Optimal. Leaf size=27 \[ \frac{7}{37} \left (x^2+1\right )^{37/14}-\frac{7}{23} \left (x^2+1\right )^{23/14} \]
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Rubi [A] time = 0.0114618, antiderivative size = 27, normalized size of antiderivative = 1., 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 = {266, 43} \[ \frac{7}{37} \left (x^2+1\right )^{37/14}-\frac{7}{23} \left (x^2+1\right )^{23/14} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int x^3 \left (1+x^2\right )^{9/14} \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int x (1+x)^{9/14} \, dx,x,x^2\right )\\ &=\frac{1}{2} \operatorname{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*}
Mathematica [A] time = 0.0063217, size = 20, normalized size = 0.74 \[ \frac{7}{851} \left (x^2+1\right )^{23/14} \left (23 x^2-14\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 17, normalized size = 0.6 \begin{align*}{\frac{161\,{x}^{2}-98}{851} \left ({x}^{2}+1 \right ) ^{{\frac{23}{14}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.945455, size = 26, normalized size = 0.96 \begin{align*} \frac{7}{37} \,{\left (x^{2} + 1\right )}^{\frac{37}{14}} - \frac{7}{23} \,{\left (x^{2} + 1\right )}^{\frac{23}{14}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.95499, size = 62, normalized size = 2.3 \begin{align*} \frac{7}{851} \,{\left (23 \, x^{4} + 9 \, x^{2} - 14\right )}{\left (x^{2} + 1\right )}^{\frac{9}{14}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 18.7864, size = 41, normalized size = 1.52 \begin{align*} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07927, size = 26, normalized size = 0.96 \begin{align*} \frac{7}{37} \,{\left (x^{2} + 1\right )}^{\frac{37}{14}} - \frac{7}{23} \,{\left (x^{2} + 1\right )}^{\frac{23}{14}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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