Optimal. Leaf size=21 \[ \frac{2 x^{3/2}}{3 a (a+b x)^{3/2}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.001626, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {37} \[ \frac{2 x^{3/2}}{3 a (a+b x)^{3/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 37
Rubi steps
\begin{align*} \int \frac{\sqrt{x}}{(a+b x)^{5/2}} \, dx &=\frac{2 x^{3/2}}{3 a (a+b x)^{3/2}}\\ \end{align*}
Mathematica [A] time = 0.005987, size = 21, normalized size = 1. \[ \frac{2 x^{3/2}}{3 a (a+b x)^{3/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 16, normalized size = 0.8 \begin{align*}{\frac{2}{3\,a}{x}^{{\frac{3}{2}}} \left ( bx+a \right ) ^{-{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.04428, size = 20, normalized size = 0.95 \begin{align*} \frac{2 \, x^{\frac{3}{2}}}{3 \,{\left (b x + a\right )}^{\frac{3}{2}} a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 2.07273, size = 77, normalized size = 3.67 \begin{align*} \frac{2 \, \sqrt{b x + a} x^{\frac{3}{2}}}{3 \,{\left (a b^{2} x^{2} + 2 \, a^{2} b x + a^{3}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 2.42667, size = 42, normalized size = 2. \begin{align*} \frac{2 x^{\frac{3}{2}}}{3 a^{\frac{5}{2}} \sqrt{1 + \frac{b x}{a}} + 3 a^{\frac{3}{2}} b x \sqrt{1 + \frac{b x}{a}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] time = 1.15023, size = 116, normalized size = 5.52 \begin{align*} \frac{4 \,{\left (3 \,{\left (\sqrt{b x + a} \sqrt{b} - \sqrt{{\left (b x + a\right )} b - a b}\right )}^{4} \sqrt{b} + a^{2} b^{\frac{5}{2}}\right )}{\left | b \right |}}{3 \,{\left ({\left (\sqrt{b x + a} \sqrt{b} - \sqrt{{\left (b x + a\right )} b - a b}\right )}^{2} + a b\right )}^{3} b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]