Optimal. Leaf size=40 \[ -\frac {25}{44} (1-2 x)^{11/2}+\frac {55}{18} (1-2 x)^{9/2}-\frac {121}{28} (1-2 x)^{7/2} \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 40, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {43} \begin {gather*} -\frac {25}{44} (1-2 x)^{11/2}+\frac {55}{18} (1-2 x)^{9/2}-\frac {121}{28} (1-2 x)^{7/2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin {align*} \int (1-2 x)^{5/2} (3+5 x)^2 \, dx &=\int \left (\frac {121}{4} (1-2 x)^{5/2}-\frac {55}{2} (1-2 x)^{7/2}+\frac {25}{4} (1-2 x)^{9/2}\right ) \, dx\\ &=-\frac {121}{28} (1-2 x)^{7/2}+\frac {55}{18} (1-2 x)^{9/2}-\frac {25}{44} (1-2 x)^{11/2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 23, normalized size = 0.58 \begin {gather*} -\frac {1}{693} (1-2 x)^{7/2} \left (1575 x^2+2660 x+1271\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.02, size = 38, normalized size = 0.95 \begin {gather*} \frac {-1575 (1-2 x)^{11/2}+8470 (1-2 x)^{9/2}-11979 (1-2 x)^{7/2}}{2772} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.50, size = 34, normalized size = 0.85 \begin {gather*} \frac {1}{693} \, {\left (12600 \, x^{5} + 2380 \, x^{4} - 12302 \, x^{3} - 867 \, x^{2} + 4966 \, x - 1271\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.95, size = 49, normalized size = 1.22 \begin {gather*} \frac {25}{44} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {55}{18} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {121}{28} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 20, normalized size = 0.50 \begin {gather*} -\frac {\left (1575 x^{2}+2660 x +1271\right ) \left (-2 x +1\right )^{\frac {7}{2}}}{693} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.60, size = 28, normalized size = 0.70 \begin {gather*} -\frac {25}{44} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {55}{18} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {121}{28} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 23, normalized size = 0.58 \begin {gather*} -\frac {{\left (1-2\,x\right )}^{7/2}\,\left (16940\,x+1575\,{\left (2\,x-1\right )}^2+3509\right )}{2772} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 1.67, size = 85, normalized size = 2.12 \begin {gather*} \frac {200 x^{5} \sqrt {1 - 2 x}}{11} + \frac {340 x^{4} \sqrt {1 - 2 x}}{99} - \frac {12302 x^{3} \sqrt {1 - 2 x}}{693} - \frac {289 x^{2} \sqrt {1 - 2 x}}{231} + \frac {4966 x \sqrt {1 - 2 x}}{693} - \frac {1271 \sqrt {1 - 2 x}}{693} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________