Optimal. Leaf size=66 \[ -\frac{15}{16} (1-2 x)^{9/2}+\frac{621}{56} (1-2 x)^{7/2}-\frac{1071}{20} (1-2 x)^{5/2}+\frac{3283}{24} (1-2 x)^{3/2}-\frac{3773}{16} \sqrt{1-2 x} \]
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Rubi [A] time = 0.0117312, antiderivative size = 66, normalized size of antiderivative = 1., 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} \[ -\frac{15}{16} (1-2 x)^{9/2}+\frac{621}{56} (1-2 x)^{7/2}-\frac{1071}{20} (1-2 x)^{5/2}+\frac{3283}{24} (1-2 x)^{3/2}-\frac{3773}{16} \sqrt{1-2 x} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x)^3 (3+5 x)}{\sqrt{1-2 x}} \, dx &=\int \left (\frac{3773}{16 \sqrt{1-2 x}}-\frac{3283}{8} \sqrt{1-2 x}+\frac{1071}{4} (1-2 x)^{3/2}-\frac{621}{8} (1-2 x)^{5/2}+\frac{135}{16} (1-2 x)^{7/2}\right ) \, dx\\ &=-\frac{3773}{16} \sqrt{1-2 x}+\frac{3283}{24} (1-2 x)^{3/2}-\frac{1071}{20} (1-2 x)^{5/2}+\frac{621}{56} (1-2 x)^{7/2}-\frac{15}{16} (1-2 x)^{9/2}\\ \end{align*}
Mathematica [A] time = 0.011894, size = 33, normalized size = 0.5 \[ -\frac{1}{105} \sqrt{1-2 x} \left (1575 x^4+6165 x^3+10881 x^2+12434 x+14954\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 30, normalized size = 0.5 \begin{align*} -{\frac{1575\,{x}^{4}+6165\,{x}^{3}+10881\,{x}^{2}+12434\,x+14954}{105}\sqrt{1-2\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.13841, size = 62, normalized size = 0.94 \begin{align*} -\frac{15}{16} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{621}{56} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{1071}{20} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{3283}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{3773}{16} \, \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.29651, size = 101, normalized size = 1.53 \begin{align*} -\frac{1}{105} \,{\left (1575 \, x^{4} + 6165 \, x^{3} + 10881 \, x^{2} + 12434 \, x + 14954\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 30.2322, size = 58, normalized size = 0.88 \begin{align*} - \frac{15 \left (1 - 2 x\right )^{\frac{9}{2}}}{16} + \frac{621 \left (1 - 2 x\right )^{\frac{7}{2}}}{56} - \frac{1071 \left (1 - 2 x\right )^{\frac{5}{2}}}{20} + \frac{3283 \left (1 - 2 x\right )^{\frac{3}{2}}}{24} - \frac{3773 \sqrt{1 - 2 x}}{16} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.99692, size = 90, normalized size = 1.36 \begin{align*} -\frac{15}{16} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{621}{56} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{1071}{20} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{3283}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{3773}{16} \, \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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