Optimal. Leaf size=31 \[ \frac{1}{90} \left (3 x^4+5\right )^{5/2}-\frac{5}{54} \left (3 x^4+5\right )^{3/2} \]
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Rubi [A] time = 0.0148999, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {266, 43} \[ \frac{1}{90} \left (3 x^4+5\right )^{5/2}-\frac{5}{54} \left (3 x^4+5\right )^{3/2} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int x^7 \sqrt{5+3 x^4} \, dx &=\frac{1}{4} \operatorname{Subst}\left (\int x \sqrt{5+3 x} \, dx,x,x^4\right )\\ &=\frac{1}{4} \operatorname{Subst}\left (\int \left (-\frac{5}{3} \sqrt{5+3 x}+\frac{1}{3} (5+3 x)^{3/2}\right ) \, dx,x,x^4\right )\\ &=-\frac{5}{54} \left (5+3 x^4\right )^{3/2}+\frac{1}{90} \left (5+3 x^4\right )^{5/2}\\ \end{align*}
Mathematica [A] time = 0.0080551, size = 22, normalized size = 0.71 \[ \frac{1}{270} \left (3 x^4+5\right )^{3/2} \left (9 x^4-10\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 19, normalized size = 0.6 \begin{align*}{\frac{9\,{x}^{4}-10}{270} \left ( 3\,{x}^{4}+5 \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.955752, size = 31, normalized size = 1. \begin{align*} \frac{1}{90} \,{\left (3 \, x^{4} + 5\right )}^{\frac{5}{2}} - \frac{5}{54} \,{\left (3 \, x^{4} + 5\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.38996, size = 62, normalized size = 2. \begin{align*} \frac{1}{270} \,{\left (27 \, x^{8} + 15 \, x^{4} - 50\right )} \sqrt{3 \, x^{4} + 5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.796639, size = 42, normalized size = 1.35 \begin{align*} \frac{x^{8} \sqrt{3 x^{4} + 5}}{10} + \frac{x^{4} \sqrt{3 x^{4} + 5}}{18} - \frac{5 \sqrt{3 x^{4} + 5}}{27} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09694, size = 31, normalized size = 1. \begin{align*} \frac{1}{90} \,{\left (3 \, x^{4} + 5\right )}^{\frac{5}{2}} - \frac{5}{54} \,{\left (3 \, x^{4} + 5\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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