Optimal. Leaf size=19 \[ -\frac {1}{4 b^2 x^3 \sqrt {b x^2}} \]
________________________________________________________________________________________
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 = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {15, 30} \begin {gather*} -\frac {1}{4 b^2 x^3 \sqrt {b x^2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{\left (b x^2\right )^{5/2}} \, dx &=\frac {x \int \frac {1}{x^5} \, dx}{b^2 \sqrt {b x^2}}\\ &=-\frac {1}{4 b^2 x^3 \sqrt {b x^2}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 14, normalized size = 0.74 \begin {gather*} -\frac {x}{4 \left (b x^2\right )^{5/2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.01, size = 14, normalized size = 0.74 \begin {gather*} -\frac {x}{4 \left (b x^2\right )^{5/2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.11, size = 15, normalized size = 0.79 \begin {gather*} -\frac {\sqrt {b x^{2}}}{4 \, b^{3} x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \mathit {sage}_{0} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 11, normalized size = 0.58 \begin {gather*} -\frac {x}{4 \left (b \,x^{2}\right )^{\frac {5}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.30, size = 8, normalized size = 0.42 \begin {gather*} -\frac {1}{4 \, b^{\frac {5}{2}} x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.91, size = 13, normalized size = 0.68 \begin {gather*} -\frac {1}{4\,b^{5/2}\,x\,{\left (x^2\right )}^{3/2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.84, size = 15, normalized size = 0.79 \begin {gather*} - \frac {x}{4 b^{\frac {5}{2}} \left (x^{2}\right )^{\frac {5}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________