Optimal. Leaf size=15 \[ \frac{1}{2} b x \sqrt{b x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0015888, antiderivative size = 15, 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, 30} \[ \frac{1}{2} b x \sqrt{b x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{\left (b x^2\right )^{3/2}}{x^2} \, dx &=\frac{\left (b \sqrt{b x^2}\right ) \int x \, dx}{x}\\ &=\frac{1}{2} b x \sqrt{b x^2}\\ \end{align*}
Mathematica [A] time = 0.00074, size = 15, normalized size = 1. \[ \frac{1}{2} b x \sqrt{b x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 13, normalized size = 0.9 \begin{align*}{\frac{1}{2\,x} \left ( b{x}^{2} \right ) ^{{\frac{3}{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 = 1.19965, size = 28, normalized size = 1.87 \begin{align*} \frac{1}{2} \, \sqrt{b x^{2}} b x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.47833, size = 14, normalized size = 0.93 \begin{align*} \frac{b^{\frac{3}{2}} \left (x^{2}\right )^{\frac{3}{2}}}{2 x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.22501, size = 14, normalized size = 0.93 \begin{align*} \frac{1}{2} \, b^{\frac{3}{2}} x^{2} \mathrm{sgn}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]