Optimal. Leaf size=19 \[ \frac {3 x}{(3-2 n) \left (b x^n\right )^{2/3}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, 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} \[ \frac {3 x}{(3-2 n) \left (b x^n\right )^{2/3}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{\left (b x^n\right )^{2/3}} \, dx &=\frac {x^{2 n/3} \int x^{-2 n/3} \, dx}{\left (b x^n\right )^{2/3}}\\ &=\frac {3 x}{(3-2 n) \left (b x^n\right )^{2/3}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 20, normalized size = 1.05 \[ \frac {x}{\left (1-\frac {2 n}{3}\right ) \left (b x^n\right )^{2/3}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (b x^{n}\right )^{\frac {2}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 18, normalized size = 0.95 \[ -\frac {3 x}{\left (2 n -3\right ) \left (b \,x^{n}\right )^{\frac {2}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.98, size = 26, normalized size = 1.37 \[ -\frac {3\,x^{1-n}\,{\left (b\,x^n\right )}^{1/3}}{b\,\left (2\,n-3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________