Optimal. Leaf size=19 \[ \frac {3 x \left (b x^n\right )^{2/3}}{2 n+3} \]
[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} \[ \frac {3 x \left (b x^n\right )^{2/3}}{2 n+3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin {align*} \int \left (b x^n\right )^{2/3} \, dx &=\left (x^{-2 n/3} \left (b x^n\right )^{2/3}\right ) \int x^{2 n/3} \, dx\\ &=\frac {3 x \left (b x^n\right )^{2/3}}{3+2 n}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 20, normalized size = 1.05 \[ \frac {x \left (b x^n\right )^{2/3}}{\frac {2 n}{3}+1} \]
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 \[ \int \left (b x^{n}\right )^{\frac {2}{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 18, normalized size = 0.95 \[ \frac {3 \left (b \,x^{n}\right )^{\frac {2}{3}} x}{2 n +3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.34, size = 17, normalized size = 0.89 \[ \frac {3 \, \left (b x^{n}\right )^{\frac {2}{3}} x}{2 \, n + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.98, size = 17, normalized size = 0.89 \[ \frac {3\,x\,{\left (b\,x^n\right )}^{2/3}}{2\,n+3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \begin {cases} \frac {3 b^{\frac {2}{3}} x \left (x^{n}\right )^{\frac {2}{3}}}{2 n + 3} & \text {for}\: n \neq - \frac {3}{2} \\\int \left (\frac {b}{x^{\frac {3}{2}}}\right )^{\frac {2}{3}}\, dx & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________