Optimal. Leaf size=19 \[ -\frac {1}{6 b^2 x^5 \sqrt {b x^2}} \]
[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} \[ -\frac {1}{6 b^2 x^5 \sqrt {b x^2}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{x^2 \left (b x^2\right )^{5/2}} \, dx &=\frac {x \int \frac {1}{x^7} \, dx}{b^2 \sqrt {b x^2}}\\ &=-\frac {1}{6 b^2 x^5 \sqrt {b x^2}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 15, normalized size = 0.79 \[ -\frac {b x}{6 \left (b x^2\right )^{7/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.65, size = 15, normalized size = 0.79 \[ -\frac {\sqrt {b x^{2}}}{6 \, b^{3} x^{7}} \]
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 \[ -\frac {1}{6 \left (b \,x^{2}\right )^{\frac {5}{2}} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.32, size = 8, normalized size = 0.42 \[ -\frac {1}{6 \, b^{\frac {5}{2}} x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.92, size = 13, normalized size = 0.68 \[ -\frac {1}{6\,b^{5/2}\,x\,{\left (x^2\right )}^{5/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 1.25, size = 17, normalized size = 0.89 \[ - \frac {1}{6 b^{\frac {5}{2}} x \left (x^{2}\right )^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________