Optimal. Leaf size=53 \[ \frac {25}{24} (1-2 x)^{9/2}-\frac {505}{56} (1-2 x)^{7/2}+\frac {1133}{40} (1-2 x)^{5/2}-\frac {847}{24} (1-2 x)^{3/2} \]
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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 = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {77} \begin {gather*} \frac {25}{24} (1-2 x)^{9/2}-\frac {505}{56} (1-2 x)^{7/2}+\frac {1133}{40} (1-2 x)^{5/2}-\frac {847}{24} (1-2 x)^{3/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \sqrt {1-2 x} (2+3 x) (3+5 x)^2 \, dx &=\int \left (\frac {847}{8} \sqrt {1-2 x}-\frac {1133}{8} (1-2 x)^{3/2}+\frac {505}{8} (1-2 x)^{5/2}-\frac {75}{8} (1-2 x)^{7/2}\right ) \, dx\\ &=-\frac {847}{24} (1-2 x)^{3/2}+\frac {1133}{40} (1-2 x)^{5/2}-\frac {505}{56} (1-2 x)^{7/2}+\frac {25}{24} (1-2 x)^{9/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 28, normalized size = 0.53 \begin {gather*} -\frac {1}{105} (1-2 x)^{3/2} \left (875 x^3+2475 x^2+2817 x+1569\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}{840} \left (875 (1-2 x)^3-7575 (1-2 x)^2+23793 (1-2 x)-29645\right ) (1-2 x)^{3/2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.48, size = 29, normalized size = 0.55 \begin {gather*} \frac {1}{105} \, {\left (1750 \, x^{4} + 4075 \, x^{3} + 3159 \, x^{2} + 321 \, x - 1569\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.14, size = 58, normalized size = 1.09 \begin {gather*} \frac {25}{24} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {505}{56} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {1133}{40} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {847}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \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 (875 x^{3}+2475 x^{2}+2817 x +1569\right ) \left (-2 x +1\right )^{\frac {3}{2}}}{105} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 37, normalized size = 0.70 \begin {gather*} \frac {25}{24} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {505}{56} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {1133}{40} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {847}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \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 )}^{5/2}}{40}-\frac {847\,{\left (1-2\,x\right )}^{3/2}}{24}-\frac {505\,{\left (1-2\,x\right )}^{7/2}}{56}+\frac {25\,{\left (1-2\,x\right )}^{9/2}}{24} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.34, size = 46, normalized size = 0.87 \begin {gather*} \frac {25 \left (1 - 2 x\right )^{\frac {9}{2}}}{24} - \frac {505 \left (1 - 2 x\right )^{\frac {7}{2}}}{56} + \frac {1133 \left (1 - 2 x\right )^{\frac {5}{2}}}{40} - \frac {847 \left (1 - 2 x\right )^{\frac {3}{2}}}{24} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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