Optimal. Leaf size=15 \[ \frac {1}{2} b x \sqrt {b x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 15, 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} \[ \frac {1}{2} b x \sqrt {b x^2} \]
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 = 0.00, size = 15, normalized size = 1.00 \[ \frac {1}{2} b x \sqrt {b x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.63, size = 11, normalized size = 0.73 \[ \frac {1}{2} \, \sqrt {b x^{2}} b x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 10, normalized size = 0.67 \[ \frac {1}{2} \, b^{\frac {3}{2}} x^{2} \mathrm {sgn}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 13, normalized size = 0.87 \[ \frac {\left (b \,x^{2}\right )^{\frac {3}{2}}}{2 x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: RuntimeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.97, size = 8, normalized size = 0.53 \[ \frac {b^{3/2}\,x\,\relax |x|}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.42, size = 14, normalized size = 0.93 \[ \frac {b^{\frac {3}{2}} \left (x^{2}\right )^{\frac {3}{2}}}{2 x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________