Optimal. Leaf size=40 \[ -\frac {15}{28} (1-2 x)^{7/2}+\frac {17}{5} (1-2 x)^{5/2}-\frac {77}{12} (1-2 x)^{3/2} \]
________________________________________________________________________________________
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 = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} -\frac {15}{28} (1-2 x)^{7/2}+\frac {17}{5} (1-2 x)^{5/2}-\frac {77}{12} (1-2 x)^{3/2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int \sqrt {1-2 x} (2+3 x) (3+5 x) \, dx &=\int \left (\frac {77}{4} \sqrt {1-2 x}-17 (1-2 x)^{3/2}+\frac {15}{4} (1-2 x)^{5/2}\right ) \, dx\\ &=-\frac {77}{12} (1-2 x)^{3/2}+\frac {17}{5} (1-2 x)^{5/2}-\frac {15}{28} (1-2 x)^{7/2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 23, normalized size = 0.58 \begin {gather*} -\frac {1}{105} (1-2 x)^{3/2} \left (225 x^2+489 x+373\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.01, size = 38, normalized size = 0.95 \begin {gather*} \frac {1}{420} \left (-225 (1-2 x)^{7/2}+1428 (1-2 x)^{5/2}-2695 (1-2 x)^{3/2}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.47, size = 24, normalized size = 0.60 \begin {gather*} \frac {1}{105} \, {\left (450 \, x^{3} + 753 \, x^{2} + 257 \, x - 373\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.16, size = 42, normalized size = 1.05 \begin {gather*} \frac {15}{28} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {17}{5} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {77}{12} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \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 (225 x^{2}+489 x +373\right ) \left (-2 x +1\right )^{\frac {3}{2}}}{105} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.52, size = 28, normalized size = 0.70 \begin {gather*} -\frac {15}{28} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {17}{5} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {77}{12} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 23, normalized size = 0.58 \begin {gather*} -\frac {{\left (1-2\,x\right )}^{3/2}\,\left (2856\,x+225\,{\left (2\,x-1\right )}^2+1267\right )}{420} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 2.20, size = 34, normalized size = 0.85 \begin {gather*} - \frac {15 \left (1 - 2 x\right )^{\frac {7}{2}}}{28} + \frac {17 \left (1 - 2 x\right )^{\frac {5}{2}}}{5} - \frac {77 \left (1 - 2 x\right )^{\frac {3}{2}}}{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________