Optimal. Leaf size=23 \[ \frac{11}{100} (5 x+3)^4-\frac{2}{125} (5 x+3)^5 \]
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Rubi [A] time = 0.0064627, 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} \[ \frac{11}{100} (5 x+3)^4-\frac{2}{125} (5 x+3)^5 \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int (1-2 x) (3+5 x)^3 \, dx &=\int \left (\frac{11}{5} (3+5 x)^3-\frac{2}{5} (3+5 x)^4\right ) \, dx\\ &=\frac{11}{100} (3+5 x)^4-\frac{2}{125} (3+5 x)^5\\ \end{align*}
Mathematica [A] time = 0.0007083, size = 28, normalized size = 1.22 \[ -50 x^5-\frac{325 x^4}{4}-15 x^3+\frac{81 x^2}{2}+27 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 25, normalized size = 1.1 \begin{align*} -50\,{x}^{5}-{\frac{325\,{x}^{4}}{4}}-15\,{x}^{3}+{\frac{81\,{x}^{2}}{2}}+27\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.16429, size = 32, normalized size = 1.39 \begin{align*} -50 \, x^{5} - \frac{325}{4} \, x^{4} - 15 \, x^{3} + \frac{81}{2} \, x^{2} + 27 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.4937, size = 65, normalized size = 2.83 \begin{align*} -50 x^{5} - \frac{325}{4} x^{4} - 15 x^{3} + \frac{81}{2} x^{2} + 27 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.059436, size = 26, normalized size = 1.13 \begin{align*} - 50 x^{5} - \frac{325 x^{4}}{4} - 15 x^{3} + \frac{81 x^{2}}{2} + 27 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.44256, size = 32, normalized size = 1.39 \begin{align*} -50 \, x^{5} - \frac{325}{4} \, x^{4} - 15 \, x^{3} + \frac{81}{2} \, x^{2} + 27 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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