Optimal. Leaf size=40 \[ -\frac{25}{12} (1-2 x)^{3/2}+\frac{55}{2} \sqrt{1-2 x}+\frac{121}{4 \sqrt{1-2 x}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0073006, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {43} \[ -\frac{25}{12} (1-2 x)^{3/2}+\frac{55}{2} \sqrt{1-2 x}+\frac{121}{4 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin{align*} \int \frac{(3+5 x)^2}{(1-2 x)^{3/2}} \, dx &=\int \left (\frac{121}{4 (1-2 x)^{3/2}}-\frac{55}{2 \sqrt{1-2 x}}+\frac{25}{4} \sqrt{1-2 x}\right ) \, dx\\ &=\frac{121}{4 \sqrt{1-2 x}}+\frac{55}{2} \sqrt{1-2 x}-\frac{25}{12} (1-2 x)^{3/2}\\ \end{align*}
Mathematica [A] time = 0.0077595, size = 23, normalized size = 0.57 \[ \frac{-25 x^2-140 x+167}{3 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 20, normalized size = 0.5 \begin{align*} -{\frac{25\,{x}^{2}+140\,x-167}{3}{\frac{1}{\sqrt{1-2\,x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.14202, size = 38, normalized size = 0.95 \begin{align*} -\frac{25}{12} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{55}{2} \, \sqrt{-2 \, x + 1} + \frac{121}{4 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.53854, size = 72, normalized size = 1.8 \begin{align*} \frac{{\left (25 \, x^{2} + 140 \, x - 167\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 [B] time = 1.2354, size = 352, normalized size = 8.8 \begin{align*} \begin{cases} \frac{25 \sqrt{55} i \left (x + \frac{3}{5}\right )^{2} \sqrt{10 x - 5}}{30 \sqrt{11} \left (x + \frac{3}{5}\right ) - 33 \sqrt{11}} + \frac{110 \sqrt{55} i \left (x + \frac{3}{5}\right ) \sqrt{10 x - 5}}{30 \sqrt{11} \left (x + \frac{3}{5}\right ) - 33 \sqrt{11}} - \frac{2420 \sqrt{5} \left (x + \frac{3}{5}\right )}{30 \sqrt{11} \left (x + \frac{3}{5}\right ) - 33 \sqrt{11}} - \frac{242 \sqrt{55} i \sqrt{10 x - 5}}{30 \sqrt{11} \left (x + \frac{3}{5}\right ) - 33 \sqrt{11}} + \frac{2662 \sqrt{5}}{30 \sqrt{11} \left (x + \frac{3}{5}\right ) - 33 \sqrt{11}} & \text{for}\: \frac{10 \left |{x + \frac{3}{5}}\right |}{11} > 1 \\\frac{25 \sqrt{55} \sqrt{5 - 10 x} \left (x + \frac{3}{5}\right )^{2}}{30 \sqrt{11} \left (x + \frac{3}{5}\right ) - 33 \sqrt{11}} + \frac{110 \sqrt{55} \sqrt{5 - 10 x} \left (x + \frac{3}{5}\right )}{30 \sqrt{11} \left (x + \frac{3}{5}\right ) - 33 \sqrt{11}} - \frac{242 \sqrt{55} \sqrt{5 - 10 x}}{30 \sqrt{11} \left (x + \frac{3}{5}\right ) - 33 \sqrt{11}} - \frac{2420 \sqrt{5} \left (x + \frac{3}{5}\right )}{30 \sqrt{11} \left (x + \frac{3}{5}\right ) - 33 \sqrt{11}} + \frac{2662 \sqrt{5}}{30 \sqrt{11} \left (x + \frac{3}{5}\right ) - 33 \sqrt{11}} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.73506, size = 38, normalized size = 0.95 \begin{align*} -\frac{25}{12} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{55}{2} \, \sqrt{-2 \, x + 1} + \frac{121}{4 \, \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]