Optimal. Leaf size=66 \[ -\frac {375}{208} (1-2 x)^{13/2}+\frac {1675}{88} (1-2 x)^{11/2}-\frac {935}{12} (1-2 x)^{9/2}+\frac {8349}{56} (1-2 x)^{7/2}-\frac {9317}{80} (1-2 x)^{5/2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 66, normalized size of antiderivative = 1.00, 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} \[ -\frac {375}{208} (1-2 x)^{13/2}+\frac {1675}{88} (1-2 x)^{11/2}-\frac {935}{12} (1-2 x)^{9/2}+\frac {8349}{56} (1-2 x)^{7/2}-\frac {9317}{80} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int (1-2 x)^{3/2} (2+3 x) (3+5 x)^3 \, dx &=\int \left (\frac {9317}{16} (1-2 x)^{3/2}-\frac {8349}{8} (1-2 x)^{5/2}+\frac {2805}{4} (1-2 x)^{7/2}-\frac {1675}{8} (1-2 x)^{9/2}+\frac {375}{16} (1-2 x)^{11/2}\right ) \, dx\\ &=-\frac {9317}{80} (1-2 x)^{5/2}+\frac {8349}{56} (1-2 x)^{7/2}-\frac {935}{12} (1-2 x)^{9/2}+\frac {1675}{88} (1-2 x)^{11/2}-\frac {375}{208} (1-2 x)^{13/2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 33, normalized size = 0.50 \[ -\frac {(1-2 x)^{5/2} \left (433125 x^4+1420125 x^3+1899800 x^2+1295695 x+421301\right )}{15015} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.87, size = 39, normalized size = 0.59 \[ -\frac {1}{15015} \, {\left (1732500 \, x^{6} + 3948000 \, x^{5} + 2351825 \, x^{4} - 996295 \, x^{3} - 1597776 \, x^{2} - 389509 \, x + 421301\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.09, size = 81, normalized size = 1.23 \[ -\frac {375}{208} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} - \frac {1675}{88} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} - \frac {935}{12} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {8349}{56} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {9317}{80} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 30, normalized size = 0.45 \[ -\frac {\left (433125 x^{4}+1420125 x^{3}+1899800 x^{2}+1295695 x +421301\right ) \left (-2 x +1\right )^{\frac {5}{2}}}{15015} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.53, size = 46, normalized size = 0.70 \[ -\frac {375}{208} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} + \frac {1675}{88} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} - \frac {935}{12} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {8349}{56} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {9317}{80} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.02, size = 46, normalized size = 0.70 \[ \frac {8349\,{\left (1-2\,x\right )}^{7/2}}{56}-\frac {9317\,{\left (1-2\,x\right )}^{5/2}}{80}-\frac {935\,{\left (1-2\,x\right )}^{9/2}}{12}+\frac {1675\,{\left (1-2\,x\right )}^{11/2}}{88}-\frac {375\,{\left (1-2\,x\right )}^{13/2}}{208} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 13.31, size = 58, normalized size = 0.88 \[ - \frac {375 \left (1 - 2 x\right )^{\frac {13}{2}}}{208} + \frac {1675 \left (1 - 2 x\right )^{\frac {11}{2}}}{88} - \frac {935 \left (1 - 2 x\right )^{\frac {9}{2}}}{12} + \frac {8349 \left (1 - 2 x\right )^{\frac {7}{2}}}{56} - \frac {9317 \left (1 - 2 x\right )^{\frac {5}{2}}}{80} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________