Optimal. Leaf size=92 \[ -\frac{1215 (1-2 x)^{19/2}}{1216}+\frac{1053}{68} (1-2 x)^{17/2}-\frac{6489}{64} (1-2 x)^{15/2}+\frac{37485}{104} (1-2 x)^{13/2}-\frac{519645}{704} (1-2 x)^{11/2}+\frac{60025}{72} (1-2 x)^{9/2}-\frac{26411}{64} (1-2 x)^{7/2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0160557, antiderivative size = 92, 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} \[ -\frac{1215 (1-2 x)^{19/2}}{1216}+\frac{1053}{68} (1-2 x)^{17/2}-\frac{6489}{64} (1-2 x)^{15/2}+\frac{37485}{104} (1-2 x)^{13/2}-\frac{519645}{704} (1-2 x)^{11/2}+\frac{60025}{72} (1-2 x)^{9/2}-\frac{26411}{64} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^{5/2} (2+3 x)^5 (3+5 x) \, dx &=\int \left (\frac{184877}{64} (1-2 x)^{5/2}-\frac{60025}{8} (1-2 x)^{7/2}+\frac{519645}{64} (1-2 x)^{9/2}-\frac{37485}{8} (1-2 x)^{11/2}+\frac{97335}{64} (1-2 x)^{13/2}-\frac{1053}{4} (1-2 x)^{15/2}+\frac{1215}{64} (1-2 x)^{17/2}\right ) \, dx\\ &=-\frac{26411}{64} (1-2 x)^{7/2}+\frac{60025}{72} (1-2 x)^{9/2}-\frac{519645}{704} (1-2 x)^{11/2}+\frac{37485}{104} (1-2 x)^{13/2}-\frac{6489}{64} (1-2 x)^{15/2}+\frac{1053}{68} (1-2 x)^{17/2}-\frac{1215 (1-2 x)^{19/2}}{1216}\\ \end{align*}
Mathematica [A] time = 0.0216755, size = 43, normalized size = 0.47 \[ -\frac{(1-2 x)^{7/2} \left (26582985 x^6+126243117 x^5+259076961 x^4+298438668 x^3+208370124 x^2+86950792 x+18122584\right )}{415701} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 40, normalized size = 0.4 \begin{align*} -{\frac{26582985\,{x}^{6}+126243117\,{x}^{5}+259076961\,{x}^{4}+298438668\,{x}^{3}+208370124\,{x}^{2}+86950792\,x+18122584}{415701} \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 = 2.87085, size = 86, normalized size = 0.93 \begin{align*} -\frac{1215}{1216} \,{\left (-2 \, x + 1\right )}^{\frac{19}{2}} + \frac{1053}{68} \,{\left (-2 \, x + 1\right )}^{\frac{17}{2}} - \frac{6489}{64} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{37485}{104} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{519645}{704} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{60025}{72} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{26411}{64} \,{\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 = 1.59597, size = 234, normalized size = 2.54 \begin{align*} \frac{1}{415701} \,{\left (212663880 \, x^{9} + 690949116 \, x^{8} + 717196194 \, x^{7} + 9461529 \, x^{6} - 486084375 \, x^{5} - 273280105 \, x^{4} + 53353244 \, x^{3} + 95863620 \, x^{2} + 21784712 \, x - 18122584\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 21.1789, size = 82, normalized size = 0.89 \begin{align*} - \frac{1215 \left (1 - 2 x\right )^{\frac{19}{2}}}{1216} + \frac{1053 \left (1 - 2 x\right )^{\frac{17}{2}}}{68} - \frac{6489 \left (1 - 2 x\right )^{\frac{15}{2}}}{64} + \frac{37485 \left (1 - 2 x\right )^{\frac{13}{2}}}{104} - \frac{519645 \left (1 - 2 x\right )^{\frac{11}{2}}}{704} + \frac{60025 \left (1 - 2 x\right )^{\frac{9}{2}}}{72} - \frac{26411 \left (1 - 2 x\right )^{\frac{7}{2}}}{64} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.49174, size = 153, normalized size = 1.66 \begin{align*} \frac{1215}{1216} \,{\left (2 \, x - 1\right )}^{9} \sqrt{-2 \, x + 1} + \frac{1053}{68} \,{\left (2 \, x - 1\right )}^{8} \sqrt{-2 \, x + 1} + \frac{6489}{64} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} + \frac{37485}{104} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{519645}{704} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{60025}{72} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{26411}{64} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]