Optimal. Leaf size=14 \[ \frac {2}{5} x \sqrt {b x^3} \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {15, 30} \begin {gather*} \frac {2}{5} x \sqrt {b x^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin {align*} \int \sqrt {b x^3} \, dx &=\frac {\sqrt {b x^3} \int x^{3/2} \, dx}{x^{3/2}}\\ &=\frac {2}{5} x \sqrt {b x^3}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {2}{5} x \sqrt {b x^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.02, size = 19, normalized size = 1.36 \begin {gather*} \frac {2 \left (b x^3\right )^{5/2}}{5 b^2 x^5} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.95, size = 10, normalized size = 0.71 \begin {gather*} \frac {2}{5} \, \sqrt {b x^{3}} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 12, normalized size = 0.86 \begin {gather*} \frac {2}{5} \, \sqrt {b x} x^{2} \mathrm {sgn}\relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 11, normalized size = 0.79 \begin {gather*} \frac {2 \sqrt {b \,x^{3}}\, x}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.34, size = 10, normalized size = 0.71 \begin {gather*} \frac {2}{5} \, \sqrt {b x^{3}} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.36, size = 10, normalized size = 0.71 \begin {gather*} \frac {2\,x\,\sqrt {b\,x^3}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.17, size = 15, normalized size = 1.07 \begin {gather*} \frac {2 \sqrt {b} x \sqrt {x^{3}}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________