Optimal. Leaf size=19 \[ -\frac {2}{7 b x^2 \sqrt {b x^3}} \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 19, 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}{7 b x^2 \sqrt {b x^3}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{\left (b x^3\right )^{3/2}} \, dx &=\frac {x^{3/2} \int \frac {1}{x^{9/2}} \, dx}{b \sqrt {b x^3}}\\ &=-\frac {2}{7 b x^2 \sqrt {b x^3}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 14, normalized size = 0.74 \begin {gather*} -\frac {2 x}{7 \left (b x^3\right )^{3/2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 2.01, size = 14, normalized size = 0.74 \begin {gather*} -\frac {2 x}{7 \left (b x^3\right )^{3/2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.93, size = 15, normalized size = 0.79 \begin {gather*} -\frac {2 \, \sqrt {b x^{3}}}{7 \, b^{2} x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \mathit {sage}_{0} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 11, normalized size = 0.58 \begin {gather*} -\frac {2 x}{7 \left (b \,x^{3}\right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.32, size = 10, normalized size = 0.53 \begin {gather*} -\frac {2 \, x}{7 \, \left (b x^{3}\right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.94, size = 15, normalized size = 0.79 \begin {gather*} -\frac {2\,\sqrt {b\,x^3}}{7\,b^2\,x^5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.51, size = 17, normalized size = 0.89 \begin {gather*} - \frac {2 x}{7 b^{\frac {3}{2}} \left (x^{3}\right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________