Optimal. Leaf size=20 \[ 6^m x \, _2F_1\left (\frac{1}{2},-m;\frac{3}{2};4 x^2\right ) \]
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Rubi [A] time = 0.0057414, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {41, 245} \[ 6^m x \, _2F_1\left (\frac{1}{2},-m;\frac{3}{2};4 x^2\right ) \]
Antiderivative was successfully verified.
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Rule 41
Rule 245
Rubi steps
\begin{align*} \int (3-6 x)^m (2+4 x)^m \, dx &=\int \left (6-24 x^2\right )^m \, dx\\ &=6^m x \, _2F_1\left (\frac{1}{2},-m;\frac{3}{2};4 x^2\right )\\ \end{align*}
Mathematica [A] time = 0.0049051, size = 20, normalized size = 1. \[ 6^m x \, _2F_1\left (\frac{1}{2},-m;\frac{3}{2};4 x^2\right ) \]
Antiderivative was successfully verified.
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Maple [F] time = 0.073, size = 0, normalized size = 0. \begin{align*} \int \left ( 3-6\,x \right ) ^{m} \left ( 2+4\,x \right ) ^{m}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (4 \, x + 2\right )}^{m}{\left (-6 \, x + 3\right )}^{m}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left ({\left (4 \, x + 2\right )}^{m}{\left (-6 \, x + 3\right )}^{m}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [C] time = 4.61746, size = 42, normalized size = 2.1 \begin{align*} \frac{24^{m} \left (x + \frac{1}{2}\right ) \left (x + \frac{1}{2}\right )^{m} \Gamma \left (m + 1\right ){{}_{2}F_{1}\left (\begin{matrix} - m, m + 1 \\ m + 2 \end{matrix}\middle |{\left (x + \frac{1}{2}\right ) e^{2 i \pi }} \right )}}{\Gamma \left (m + 2\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (4 \, x + 2\right )}^{m}{\left (-6 \, x + 3\right )}^{m}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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