Optimal. Leaf size=53 \[ \frac{45}{104} (1-2 x)^{13/2}-\frac{309}{88} (1-2 x)^{11/2}+\frac{707}{72} (1-2 x)^{9/2}-\frac{77}{8} (1-2 x)^{7/2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0111987, antiderivative size = 53, 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} \[ \frac{45}{104} (1-2 x)^{13/2}-\frac{309}{88} (1-2 x)^{11/2}+\frac{707}{72} (1-2 x)^{9/2}-\frac{77}{8} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^{5/2} (2+3 x)^2 (3+5 x) \, dx &=\int \left (\frac{539}{8} (1-2 x)^{5/2}-\frac{707}{8} (1-2 x)^{7/2}+\frac{309}{8} (1-2 x)^{9/2}-\frac{45}{8} (1-2 x)^{11/2}\right ) \, dx\\ &=-\frac{77}{8} (1-2 x)^{7/2}+\frac{707}{72} (1-2 x)^{9/2}-\frac{309}{88} (1-2 x)^{11/2}+\frac{45}{104} (1-2 x)^{13/2}\\ \end{align*}
Mathematica [A] time = 0.0140419, size = 28, normalized size = 0.53 \[ -\frac{(1-2 x)^{7/2} \left (4455 x^3+11394 x^2+10540 x+3712\right )}{1287} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 25, normalized size = 0.5 \begin{align*} -{\frac{4455\,{x}^{3}+11394\,{x}^{2}+10540\,x+3712}{1287} \left ( 1-2\,x \right ) ^{{\frac{7}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.17884, size = 50, normalized size = 0.94 \begin{align*} \frac{45}{104} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{309}{88} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{707}{72} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{77}{8} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.45137, size = 134, normalized size = 2.53 \begin{align*} \frac{1}{1287} \,{\left (35640 \, x^{6} + 37692 \, x^{5} - 25678 \, x^{4} - 32875 \, x^{3} + 7302 \, x^{2} + 11732 \, x - 3712\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 1.99465, size = 100, normalized size = 1.89 \begin{align*} \frac{360 x^{6} \sqrt{1 - 2 x}}{13} + \frac{4188 x^{5} \sqrt{1 - 2 x}}{143} - \frac{25678 x^{4} \sqrt{1 - 2 x}}{1287} - \frac{32875 x^{3} \sqrt{1 - 2 x}}{1287} + \frac{2434 x^{2} \sqrt{1 - 2 x}}{429} + \frac{11732 x \sqrt{1 - 2 x}}{1287} - \frac{3712 \sqrt{1 - 2 x}}{1287} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.79047, size = 88, normalized size = 1.66 \begin{align*} \frac{45}{104} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{309}{88} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{707}{72} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{77}{8} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]