Optimal. Leaf size=92 \[ -\frac{375}{64} (1-2 x)^{9/2}+\frac{11475}{112} (1-2 x)^{7/2}-\frac{52011}{64} (1-2 x)^{5/2}+\frac{98209}{24} (1-2 x)^{3/2}-\frac{1334949}{64} \sqrt{1-2 x}-\frac{302379}{16 \sqrt{1-2 x}}+\frac{456533}{192 (1-2 x)^{3/2}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0170915, antiderivative size = 92, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042, Rules used = {88} \[ -\frac{375}{64} (1-2 x)^{9/2}+\frac{11475}{112} (1-2 x)^{7/2}-\frac{52011}{64} (1-2 x)^{5/2}+\frac{98209}{24} (1-2 x)^{3/2}-\frac{1334949}{64} \sqrt{1-2 x}-\frac{302379}{16 \sqrt{1-2 x}}+\frac{456533}{192 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^3 (3+5 x)^3}{(1-2 x)^{5/2}} \, dx &=\int \left (\frac{456533}{64 (1-2 x)^{5/2}}-\frac{302379}{16 (1-2 x)^{3/2}}+\frac{1334949}{64 \sqrt{1-2 x}}-\frac{98209}{8} \sqrt{1-2 x}+\frac{260055}{64} (1-2 x)^{3/2}-\frac{11475}{16} (1-2 x)^{5/2}+\frac{3375}{64} (1-2 x)^{7/2}\right ) \, dx\\ &=\frac{456533}{192 (1-2 x)^{3/2}}-\frac{302379}{16 \sqrt{1-2 x}}-\frac{1334949}{64} \sqrt{1-2 x}+\frac{98209}{24} (1-2 x)^{3/2}-\frac{52011}{64} (1-2 x)^{5/2}+\frac{11475}{112} (1-2 x)^{7/2}-\frac{375}{64} (1-2 x)^{9/2}\\ \end{align*}
Mathematica [A] time = 0.0178555, size = 43, normalized size = 0.47 \[ -\frac{7875 x^6+45225 x^5+130464 x^4+293785 x^3+1051833 x^2-2146758 x+714074}{21 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 40, normalized size = 0.4 \begin{align*} -{\frac{7875\,{x}^{6}+45225\,{x}^{5}+130464\,{x}^{4}+293785\,{x}^{3}+1051833\,{x}^{2}-2146758\,x+714074}{21} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 2.47299, size = 81, normalized size = 0.88 \begin{align*} -\frac{375}{64} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{11475}{112} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{52011}{64} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{98209}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{1334949}{64} \, \sqrt{-2 \, x + 1} + \frac{5929 \,{\left (1224 \, x - 535\right )}}{192 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.50993, size = 167, normalized size = 1.82 \begin{align*} -\frac{{\left (7875 \, x^{6} + 45225 \, x^{5} + 130464 \, x^{4} + 293785 \, x^{3} + 1051833 \, x^{2} - 2146758 \, x + 714074\right )} \sqrt{-2 \, x + 1}}{21 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 24.6692, size = 82, normalized size = 0.89 \begin{align*} - \frac{375 \left (1 - 2 x\right )^{\frac{9}{2}}}{64} + \frac{11475 \left (1 - 2 x\right )^{\frac{7}{2}}}{112} - \frac{52011 \left (1 - 2 x\right )^{\frac{5}{2}}}{64} + \frac{98209 \left (1 - 2 x\right )^{\frac{3}{2}}}{24} - \frac{1334949 \sqrt{1 - 2 x}}{64} - \frac{302379}{16 \sqrt{1 - 2 x}} + \frac{456533}{192 \left (1 - 2 x\right )^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.38325, size = 119, normalized size = 1.29 \begin{align*} -\frac{375}{64} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{11475}{112} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{52011}{64} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{98209}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{1334949}{64} \, \sqrt{-2 \, x + 1} - \frac{5929 \,{\left (1224 \, x - 535\right )}}{192 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]