Optimal. Leaf size=34 \[ \frac{3 (a+b x)^{7/3}}{7 b^2}-\frac{3 a (a+b x)^{4/3}}{4 b^2} \]
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Rubi [A] time = 0.0082427, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {43} \[ \frac{3 (a+b x)^{7/3}}{7 b^2}-\frac{3 a (a+b x)^{4/3}}{4 b^2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x \sqrt [3]{a+b x} \, dx &=\int \left (-\frac{a \sqrt [3]{a+b x}}{b}+\frac{(a+b x)^{4/3}}{b}\right ) \, dx\\ &=-\frac{3 a (a+b x)^{4/3}}{4 b^2}+\frac{3 (a+b x)^{7/3}}{7 b^2}\\ \end{align*}
Mathematica [A] time = 0.0245567, size = 24, normalized size = 0.71 \[ \frac{3 (a+b x)^{4/3} (4 b x-3 a)}{28 b^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 21, normalized size = 0.6 \begin{align*} -{\frac{-12\,bx+9\,a}{28\,{b}^{2}} \left ( bx+a \right ) ^{{\frac{4}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.08618, size = 35, normalized size = 1.03 \begin{align*} \frac{3 \,{\left (b x + a\right )}^{\frac{7}{3}}}{7 \, b^{2}} - \frac{3 \,{\left (b x + a\right )}^{\frac{4}{3}} a}{4 \, b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.70608, size = 73, normalized size = 2.15 \begin{align*} \frac{3 \,{\left (4 \, b^{2} x^{2} + a b x - 3 \, a^{2}\right )}{\left (b x + a\right )}^{\frac{1}{3}}}{28 \, b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.63821, size = 202, normalized size = 5.94 \begin{align*} - \frac{9 a^{\frac{13}{3}} \sqrt [3]{1 + \frac{b x}{a}}}{28 a^{2} b^{2} + 28 a b^{3} x} + \frac{9 a^{\frac{13}{3}}}{28 a^{2} b^{2} + 28 a b^{3} x} - \frac{6 a^{\frac{10}{3}} b x \sqrt [3]{1 + \frac{b x}{a}}}{28 a^{2} b^{2} + 28 a b^{3} x} + \frac{9 a^{\frac{10}{3}} b x}{28 a^{2} b^{2} + 28 a b^{3} x} + \frac{15 a^{\frac{7}{3}} b^{2} x^{2} \sqrt [3]{1 + \frac{b x}{a}}}{28 a^{2} b^{2} + 28 a b^{3} x} + \frac{12 a^{\frac{4}{3}} b^{3} x^{3} \sqrt [3]{1 + \frac{b x}{a}}}{28 a^{2} b^{2} + 28 a b^{3} x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.22147, size = 34, normalized size = 1. \begin{align*} \frac{3 \,{\left (4 \,{\left (b x + a\right )}^{\frac{7}{3}} - 7 \,{\left (b x + a\right )}^{\frac{4}{3}} a\right )}}{28 \, b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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