Optimal. Leaf size=23 \[ \frac{1}{4} (1-2 x)^5-\frac{11}{16} (1-2 x)^4 \]
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Rubi [A] time = 0.0051903, antiderivative size = 23, 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} \[ \frac{1}{4} (1-2 x)^5-\frac{11}{16} (1-2 x)^4 \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int (1-2 x)^3 (3+5 x) \, dx &=\int \left (\frac{11}{2} (1-2 x)^3-\frac{5}{2} (1-2 x)^4\right ) \, dx\\ &=-\frac{11}{16} (1-2 x)^4+\frac{1}{4} (1-2 x)^5\\ \end{align*}
Mathematica [A] time = 0.0006997, size = 26, normalized size = 1.13 \[ -8 x^5+9 x^4+2 x^3-\frac{13 x^2}{2}+3 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 25, normalized size = 1.1 \begin{align*} -8\,{x}^{5}+9\,{x}^{4}+2\,{x}^{3}-{\frac{13\,{x}^{2}}{2}}+3\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03892, size = 32, normalized size = 1.39 \begin{align*} -8 \, x^{5} + 9 \, x^{4} + 2 \, x^{3} - \frac{13}{2} \, x^{2} + 3 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.1303, size = 55, normalized size = 2.39 \begin{align*} -8 x^{5} + 9 x^{4} + 2 x^{3} - \frac{13}{2} x^{2} + 3 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.059095, size = 24, normalized size = 1.04 \begin{align*} - 8 x^{5} + 9 x^{4} + 2 x^{3} - \frac{13 x^{2}}{2} + 3 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.45975, size = 32, normalized size = 1.39 \begin{align*} -8 \, x^{5} + 9 \, x^{4} + 2 \, x^{3} - \frac{13}{2} \, x^{2} + 3 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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