Optimal. Leaf size=13 \[ b^2 \sqrt{b x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0012499, antiderivative size = 13, normalized size of antiderivative = 1., 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, 8} \[ b^2 \sqrt{b x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 8
Rubi steps
\begin{align*} \int \frac{\left (b x^2\right )^{5/2}}{x^5} \, dx &=\frac{\left (b^2 \sqrt{b x^2}\right ) \int 1 \, dx}{x}\\ &=b^2 \sqrt{b x^2}\\ \end{align*}
Mathematica [A] time = 0.0011131, size = 13, normalized size = 1. \[ \frac{\left (b x^2\right )^{5/2}}{x^4} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 12, normalized size = 0.9 \begin{align*}{\frac{1}{{x}^{4}} \left ( b{x}^{2} \right ) ^{{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: RuntimeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.21152, size = 23, normalized size = 1.77 \begin{align*} \sqrt{b x^{2}} b^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 1.20033, size = 14, normalized size = 1.08 \begin{align*} \frac{b^{\frac{5}{2}} \left (x^{2}\right )^{\frac{5}{2}}}{x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.53789, size = 9, normalized size = 0.69 \begin{align*} b^{\frac{5}{2}} x \mathrm{sgn}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]