Optimal. Leaf size=40 \[ -\frac {5}{4} (1-2 x)^{5/2}+\frac {55}{6} (1-2 x)^{3/2}-\frac {121}{4} \sqrt {1-2 x} \]
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Rubi [A] time = 0.01, antiderivative size = 40, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {43} \[ -\frac {5}{4} (1-2 x)^{5/2}+\frac {55}{6} (1-2 x)^{3/2}-\frac {121}{4} \sqrt {1-2 x} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(3+5 x)^2}{\sqrt {1-2 x}} \, dx &=\int \left (\frac {121}{4 \sqrt {1-2 x}}-\frac {55}{2} \sqrt {1-2 x}+\frac {25}{4} (1-2 x)^{3/2}\right ) \, dx\\ &=-\frac {121}{4} \sqrt {1-2 x}+\frac {55}{6} (1-2 x)^{3/2}-\frac {5}{4} (1-2 x)^{5/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 0.58 \[ -\frac {1}{3} \sqrt {1-2 x} \left (15 x^2+40 x+67\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.93, size = 19, normalized size = 0.48 \[ -\frac {1}{3} \, {\left (15 \, x^{2} + 40 \, x + 67\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.02, size = 35, normalized size = 0.88 \[ -\frac {5}{4} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {55}{6} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {121}{4} \, \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 20, normalized size = 0.50 \[ -\frac {\left (15 x^{2}+40 x +67\right ) \sqrt {-2 x +1}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.64, size = 28, normalized size = 0.70 \[ -\frac {5}{4} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {55}{6} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {121}{4} \, \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 23, normalized size = 0.58 \[ -\frac {\sqrt {1-2\,x}\,\left (220\,x+15\,{\left (2\,x-1\right )}^2+253\right )}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.39, size = 134, normalized size = 3.35 \[ \begin {cases} - \sqrt {5} i \left (x + \frac {3}{5}\right )^{2} \sqrt {10 x - 5} - \frac {22 \sqrt {5} i \left (x + \frac {3}{5}\right ) \sqrt {10 x - 5}}{15} - \frac {242 \sqrt {5} i \sqrt {10 x - 5}}{75} & \text {for}\: \frac {10 \left |{x + \frac {3}{5}}\right |}{11} > 1 \\- \sqrt {5} \sqrt {5 - 10 x} \left (x + \frac {3}{5}\right )^{2} - \frac {22 \sqrt {5} \sqrt {5 - 10 x} \left (x + \frac {3}{5}\right )}{15} - \frac {242 \sqrt {5} \sqrt {5 - 10 x}}{75} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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