Optimal. Leaf size=24 \[ \frac{3}{7} (c+x)^{7/3}-\frac{3}{4} c (c+x)^{4/3} \]
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Rubi [A] time = 0.0044251, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {43} \[ \frac{3}{7} (c+x)^{7/3}-\frac{3}{4} c (c+x)^{4/3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x \sqrt [3]{c+x} \, dx &=\int \left (-c \sqrt [3]{c+x}+(c+x)^{4/3}\right ) \, dx\\ &=-\frac{3}{4} c (c+x)^{4/3}+\frac{3}{7} (c+x)^{7/3}\\ \end{align*}
Mathematica [A] time = 0.0064194, size = 18, normalized size = 0.75 \[ \frac{3}{28} (c+x)^{4/3} (4 x-3 c) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 15, normalized size = 0.6 \begin{align*} -{\frac{9\,c-12\,x}{28} \left ( c+x \right ) ^{{\frac{4}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.936892, size = 22, normalized size = 0.92 \begin{align*} \frac{3}{7} \,{\left (c + x\right )}^{\frac{7}{3}} - \frac{3}{4} \,{\left (c + x\right )}^{\frac{4}{3}} c \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.99004, size = 58, normalized size = 2.42 \begin{align*} -\frac{3}{28} \,{\left (3 \, c^{2} - c x - 4 \, x^{2}\right )}{\left (c + x\right )}^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.926045, size = 144, normalized size = 6. \begin{align*} - \frac{9 c^{\frac{13}{3}} \sqrt [3]{1 + \frac{x}{c}}}{28 c^{2} + 28 c x} + \frac{9 c^{\frac{13}{3}}}{28 c^{2} + 28 c x} - \frac{6 c^{\frac{10}{3}} x \sqrt [3]{1 + \frac{x}{c}}}{28 c^{2} + 28 c x} + \frac{9 c^{\frac{10}{3}} x}{28 c^{2} + 28 c x} + \frac{15 c^{\frac{7}{3}} x^{2} \sqrt [3]{1 + \frac{x}{c}}}{28 c^{2} + 28 c x} + \frac{12 c^{\frac{4}{3}} x^{3} \sqrt [3]{1 + \frac{x}{c}}}{28 c^{2} + 28 c x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05171, size = 22, normalized size = 0.92 \begin{align*} \frac{3}{7} \,{\left (c + x\right )}^{\frac{7}{3}} - \frac{3}{4} \,{\left (c + x\right )}^{\frac{4}{3}} c \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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