Optimal. Leaf size=34 \[ \frac{2}{375} (5 x+3)^6-\frac{44}{625} (5 x+3)^5+\frac{121}{500} (5 x+3)^4 \]
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Rubi [A] time = 0.0140187, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {43} \[ \frac{2}{375} (5 x+3)^6-\frac{44}{625} (5 x+3)^5+\frac{121}{500} (5 x+3)^4 \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int (1-2 x)^2 (3+5 x)^3 \, dx &=\int \left (\frac{121}{25} (3+5 x)^3-\frac{44}{25} (3+5 x)^4+\frac{4}{25} (3+5 x)^5\right ) \, dx\\ &=\frac{121}{500} (3+5 x)^4-\frac{44}{625} (3+5 x)^5+\frac{2}{375} (3+5 x)^6\\ \end{align*}
Mathematica [A] time = 0.0007796, size = 35, normalized size = 1.03 \[ \frac{250 x^6}{3}+80 x^5-\frac{235 x^4}{4}-69 x^3+\frac{27 x^2}{2}+27 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 30, normalized size = 0.9 \begin{align*}{\frac{250\,{x}^{6}}{3}}+80\,{x}^{5}-{\frac{235\,{x}^{4}}{4}}-69\,{x}^{3}+{\frac{27\,{x}^{2}}{2}}+27\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.29515, size = 39, normalized size = 1.15 \begin{align*} \frac{250}{3} \, x^{6} + 80 \, x^{5} - \frac{235}{4} \, x^{4} - 69 \, x^{3} + \frac{27}{2} \, x^{2} + 27 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.27729, size = 80, normalized size = 2.35 \begin{align*} \frac{250}{3} x^{6} + 80 x^{5} - \frac{235}{4} x^{4} - 69 x^{3} + \frac{27}{2} x^{2} + 27 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.058746, size = 32, normalized size = 0.94 \begin{align*} \frac{250 x^{6}}{3} + 80 x^{5} - \frac{235 x^{4}}{4} - 69 x^{3} + \frac{27 x^{2}}{2} + 27 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.67304, size = 39, normalized size = 1.15 \begin{align*} \frac{250}{3} \, x^{6} + 80 \, x^{5} - \frac{235}{4} \, x^{4} - 69 \, x^{3} + \frac{27}{2} \, x^{2} + 27 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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