Optimal. Leaf size=40 \[ -\frac {3}{4} (1-2 x)^{5/2}+\frac {17}{3} (1-2 x)^{3/2}-\frac {77}{4} \sqrt {1-2 x} \]
________________________________________________________________________________________
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 {3}{4} (1-2 x)^{5/2}+\frac {17}{3} (1-2 x)^{3/2}-\frac {77}{4} \sqrt {1-2 x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x) (3+5 x)}{\sqrt {1-2 x}} \, dx &=\int \left (\frac {77}{4 \sqrt {1-2 x}}-17 \sqrt {1-2 x}+\frac {15}{4} (1-2 x)^{3/2}\right ) \, dx\\ &=-\frac {77}{4} \sqrt {1-2 x}+\frac {17}{3} (1-2 x)^{3/2}-\frac {3}{4} (1-2 x)^{5/2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 23, normalized size = 0.58 \begin {gather*} -\frac {1}{3} \sqrt {1-2 x} \left (9 x^2+25 x+43\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.01, size = 31, normalized size = 0.78 \begin {gather*} -\frac {1}{12} \left (9 (1-2 x)^2-68 (1-2 x)+231\right ) \sqrt {1-2 x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.50, size = 19, normalized size = 0.48 \begin {gather*} -\frac {1}{3} \, {\left (9 \, x^{2} + 25 \, x + 43\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.88, size = 35, normalized size = 0.88 \begin {gather*} -\frac {3}{4} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {17}{3} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {77}{4} \, \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 (9 x^{2}+25 x +43\right ) \sqrt {-2 x +1}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.55, size = 28, normalized size = 0.70 \begin {gather*} -\frac {3}{4} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {17}{3} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {77}{4} \, \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.14, size = 23, normalized size = 0.58 \begin {gather*} -\frac {\sqrt {1-2\,x}\,\left (136\,x+9\,{\left (2\,x-1\right )}^2+163\right )}{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 16.84, size = 34, normalized size = 0.85 \begin {gather*} - \frac {3 \left (1 - 2 x\right )^{\frac {5}{2}}}{4} + \frac {17 \left (1 - 2 x\right )^{\frac {3}{2}}}{3} - \frac {77 \sqrt {1 - 2 x}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________