Optimal. Leaf size=53 \[ \frac {45}{56} (1-2 x)^{7/2}-\frac {309}{40} (1-2 x)^{5/2}+\frac {707}{24} (1-2 x)^{3/2}-\frac {539}{8} \sqrt {1-2 x} \]
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Rubi [A] time = 0.01, antiderivative size = 53, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {77} \[ \frac {45}{56} (1-2 x)^{7/2}-\frac {309}{40} (1-2 x)^{5/2}+\frac {707}{24} (1-2 x)^{3/2}-\frac {539}{8} \sqrt {1-2 x} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x)^2 (3+5 x)}{\sqrt {1-2 x}} \, dx &=\int \left (\frac {539}{8 \sqrt {1-2 x}}-\frac {707}{8} \sqrt {1-2 x}+\frac {309}{8} (1-2 x)^{3/2}-\frac {45}{8} (1-2 x)^{5/2}\right ) \, dx\\ &=-\frac {539}{8} \sqrt {1-2 x}+\frac {707}{24} (1-2 x)^{3/2}-\frac {309}{40} (1-2 x)^{5/2}+\frac {45}{56} (1-2 x)^{7/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 28, normalized size = 0.53 \[ -\frac {1}{105} \sqrt {1-2 x} \left (675 x^3+2232 x^2+3448 x+4708\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.87, size = 24, normalized size = 0.45 \[ -\frac {1}{105} \, {\left (675 \, x^{3} + 2232 \, x^{2} + 3448 \, x + 4708\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.94, size = 51, normalized size = 0.96 \[ -\frac {45}{56} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {309}{40} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {707}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {539}{8} \, \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.47 \[ -\frac {\left (675 x^{3}+2232 x^{2}+3448 x +4708\right ) \sqrt {-2 x +1}}{105} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 37, normalized size = 0.70 \[ \frac {45}{56} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {309}{40} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {707}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {539}{8} \, \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 37, normalized size = 0.70 \[ \frac {707\,{\left (1-2\,x\right )}^{3/2}}{24}-\frac {539\,\sqrt {1-2\,x}}{8}-\frac {309\,{\left (1-2\,x\right )}^{5/2}}{40}+\frac {45\,{\left (1-2\,x\right )}^{7/2}}{56} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 28.64, size = 46, normalized size = 0.87 \[ \frac {45 \left (1 - 2 x\right )^{\frac {7}{2}}}{56} - \frac {309 \left (1 - 2 x\right )^{\frac {5}{2}}}{40} + \frac {707 \left (1 - 2 x\right )^{\frac {3}{2}}}{24} - \frac {539 \sqrt {1 - 2 x}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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