Optimal. Leaf size=14 \[ -\frac {1}{b \sqrt {b x^2}} \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {15, 30} \begin {gather*} -\frac {1}{b \sqrt {b x^2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {x}{\left (b x^2\right )^{3/2}} \, dx &=\frac {x \int \frac {1}{x^2} \, dx}{b \sqrt {b x^2}}\\ &=-\frac {1}{b \sqrt {b x^2}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} -\frac {x^2}{\left (b x^2\right )^{3/2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.01, size = 17, normalized size = 1.21 \begin {gather*} -\frac {\sqrt {b x^2}}{b^2 x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.04, size = 15, normalized size = 1.07 \begin {gather*} -\frac {\sqrt {b x^{2}}}{b^{2} x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 12, normalized size = 0.86 \begin {gather*} -\frac {1}{\sqrt {b x^{2}} b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 13, normalized size = 0.93 \begin {gather*} -\frac {x^{2}}{\left (b \,x^{2}\right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.33, size = 12, normalized size = 0.86 \begin {gather*} -\frac {1}{\sqrt {b x^{2}} b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.93, size = 10, normalized size = 0.71 \begin {gather*} -\frac {1}{b^{3/2}\,\sqrt {x^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.52, size = 15, normalized size = 1.07 \begin {gather*} - \frac {x^{2}}{b^{\frac {3}{2}} \left (x^{2}\right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________