Optimal. Leaf size=16 \[ \frac{x^2}{b \sqrt{b x^2}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0014285, antiderivative size = 16, 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} \[ \frac{x^2}{b \sqrt{b x^2}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 8
Rubi steps
\begin{align*} \int \frac{x^3}{\left (b x^2\right )^{3/2}} \, dx &=\frac{x \int 1 \, dx}{b \sqrt{b x^2}}\\ &=\frac{x^2}{b \sqrt{b x^2}}\\ \end{align*}
Mathematica [A] time = 0.0010927, size = 13, normalized size = 0.81 \[ \frac{x^4}{\left (b x^2\right )^{3/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 12, normalized size = 0.8 \begin{align*}{{x}^{4} \left ( b{x}^{2} \right ) ^{-{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.01686, size = 19, normalized size = 1.19 \begin{align*} \frac{x^{2}}{\sqrt{b x^{2}} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.43097, size = 23, normalized size = 1.44 \begin{align*} \frac{\sqrt{b x^{2}}}{b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.658561, size = 14, normalized size = 0.88 \begin{align*} \frac{x^{4}}{b^{\frac{3}{2}} \left (x^{2}\right )^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.13824, size = 15, normalized size = 0.94 \begin{align*} \frac{\sqrt{b x^{2}}}{b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]