Optimal. Leaf size=66 \[ -\frac {135}{112} (1-2 x)^{7/2}+\frac {621}{40} (1-2 x)^{5/2}-\frac {357}{4} (1-2 x)^{3/2}+\frac {3283}{8} \sqrt {1-2 x}+\frac {3773}{16 \sqrt {1-2 x}} \]
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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} \begin {gather*} -\frac {135}{112} (1-2 x)^{7/2}+\frac {621}{40} (1-2 x)^{5/2}-\frac {357}{4} (1-2 x)^{3/2}+\frac {3283}{8} \sqrt {1-2 x}+\frac {3773}{16 \sqrt {1-2 x}} \end {gather*}
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)^{3/2}} \, dx &=\int \left (\frac {3773}{16 (1-2 x)^{3/2}}-\frac {3283}{8 \sqrt {1-2 x}}+\frac {1071}{4} \sqrt {1-2 x}-\frac {621}{8} (1-2 x)^{3/2}+\frac {135}{16} (1-2 x)^{5/2}\right ) \, dx\\ &=\frac {3773}{16 \sqrt {1-2 x}}+\frac {3283}{8} \sqrt {1-2 x}-\frac {357}{4} (1-2 x)^{3/2}+\frac {621}{40} (1-2 x)^{5/2}-\frac {135}{112} (1-2 x)^{7/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 33, normalized size = 0.50 \begin {gather*} \frac {-675 x^4-2997 x^3-6987 x^2-19154 x+19994}{35 \sqrt {1-2 x}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 49, normalized size = 0.74 \begin {gather*} \frac {-675 (1-2 x)^4+8694 (1-2 x)^3-49980 (1-2 x)^2+229810 (1-2 x)+132055}{560 \sqrt {1-2 x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.52, size = 36, normalized size = 0.55 \begin {gather*} \frac {{\left (675 \, x^{4} + 2997 \, x^{3} + 6987 \, x^{2} + 19154 \, x - 19994\right )} \sqrt {-2 \, x + 1}}{35 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.22, size = 60, normalized size = 0.91 \begin {gather*} \frac {135}{112} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {621}{40} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {357}{4} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {3283}{8} \, \sqrt {-2 \, x + 1} + \frac {3773}{16 \, \sqrt {-2 \, x + 1}} \end {gather*}
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 \begin {gather*} -\frac {675 x^{4}+2997 x^{3}+6987 x^{2}+19154 x -19994}{35 \sqrt {-2 x +1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 46, normalized size = 0.70 \begin {gather*} -\frac {135}{112} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {621}{40} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {357}{4} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {3283}{8} \, \sqrt {-2 \, x + 1} + \frac {3773}{16 \, \sqrt {-2 \, x + 1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 46, normalized size = 0.70 \begin {gather*} \frac {3773}{16\,\sqrt {1-2\,x}}+\frac {3283\,\sqrt {1-2\,x}}{8}-\frac {357\,{\left (1-2\,x\right )}^{3/2}}{4}+\frac {621\,{\left (1-2\,x\right )}^{5/2}}{40}-\frac {135\,{\left (1-2\,x\right )}^{7/2}}{112} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 24.80, size = 58, normalized size = 0.88 \begin {gather*} - \frac {135 \left (1 - 2 x\right )^{\frac {7}{2}}}{112} + \frac {621 \left (1 - 2 x\right )^{\frac {5}{2}}}{40} - \frac {357 \left (1 - 2 x\right )^{\frac {3}{2}}}{4} + \frac {3283 \sqrt {1 - 2 x}}{8} + \frac {3773}{16 \sqrt {1 - 2 x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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