Optimal. Leaf size=40 \[ -\frac{1}{117} (4-3 x)^{13/3}+\frac{4}{45} (4-3 x)^{10/3}-\frac{16}{63} (4-3 x)^{7/3} \]
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Rubi [A] time = 0.0072651, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {43} \[ -\frac{1}{117} (4-3 x)^{13/3}+\frac{4}{45} (4-3 x)^{10/3}-\frac{16}{63} (4-3 x)^{7/3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int (4-3 x)^{4/3} x^2 \, dx &=\int \left (\frac{16}{9} (4-3 x)^{4/3}-\frac{8}{9} (4-3 x)^{7/3}+\frac{1}{9} (4-3 x)^{10/3}\right ) \, dx\\ &=-\frac{16}{63} (4-3 x)^{7/3}+\frac{4}{45} (4-3 x)^{10/3}-\frac{1}{117} (4-3 x)^{13/3}\\ \end{align*}
Mathematica [A] time = 0.012353, size = 23, normalized size = 0.57 \[ -\frac{1}{455} (4-3 x)^{7/3} \left (35 x^2+28 x+16\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 20, normalized size = 0.5 \begin{align*} -{\frac{35\,{x}^{2}+28\,x+16}{455} \left ( 4-3\,x \right ) ^{{\frac{7}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.959427, size = 38, normalized size = 0.95 \begin{align*} -\frac{1}{117} \,{\left (-3 \, x + 4\right )}^{\frac{13}{3}} + \frac{4}{45} \,{\left (-3 \, x + 4\right )}^{\frac{10}{3}} - \frac{16}{63} \,{\left (-3 \, x + 4\right )}^{\frac{7}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.76462, size = 90, normalized size = 2.25 \begin{align*} -\frac{1}{455} \,{\left (315 \, x^{4} - 588 \, x^{3} + 32 \, x^{2} + 64 \, x + 256\right )}{\left (-3 \, x + 4\right )}^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.71752, size = 180, normalized size = 4.5 \begin{align*} \begin{cases} - \frac{9 x^{4} \sqrt [3]{3 x - 4} e^{\frac{i \pi }{3}}}{13} + \frac{84 x^{3} \sqrt [3]{3 x - 4} e^{\frac{i \pi }{3}}}{65} - \frac{32 x^{2} \sqrt [3]{3 x - 4} e^{\frac{i \pi }{3}}}{455} - \frac{64 x \sqrt [3]{3 x - 4} e^{\frac{i \pi }{3}}}{455} - \frac{256 \sqrt [3]{3 x - 4} e^{\frac{i \pi }{3}}}{455} & \text{for}\: \frac{3 \left |{x}\right |}{4} > 1 \\- \frac{9 x^{4} \sqrt [3]{4 - 3 x}}{13} + \frac{84 x^{3} \sqrt [3]{4 - 3 x}}{65} - \frac{32 x^{2} \sqrt [3]{4 - 3 x}}{455} - \frac{64 x \sqrt [3]{4 - 3 x}}{455} - \frac{256 \sqrt [3]{4 - 3 x}}{455} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07843, size = 66, normalized size = 1.65 \begin{align*} -\frac{1}{117} \,{\left (3 \, x - 4\right )}^{4}{\left (-3 \, x + 4\right )}^{\frac{1}{3}} - \frac{4}{45} \,{\left (3 \, x - 4\right )}^{3}{\left (-3 \, x + 4\right )}^{\frac{1}{3}} - \frac{16}{63} \,{\left (3 \, x - 4\right )}^{2}{\left (-3 \, x + 4\right )}^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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