Optimal. Leaf size=53 \[ \frac{15}{8} (1-2 x)^{5/2}-\frac{505}{24} (1-2 x)^{3/2}+\frac{1133}{8} \sqrt{1-2 x}+\frac{847}{8 \sqrt{1-2 x}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0099816, antiderivative size = 53, 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} \[ \frac{15}{8} (1-2 x)^{5/2}-\frac{505}{24} (1-2 x)^{3/2}+\frac{1133}{8} \sqrt{1-2 x}+\frac{847}{8 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x) (3+5 x)^2}{(1-2 x)^{3/2}} \, dx &=\int \left (\frac{847}{8 (1-2 x)^{3/2}}-\frac{1133}{8 \sqrt{1-2 x}}+\frac{505}{8} \sqrt{1-2 x}-\frac{75}{8} (1-2 x)^{3/2}\right ) \, dx\\ &=\frac{847}{8 \sqrt{1-2 x}}+\frac{1133}{8} \sqrt{1-2 x}-\frac{505}{24} (1-2 x)^{3/2}+\frac{15}{8} (1-2 x)^{5/2}\\ \end{align*}
Mathematica [A] time = 0.0101174, size = 28, normalized size = 0.53 \[ \frac{-45 x^3-185 x^2-631 x+685}{3 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 25, normalized size = 0.5 \begin{align*} -{\frac{45\,{x}^{3}+185\,{x}^{2}+631\,x-685}{3}{\frac{1}{\sqrt{1-2\,x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.23728, size = 50, normalized size = 0.94 \begin{align*} \frac{15}{8} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{505}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{1133}{8} \, \sqrt{-2 \, x + 1} + \frac{847}{8 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.59331, size = 85, normalized size = 1.6 \begin{align*} \frac{{\left (45 \, x^{3} + 185 \, x^{2} + 631 \, x - 685\right )} \sqrt{-2 \, x + 1}}{3 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 11.6723, size = 46, normalized size = 0.87 \begin{align*} \frac{15 \left (1 - 2 x\right )^{\frac{5}{2}}}{8} - \frac{505 \left (1 - 2 x\right )^{\frac{3}{2}}}{24} + \frac{1133 \sqrt{1 - 2 x}}{8} + \frac{847}{8 \sqrt{1 - 2 x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.27465, size = 59, normalized size = 1.11 \begin{align*} \frac{15}{8} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{505}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{1133}{8} \, \sqrt{-2 \, x + 1} + \frac{847}{8 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]