Optimal. Leaf size=18 \[ \frac {x^3 \left (b x^2\right )^p}{2 p+3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {15, 30} \[ \frac {x^3 \left (b x^2\right )^p}{2 p+3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin {align*} \int x^2 \left (b x^2\right )^p \, dx &=\left (x^{-2 p} \left (b x^2\right )^p\right ) \int x^{2+2 p} \, dx\\ &=\frac {x^3 \left (b x^2\right )^p}{3+2 p}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \[ \frac {x^3 \left (b x^2\right )^p}{2 p+3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.83, size = 18, normalized size = 1.00 \[ \frac {\left (b x^{2}\right )^{p} x^{3}}{2 \, p + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.18, size = 18, normalized size = 1.00 \[ \frac {\left (b x^{2}\right )^{p} x^{3}}{2 \, p + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 19, normalized size = 1.06 \[ \frac {x^{3} \left (b \,x^{2}\right )^{p}}{2 p +3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.36, size = 19, normalized size = 1.06 \[ \frac {b^{p} x^{3} x^{2 \, p}}{2 \, p + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.98, size = 18, normalized size = 1.00 \[ \frac {x^3\,{\left (b\,x^2\right )}^p}{2\,p+3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \begin {cases} \frac {b^{p} x^{3} \left (x^{2}\right )^{p}}{2 p + 3} & \text {for}\: p \neq - \frac {3}{2} \\\int \frac {x^{2}}{\left (b x^{2}\right )^{\frac {3}{2}}}\, dx & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________