Optimal. Leaf size=16 \[ \frac{1}{5} x^4 \sqrt{b x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0015588, 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, 30} \[ \frac{1}{5} x^4 \sqrt{b x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin{align*} \int x^3 \sqrt{b x^2} \, dx &=\frac{\sqrt{b x^2} \int x^4 \, dx}{x}\\ &=\frac{1}{5} x^4 \sqrt{b x^2}\\ \end{align*}
Mathematica [A] time = 0.0016718, size = 16, normalized size = 1. \[ \frac{1}{5} x^4 \sqrt{b x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 13, normalized size = 0.8 \begin{align*}{\frac{{x}^{4}}{5}\sqrt{b{x}^{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: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.15891, size = 28, normalized size = 1.75 \begin{align*} \frac{1}{5} \, \sqrt{b x^{2}} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.409797, size = 15, normalized size = 0.94 \begin{align*} \frac{\sqrt{b} x^{4} \sqrt{x^{2}}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.13399, size = 14, normalized size = 0.88 \begin{align*} \frac{1}{5} \, \sqrt{b} x^{5} \mathrm{sgn}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]