Optimal. Leaf size=27 \[ \frac {5}{18} (1-2 x)^{9/2}-\frac {11}{14} (1-2 x)^{7/2} \]
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Rubi [A] time = 0.00, antiderivative size = 27, normalized size of antiderivative = 1.00, 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} \[ \frac {5}{18} (1-2 x)^{9/2}-\frac {11}{14} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int (1-2 x)^{5/2} (3+5 x) \, dx &=\int \left (\frac {11}{2} (1-2 x)^{5/2}-\frac {5}{2} (1-2 x)^{7/2}\right ) \, dx\\ &=-\frac {11}{14} (1-2 x)^{7/2}+\frac {5}{18} (1-2 x)^{9/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 18, normalized size = 0.67 \[ -\frac {1}{63} (1-2 x)^{7/2} (35 x+32) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 29, normalized size = 1.07 \[ \frac {1}{63} \, {\left (280 \, x^{4} - 164 \, x^{3} - 174 \, x^{2} + 157 \, x - 32\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.95, size = 33, normalized size = 1.22 \[ \frac {5}{18} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {11}{14} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.56 \[ -\frac {\left (35 x +32\right ) \left (-2 x +1\right )^{\frac {7}{2}}}{63} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 19, normalized size = 0.70 \[ \frac {5}{18} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {11}{14} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 14, normalized size = 0.52 \[ -\frac {{\left (1-2\,x\right )}^{7/2}\,\left (70\,x+64\right )}{126} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.14, size = 70, normalized size = 2.59 \[ \frac {40 x^{4} \sqrt {1 - 2 x}}{9} - \frac {164 x^{3} \sqrt {1 - 2 x}}{63} - \frac {58 x^{2} \sqrt {1 - 2 x}}{21} + \frac {157 x \sqrt {1 - 2 x}}{63} - \frac {32 \sqrt {1 - 2 x}}{63} \]
Verification of antiderivative is not currently implemented for this CAS.
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