Optimal. Leaf size=34 \[ \frac {3 (a+b x)^{10/3}}{10 b^2}-\frac {3 a (a+b x)^{7/3}}{7 b^2} \]
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Rubi [A] time = 0.01, antiderivative size = 34, normalized size of antiderivative = 1.00, 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} \[ \frac {3 (a+b x)^{10/3}}{10 b^2}-\frac {3 a (a+b x)^{7/3}}{7 b^2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int x (a+b x)^{4/3} \, dx &=\int \left (-\frac {a (a+b x)^{4/3}}{b}+\frac {(a+b x)^{7/3}}{b}\right ) \, dx\\ &=-\frac {3 a (a+b x)^{7/3}}{7 b^2}+\frac {3 (a+b x)^{10/3}}{10 b^2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 24, normalized size = 0.71 \[ \frac {3 (a+b x)^{7/3} (7 b x-3 a)}{70 b^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 41, normalized size = 1.21 \[ \frac {3 \, {\left (7 \, b^{3} x^{3} + 11 \, a b^{2} x^{2} + a^{2} b x - 3 \, a^{3}\right )} {\left (b x + a\right )}^{\frac {1}{3}}}{70 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.02, size = 118, normalized size = 3.47 \[ \frac {3 \, {\left (\frac {35 \, {\left ({\left (b x + a\right )}^{\frac {4}{3}} - 4 \, {\left (b x + a\right )}^{\frac {1}{3}} a\right )} a^{2}}{b} + \frac {20 \, {\left (2 \, {\left (b x + a\right )}^{\frac {7}{3}} - 7 \, {\left (b x + a\right )}^{\frac {4}{3}} a + 14 \, {\left (b x + a\right )}^{\frac {1}{3}} a^{2}\right )} a}{b} + \frac {14 \, {\left (b x + a\right )}^{\frac {10}{3}} - 60 \, {\left (b x + a\right )}^{\frac {7}{3}} a + 105 \, {\left (b x + a\right )}^{\frac {4}{3}} a^{2} - 140 \, {\left (b x + a\right )}^{\frac {1}{3}} a^{3}}{b}\right )}}{140 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 21, normalized size = 0.62 \[ -\frac {3 \left (b x +a \right )^{\frac {7}{3}} \left (-7 b x +3 a \right )}{70 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.29, size = 26, normalized size = 0.76 \[ \frac {3 \, {\left (b x + a\right )}^{\frac {10}{3}}}{10 \, b^{2}} - \frac {3 \, {\left (b x + a\right )}^{\frac {7}{3}} a}{7 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 25, normalized size = 0.74 \[ -\frac {30\,a\,{\left (a+b\,x\right )}^{7/3}-21\,{\left (a+b\,x\right )}^{10/3}}{70\,b^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.49, size = 80, normalized size = 2.35 \[ \begin {cases} - \frac {9 a^{3} \sqrt [3]{a + b x}}{70 b^{2}} + \frac {3 a^{2} x \sqrt [3]{a + b x}}{70 b} + \frac {33 a x^{2} \sqrt [3]{a + b x}}{70} + \frac {3 b x^{3} \sqrt [3]{a + b x}}{10} & \text {for}\: b \neq 0 \\\frac {a^{\frac {4}{3}} x^{2}}{2} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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