Optimal. Leaf size=16 \[ \frac {1}{4} x^3 \sqrt {b x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 16, 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} \[ \frac {1}{4} x^3 \sqrt {b x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin {align*} \int x^2 \sqrt {b x^2} \, dx &=\frac {\sqrt {b x^2} \int x^3 \, dx}{x}\\ &=\frac {1}{4} x^3 \sqrt {b x^2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ \frac {1}{4} x^3 \sqrt {b x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.68, size = 12, normalized size = 0.75 \[ \frac {1}{4} \, \sqrt {b x^{2}} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 10, normalized size = 0.62 \[ \frac {1}{4} \, \sqrt {b} x^{4} \mathrm {sgn}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 13, normalized size = 0.81 \[ \frac {\sqrt {b \,x^{2}}\, x^{3}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.32, size = 13, normalized size = 0.81 \[ \frac {\left (b x^{2}\right )^{\frac {3}{2}} x}{4 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.06 \[ \int x^2\,\sqrt {b\,x^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.24, size = 15, normalized size = 0.94 \[ \frac {\sqrt {b} x^{3} \sqrt {x^{2}}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________