Optimal. Leaf size=27 \[ -\frac {7}{23} \left (1+x^2\right )^{23/14}+\frac {7}{37} \left (1+x^2\right )^{37/14} \]
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Rubi [A]
time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {272, 45}
\begin {gather*} \frac {7}{37} \left (x^2+1\right )^{37/14}-\frac {7}{23} \left (x^2+1\right )^{23/14} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 272
Rubi steps
\begin {align*} \int x^3 \left (1+x^2\right )^{9/14} \, dx &=\frac {1}{2} \text {Subst}\left (\int x (1+x)^{9/14} \, dx,x,x^2\right )\\ &=\frac {1}{2} \text {Subst}\left (\int \left (-(1+x)^{9/14}+(1+x)^{23/14}\right ) \, dx,x,x^2\right )\\ &=-\frac {7}{23} \left (1+x^2\right )^{23/14}+\frac {7}{37} \left (1+x^2\right )^{37/14}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 25, normalized size = 0.93 \begin {gather*} \frac {7}{851} \left (1+x^2\right )^{9/14} \left (-14+9 x^2+23 x^4\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 17, normalized size = 0.63
method | result | size |
gosper | \(\frac {7 \left (x^{2}+1\right )^{\frac {23}{14}} \left (23 x^{2}-14\right )}{851}\) | \(17\) |
meijerg | \(\frac {x^{4} \hypergeom \left (\left [-\frac {9}{14}, 2\right ], \left [3\right ], -x^{2}\right )}{4}\) | \(17\) |
trager | \(\left (\frac {7}{37} x^{4}+\frac {63}{851} x^{2}-\frac {98}{851}\right ) \left (x^{2}+1\right )^{\frac {9}{14}}\) | \(21\) |
risch | \(\frac {7 \left (x^{2}+1\right )^{\frac {9}{14}} \left (23 x^{4}+9 x^{2}-14\right )}{851}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.26, size = 19, normalized size = 0.70 \begin {gather*} \frac {7}{37} \, {\left (x^{2} + 1\right )}^{\frac {37}{14}} - \frac {7}{23} \, {\left (x^{2} + 1\right )}^{\frac {23}{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.64, size = 21, normalized size = 0.78 \begin {gather*} \frac {7}{851} \, {\left (23 \, x^{4} + 9 \, x^{2} - 14\right )} {\left (x^{2} + 1\right )}^{\frac {9}{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 3.83, size = 41, normalized size = 1.52 \begin {gather*} \frac {7 x^{4} \left (x^{2} + 1\right )^{\frac {9}{14}}}{37} + \frac {63 x^{2} \left (x^{2} + 1\right )^{\frac {9}{14}}}{851} - \frac {98 \left (x^{2} + 1\right )^{\frac {9}{14}}}{851} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.10, size = 19, normalized size = 0.70 \begin {gather*} \frac {7}{37} \, {\left (x^{2} + 1\right )}^{\frac {37}{14}} - \frac {7}{23} \, {\left (x^{2} + 1\right )}^{\frac {23}{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.38, size = 20, normalized size = 0.74 \begin {gather*} {\left (x^2+1\right )}^{9/14}\,\left (\frac {7\,x^4}{37}+\frac {63\,x^2}{851}-\frac {98}{851}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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