |
risch | \(\frac {2 \left (x^{2}+1\right )^{\frac {3}{4}}}{3}\) | \(10\) |
meijerg | \(\frac {x^{2} \hypergeom \left (\left [\frac {1}{4}, 1\right ], \left [2\right ], -x^{2}\right )}{2}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 9, normalized size = 0.69 \begin {gather*} \frac {2}{3} \, {\left (x^{2} + 1\right )}^{\frac {3}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 9, normalized size = 0.69 \begin {gather*} \frac {2}{3} \, {\left (x^{2} + 1\right )}^{\frac {3}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 10, normalized size = 0.77 \begin {gather*} \frac {2 \left (x^{2} + 1\right )^{\frac {3}{4}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 9, normalized size = 0.69 \begin {gather*} \frac {2}{3} \, {\left (x^{2} + 1\right )}^{\frac {3}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.09, size = 9, normalized size = 0.69 \begin {gather*} \frac {2\,{\left (x^2+1\right )}^{3/4}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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