Optimal. Leaf size=17 \[ -\frac{b^2 \sqrt{b x^2}}{x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0018603, antiderivative size = 17, 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} \[ -\frac{b^2 \sqrt{b x^2}}{x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{\left (b x^2\right )^{5/2}}{x^7} \, dx &=\frac{\left (b^2 \sqrt{b x^2}\right ) \int \frac{1}{x^2} \, dx}{x}\\ &=-\frac{b^2 \sqrt{b x^2}}{x^2}\\ \end{align*}
Mathematica [A] time = 0.0016155, size = 14, normalized size = 0.82 \[ -\frac{\left (b x^2\right )^{5/2}}{x^6} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 13, normalized size = 0.8 \begin{align*} -{\frac{1}{{x}^{6}} \left ( b{x}^{2} \right ) ^{{\frac{5}{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: RuntimeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.19759, size = 30, normalized size = 1.76 \begin{align*} -\frac{\sqrt{b x^{2}} b^{2}}{x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 1.82015, size = 15, normalized size = 0.88 \begin{align*} - \frac{b^{\frac{5}{2}} \left (x^{2}\right )^{\frac{5}{2}}}{x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.28639, size = 14, normalized size = 0.82 \begin{align*} -\frac{b^{\frac{5}{2}} \mathrm{sgn}\left (x\right )}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]