Optimal. Leaf size=53 \[ \frac {15}{8} (1-2 x)^{5/2}-\frac {505}{24} (1-2 x)^{3/2}+\frac {1133}{8} \sqrt {1-2 x}+\frac {847}{8 \sqrt {1-2 x}} \]
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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} \[ \frac {15}{8} (1-2 x)^{5/2}-\frac {505}{24} (1-2 x)^{3/2}+\frac {1133}{8} \sqrt {1-2 x}+\frac {847}{8 \sqrt {1-2 x}} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x) (3+5 x)^2}{(1-2 x)^{3/2}} \, dx &=\int \left (\frac {847}{8 (1-2 x)^{3/2}}-\frac {1133}{8 \sqrt {1-2 x}}+\frac {505}{8} \sqrt {1-2 x}-\frac {75}{8} (1-2 x)^{3/2}\right ) \, dx\\ &=\frac {847}{8 \sqrt {1-2 x}}+\frac {1133}{8} \sqrt {1-2 x}-\frac {505}{24} (1-2 x)^{3/2}+\frac {15}{8} (1-2 x)^{5/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 28, normalized size = 0.53 \[ \frac {-45 x^3-185 x^2-631 x+685}{3 \sqrt {1-2 x}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 31, normalized size = 0.58 \[ \frac {{\left (45 \, x^{3} + 185 \, x^{2} + 631 \, x - 685\right )} \sqrt {-2 \, x + 1}}{3 \, {\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.20, size = 44, normalized size = 0.83 \[ \frac {15}{8} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {505}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {1133}{8} \, \sqrt {-2 \, x + 1} + \frac {847}{8 \, \sqrt {-2 \, x + 1}} \]
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 \[ -\frac {45 x^{3}+185 x^{2}+631 x -685}{3 \sqrt {-2 x +1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 37, normalized size = 0.70 \[ \frac {15}{8} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {505}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {1133}{8} \, \sqrt {-2 \, x + 1} + \frac {847}{8 \, \sqrt {-2 \, x + 1}} \]
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 \[ \frac {847}{8\,\sqrt {1-2\,x}}+\frac {1133\,\sqrt {1-2\,x}}{8}-\frac {505\,{\left (1-2\,x\right )}^{3/2}}{24}+\frac {15\,{\left (1-2\,x\right )}^{5/2}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 17.66, size = 46, normalized size = 0.87 \[ \frac {15 \left (1 - 2 x\right )^{\frac {5}{2}}}{8} - \frac {505 \left (1 - 2 x\right )^{\frac {3}{2}}}{24} + \frac {1133 \sqrt {1 - 2 x}}{8} + \frac {847}{8 \sqrt {1 - 2 x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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