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 = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, 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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fricas [A] time = 0.68, size = 24, normalized size = 1.04 \[ -8 x^{5} + 9 x^{4} + 2 x^{3} - \frac {13}{2} x^{2} + 3 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.90, size = 24, normalized size = 1.04 \[ -8 \, x^{5} + 9 \, x^{4} + 2 \, x^{3} - \frac {13}{2} \, x^{2} + 3 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 1.09 \[ -8 x^{5}+9 x^{4}+2 x^{3}-\frac {13}{2} x^{2}+3 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 24, normalized size = 1.04 \[ -8 \, x^{5} + 9 \, x^{4} + 2 \, x^{3} - \frac {13}{2} \, x^{2} + 3 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 24, normalized size = 1.04 \[ -8\,x^5+9\,x^4+2\,x^3-\frac {13\,x^2}{2}+3\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 24, normalized size = 1.04 \[ - 8 x^{5} + 9 x^{4} + 2 x^{3} - \frac {13 x^{2}}{2} + 3 x \]
Verification of antiderivative is not currently implemented for this CAS.
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