Optimal. Leaf size=40 \[ -\frac{3}{4} (1-2 x)^{5/2}+\frac{17}{3} (1-2 x)^{3/2}-\frac{77}{4} \sqrt{1-2 x} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0076623, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{3}{4} (1-2 x)^{5/2}+\frac{17}{3} (1-2 x)^{3/2}-\frac{77}{4} \sqrt{1-2 x} \]
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 = 0.0081149, size = 23, normalized size = 0.57 \[ -\frac{1}{3} \sqrt{1-2 x} \left (9 x^2+25 x+43\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 20, normalized size = 0.5 \begin{align*} -{\frac{9\,{x}^{2}+25\,x+43}{3}\sqrt{1-2\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.33422, size = 38, normalized size = 0.95 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.35554, size = 55, normalized size = 1.38 \begin{align*} -\frac{1}{3} \,{\left (9 \, x^{2} + 25 \, x + 43\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 11.9852, size = 34, normalized size = 0.85 \begin{align*} - \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.58397, size = 47, normalized size = 1.18 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]