Optimal. Leaf size=66 \[ -\frac {27}{16} (1-2 x)^{5/2}+\frac {207}{8} (1-2 x)^{3/2}-\frac {1071}{4} \sqrt {1-2 x}-\frac {3283}{8 \sqrt {1-2 x}}+\frac {3773}{48 (1-2 x)^{3/2}} \]
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Rubi [A] time = 0.01, antiderivative size = 66, 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} \[ -\frac {27}{16} (1-2 x)^{5/2}+\frac {207}{8} (1-2 x)^{3/2}-\frac {1071}{4} \sqrt {1-2 x}-\frac {3283}{8 \sqrt {1-2 x}}+\frac {3773}{48 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x)^3 (3+5 x)}{(1-2 x)^{5/2}} \, dx &=\int \left (\frac {3773}{16 (1-2 x)^{5/2}}-\frac {3283}{8 (1-2 x)^{3/2}}+\frac {1071}{4 \sqrt {1-2 x}}-\frac {621}{8} \sqrt {1-2 x}+\frac {135}{16} (1-2 x)^{3/2}\right ) \, dx\\ &=\frac {3773}{48 (1-2 x)^{3/2}}-\frac {3283}{8 \sqrt {1-2 x}}-\frac {1071}{4} \sqrt {1-2 x}+\frac {207}{8} (1-2 x)^{3/2}-\frac {27}{16} (1-2 x)^{5/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 33, normalized size = 0.50 \[ -\frac {81 x^4+459 x^3+2403 x^2-5250 x+1726}{3 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.06, size = 41, normalized size = 0.62 \[ -\frac {{\left (81 \, x^{4} + 459 \, x^{3} + 2403 \, x^{2} - 5250 \, x + 1726\right )} \sqrt {-2 \, x + 1}}{3 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.24, size = 56, normalized size = 0.85 \[ -\frac {27}{16} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {207}{8} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {1071}{4} \, \sqrt {-2 \, x + 1} - \frac {49 \, {\left (804 \, x - 325\right )}}{48 \, {\left (2 \, x - 1\right )} \sqrt {-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 30, normalized size = 0.45 \[ -\frac {81 x^{4}+459 x^{3}+2403 x^{2}-5250 x +1726}{3 \left (-2 x +1\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 42, normalized size = 0.64 \[ -\frac {27}{16} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {207}{8} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {1071}{4} \, \sqrt {-2 \, x + 1} + \frac {49 \, {\left (804 \, x - 325\right )}}{48 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 41, normalized size = 0.62 \[ \frac {\frac {3283\,x}{4}-\frac {15925}{48}}{{\left (1-2\,x\right )}^{3/2}}-\frac {1071\,\sqrt {1-2\,x}}{4}+\frac {207\,{\left (1-2\,x\right )}^{3/2}}{8}-\frac {27\,{\left (1-2\,x\right )}^{5/2}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 23.23, size = 58, normalized size = 0.88 \[ - \frac {27 \left (1 - 2 x\right )^{\frac {5}{2}}}{16} + \frac {207 \left (1 - 2 x\right )^{\frac {3}{2}}}{8} - \frac {1071 \sqrt {1 - 2 x}}{4} - \frac {3283}{8 \sqrt {1 - 2 x}} + \frac {3773}{48 \left (1 - 2 x\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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