Optimal. Leaf size=19 \[ -\frac {1}{2 b^2 x \sqrt {b x^2}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {15, 30} \[ -\frac {1}{2 b^2 x \sqrt {b x^2}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {x^2}{\left (b x^2\right )^{5/2}} \, dx &=\frac {x \int \frac {1}{x^3} \, dx}{b^2 \sqrt {b x^2}}\\ &=-\frac {1}{2 b^2 x \sqrt {b x^2}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 16, normalized size = 0.84 \[ -\frac {x^3}{2 \left (b x^2\right )^{5/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.56, size = 15, normalized size = 0.79 \[ -\frac {\sqrt {b x^{2}}}{2 \, b^{3} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \mathit {sage}_{0} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 13, normalized size = 0.68 \[ -\frac {x^{3}}{2 \left (b \,x^{2}\right )^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.28, size = 8, normalized size = 0.42 \[ -\frac {1}{2 \, b^{\frac {5}{2}} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.92, size = 13, normalized size = 0.68 \[ -\frac {1}{2\,b^{5/2}\,x\,\sqrt {x^2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.85, size = 17, normalized size = 0.89 \[ - \frac {x^{3}}{2 b^{\frac {5}{2}} \left (x^{2}\right )^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________