Optimal. Leaf size=27 \[ -\frac{2 \sqrt{a x^2+b x^5}}{3 a x^{5/2}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0400189, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048, Rules used = {2014} \[ -\frac{2 \sqrt{a x^2+b x^5}}{3 a x^{5/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2014
Rubi steps
\begin{align*} \int \frac{1}{x^{3/2} \sqrt{a x^2+b x^5}} \, dx &=-\frac{2 \sqrt{a x^2+b x^5}}{3 a x^{5/2}}\\ \end{align*}
Mathematica [A] time = 0.0108333, size = 27, normalized size = 1. \[ -\frac{2 \sqrt{x^2 \left (a+b x^3\right )}}{3 a x^{5/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 29, normalized size = 1.1 \begin{align*} -{\frac{2\,b{x}^{3}+2\,a}{3\,a}{\frac{1}{\sqrt{x}}}{\frac{1}{\sqrt{b{x}^{5}+a{x}^{2}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.11984, size = 35, normalized size = 1.3 \begin{align*} -\frac{2 \,{\left (b x^{4} + a x\right )}}{3 \, \sqrt{b x^{3} + a} a x^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0.920576, size = 51, normalized size = 1.89 \begin{align*} -\frac{2 \, \sqrt{b x^{5} + a x^{2}}}{3 \, a x^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x^{\frac{3}{2}} \sqrt{x^{2} \left (a + b x^{3}\right )}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.4494, size = 31, normalized size = 1.15 \begin{align*} -\frac{2 \, \sqrt{b + \frac{a}{x^{3}}}}{3 \, a} + \frac{2 \, \sqrt{b}}{3 \, a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]