Optimal. Leaf size=53 \[ \frac {75}{56} (1-2 x)^{7/2}-\frac {101}{8} (1-2 x)^{5/2}+\frac {1133}{24} (1-2 x)^{3/2}-\frac {847}{8} \sqrt {1-2 x} \]
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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} \begin {gather*} \frac {75}{56} (1-2 x)^{7/2}-\frac {101}{8} (1-2 x)^{5/2}+\frac {1133}{24} (1-2 x)^{3/2}-\frac {847}{8} \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+5 x)^2}{\sqrt {1-2 x}} \, dx &=\int \left (\frac {847}{8 \sqrt {1-2 x}}-\frac {1133}{8} \sqrt {1-2 x}+\frac {505}{8} (1-2 x)^{3/2}-\frac {75}{8} (1-2 x)^{5/2}\right ) \, dx\\ &=-\frac {847}{8} \sqrt {1-2 x}+\frac {1133}{24} (1-2 x)^{3/2}-\frac {101}{8} (1-2 x)^{5/2}+\frac {75}{56} (1-2 x)^{7/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 28, normalized size = 0.53 \begin {gather*} -\frac {1}{21} \sqrt {1-2 x} \left (225 x^3+723 x^2+1091 x+1469\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 40, normalized size = 0.75 \begin {gather*} \frac {1}{168} \left (225 (1-2 x)^3-2121 (1-2 x)^2+7931 (1-2 x)-17787\right ) \sqrt {1-2 x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 24, normalized size = 0.45 \begin {gather*} -\frac {1}{21} \, {\left (225 \, x^{3} + 723 \, x^{2} + 1091 \, x + 1469\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.08, size = 51, normalized size = 0.96 \begin {gather*} -\frac {75}{56} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {101}{8} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {1133}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {847}{8} \, \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 = 25, normalized size = 0.47 \begin {gather*} -\frac {\left (225 x^{3}+723 x^{2}+1091 x +1469\right ) \sqrt {-2 x +1}}{21} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 37, normalized size = 0.70 \begin {gather*} \frac {75}{56} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {101}{8} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {1133}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {847}{8} \, \sqrt {-2 \, x + 1} \end {gather*}
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 \begin {gather*} \frac {1133\,{\left (1-2\,x\right )}^{3/2}}{24}-\frac {847\,\sqrt {1-2\,x}}{8}-\frac {101\,{\left (1-2\,x\right )}^{5/2}}{8}+\frac {75\,{\left (1-2\,x\right )}^{7/2}}{56} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 29.08, size = 46, normalized size = 0.87 \begin {gather*} \frac {75 \left (1 - 2 x\right )^{\frac {7}{2}}}{56} - \frac {101 \left (1 - 2 x\right )^{\frac {5}{2}}}{8} + \frac {1133 \left (1 - 2 x\right )^{\frac {3}{2}}}{24} - \frac {847 \sqrt {1 - 2 x}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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