Optimal. Leaf size=53 \[ \frac {125}{24} (1-2 x)^{3/2}-\frac {825}{8} \sqrt {1-2 x}-\frac {1815}{8 \sqrt {1-2 x}}+\frac {1331}{24 (1-2 x)^{3/2}} \]
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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 = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {43} \[ \frac {125}{24} (1-2 x)^{3/2}-\frac {825}{8} \sqrt {1-2 x}-\frac {1815}{8 \sqrt {1-2 x}}+\frac {1331}{24 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(3+5 x)^3}{(1-2 x)^{5/2}} \, dx &=\int \left (\frac {1331}{8 (1-2 x)^{5/2}}-\frac {1815}{8 (1-2 x)^{3/2}}+\frac {825}{8 \sqrt {1-2 x}}-\frac {125}{8} \sqrt {1-2 x}\right ) \, dx\\ &=\frac {1331}{24 (1-2 x)^{3/2}}-\frac {1815}{8 \sqrt {1-2 x}}-\frac {825}{8} \sqrt {1-2 x}+\frac {125}{24} (1-2 x)^{3/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 28, normalized size = 0.53 \[ -\frac {125 x^3+1050 x^2-2505 x+808}{3 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 36, normalized size = 0.68 \[ -\frac {{\left (125 \, x^{3} + 1050 \, x^{2} - 2505 \, x + 808\right )} \sqrt {-2 \, x + 1}}{3 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.23, size = 40, normalized size = 0.75 \[ \frac {125}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {825}{8} \, \sqrt {-2 \, x + 1} - \frac {121 \, {\left (45 \, x - 17\right )}}{12 \, {\left (2 \, x - 1\right )} \sqrt {-2 \, x + 1}} \]
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 \[ -\frac {125 x^{3}+1050 x^{2}-2505 x +808}{3 \left (-2 x +1\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 33, normalized size = 0.62 \[ \frac {125}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {825}{8} \, \sqrt {-2 \, x + 1} + \frac {121 \, {\left (45 \, x - 17\right )}}{12 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 38, normalized size = 0.72 \[ \frac {2475\,{\left (2\,x-1\right )}^2-10890\,x+125\,{\left (2\,x-1\right )}^3+4114}{\sqrt {1-2\,x}\,\left (48\,x-24\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.68, size = 102, normalized size = 1.92 \[ \frac {125 x^{3}}{6 x \sqrt {1 - 2 x} - 3 \sqrt {1 - 2 x}} + \frac {1050 x^{2}}{6 x \sqrt {1 - 2 x} - 3 \sqrt {1 - 2 x}} - \frac {2505 x}{6 x \sqrt {1 - 2 x} - 3 \sqrt {1 - 2 x}} + \frac {808}{6 x \sqrt {1 - 2 x} - 3 \sqrt {1 - 2 x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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