Optimal. Leaf size=16 \[ -\frac {1}{b \sqrt {a+b x^2}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {261} \[ -\frac {1}{b \sqrt {a+b x^2}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 261
Rubi steps
\begin {align*} \int \frac {x}{\left (a+b x^2\right )^{3/2}} \, dx &=-\frac {1}{b \sqrt {a+b x^2}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ -\frac {1}{b \sqrt {a+b x^2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.70, size = 24, normalized size = 1.50 \[ -\frac {\sqrt {b x^{2} + a}}{b^{2} x^{2} + a b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.05, size = 14, normalized size = 0.88 \[ -\frac {1}{\sqrt {b x^{2} + a} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 15, normalized size = 0.94 \[ -\frac {1}{\sqrt {b \,x^{2}+a}\, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.32, size = 14, normalized size = 0.88 \[ -\frac {1}{\sqrt {b x^{2} + a} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 14, normalized size = 0.88 \[ -\frac {1}{b\,\sqrt {b\,x^2+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.54, size = 24, normalized size = 1.50 \[ \begin {cases} - \frac {1}{b \sqrt {a + b x^{2}}} & \text {for}\: b \neq 0 \\\frac {x^{2}}{2 a^{\frac {3}{2}}} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________