Optimal. Leaf size=30 \[ \frac{2 x^{3-n}}{3 b (2-n) \sqrt{b x^n}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0078502, antiderivative size = 30, 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} \[ \frac{2 x^{3-n}}{3 b (2-n) \sqrt{b x^n}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{x^2}{\left (b x^n\right )^{3/2}} \, dx &=\frac{x^{n/2} \int x^{2-\frac{3 n}{2}} \, dx}{b \sqrt{b x^n}}\\ &=\frac{2 x^{3-n}}{3 b (2-n) \sqrt{b x^n}}\\ \end{align*}
Mathematica [A] time = 0.0076018, size = 22, normalized size = 0.73 \[ \frac{x^3}{\left (3-\frac{3 n}{2}\right ) \left (b x^n\right )^{3/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 18, normalized size = 0.6 \begin{align*} -{\frac{2\,{x}^{3}}{-6+3\,n} \left ( b{x}^{n} \right ) ^{-{\frac{3}{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: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{2}}{\left (b x^{n}\right )^{\frac{3}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]