Optimal. Leaf size=79 \[ \frac{405}{544} (1-2 x)^{17/2}-\frac{1557}{160} (1-2 x)^{15/2}+\frac{10773}{208} (1-2 x)^{13/2}-\frac{24843}{176} (1-2 x)^{11/2}+\frac{57281}{288} (1-2 x)^{9/2}-\frac{3773}{32} (1-2 x)^{7/2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0144892, antiderivative size = 79, 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} \[ \frac{405}{544} (1-2 x)^{17/2}-\frac{1557}{160} (1-2 x)^{15/2}+\frac{10773}{208} (1-2 x)^{13/2}-\frac{24843}{176} (1-2 x)^{11/2}+\frac{57281}{288} (1-2 x)^{9/2}-\frac{3773}{32} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^{5/2} (2+3 x)^4 (3+5 x) \, dx &=\int \left (\frac{26411}{32} (1-2 x)^{5/2}-\frac{57281}{32} (1-2 x)^{7/2}+\frac{24843}{16} (1-2 x)^{9/2}-\frac{10773}{16} (1-2 x)^{11/2}+\frac{4671}{32} (1-2 x)^{13/2}-\frac{405}{32} (1-2 x)^{15/2}\right ) \, dx\\ &=-\frac{3773}{32} (1-2 x)^{7/2}+\frac{57281}{288} (1-2 x)^{9/2}-\frac{24843}{176} (1-2 x)^{11/2}+\frac{10773}{208} (1-2 x)^{13/2}-\frac{1557}{160} (1-2 x)^{15/2}+\frac{405}{544} (1-2 x)^{17/2}\\ \end{align*}
Mathematica [A] time = 0.0190027, size = 38, normalized size = 0.48 \[ -\frac{(1-2 x)^{7/2} \left (2606175 x^5+10517364 x^4+17777232 x^3+16066296 x^2+8043328 x+1899184\right )}{109395} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 35, normalized size = 0.4 \begin{align*} -{\frac{2606175\,{x}^{5}+10517364\,{x}^{4}+17777232\,{x}^{3}+16066296\,{x}^{2}+8043328\,x+1899184}{109395} \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 = 1.15629, size = 74, normalized size = 0.94 \begin{align*} \frac{405}{544} \,{\left (-2 \, x + 1\right )}^{\frac{17}{2}} - \frac{1557}{160} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{10773}{208} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{24843}{176} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{57281}{288} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{3773}{32} \,{\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 = 1.51103, size = 203, normalized size = 2.57 \begin{align*} \frac{1}{109395} \,{\left (20849400 \, x^{8} + 52864812 \, x^{7} + 31646538 \, x^{6} - 24298407 \, x^{5} - 32302900 \, x^{4} - 2705920 \, x^{3} + 9403464 \, x^{2} + 3351776 \, x - 1899184\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 17.2586, size = 70, normalized size = 0.89 \begin{align*} \frac{405 \left (1 - 2 x\right )^{\frac{17}{2}}}{544} - \frac{1557 \left (1 - 2 x\right )^{\frac{15}{2}}}{160} + \frac{10773 \left (1 - 2 x\right )^{\frac{13}{2}}}{208} - \frac{24843 \left (1 - 2 x\right )^{\frac{11}{2}}}{176} + \frac{57281 \left (1 - 2 x\right )^{\frac{9}{2}}}{288} - \frac{3773 \left (1 - 2 x\right )^{\frac{7}{2}}}{32} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.22108, size = 131, normalized size = 1.66 \begin{align*} \frac{405}{544} \,{\left (2 \, x - 1\right )}^{8} \sqrt{-2 \, x + 1} + \frac{1557}{160} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} + \frac{10773}{208} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{24843}{176} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{57281}{288} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{3773}{32} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]