Optimal. Leaf size=16 \[ \frac {2}{b \sqrt {a+\frac {b}{x}}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, 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 = {261} \[ \frac {2}{b \sqrt {a+\frac {b}{x}}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 261
Rubi steps
\begin {align*} \int \frac {1}{\left (a+\frac {b}{x}\right )^{3/2} x^2} \, dx &=\frac {2}{b \sqrt {a+\frac {b}{x}}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 16, normalized size = 1.00 \[ \frac {2}{b \sqrt {a+\frac {b}{x}}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.01, size = 24, normalized size = 1.50 \[ \frac {2 \, x \sqrt {\frac {a x + b}{x}}}{a b x + b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.16, size = 16, normalized size = 1.00 \[ \frac {2}{b \sqrt {\frac {a x + b}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 25, normalized size = 1.56 \[ \frac {2 a x +2 b}{\left (\frac {a x +b}{x}\right )^{\frac {3}{2}} b x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.99, size = 14, normalized size = 0.88 \[ \frac {2}{\sqrt {a + \frac {b}{x}} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.31, size = 14, normalized size = 0.88 \[ \frac {2}{b\,\sqrt {a+\frac {b}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 1.80, size = 20, normalized size = 1.25 \[ \begin {cases} \frac {2}{b \sqrt {a + \frac {b}{x}}} & \text {for}\: b \neq 0 \\- \frac {1}{a^{\frac {3}{2}} x} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________