Optimal. Leaf size=14 \[ \frac{\left (b x^2\right )^p}{2 p} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0028232, antiderivative size = 14, normalized size of antiderivative = 1., 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} \[ \frac{\left (b x^2\right )^p}{2 p} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{\left (b x^2\right )^p}{x} \, dx &=\left (x^{-2 p} \left (b x^2\right )^p\right ) \int x^{-1+2 p} \, dx\\ &=\frac{\left (b x^2\right )^p}{2 p}\\ \end{align*}
Mathematica [A] time = 0.0009849, size = 14, normalized size = 1. \[ \frac{\left (b x^2\right )^p}{2 p} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 13, normalized size = 0.9 \begin{align*}{\frac{ \left ( b{x}^{2} \right ) ^{p}}{2\,p}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.984661, size = 18, normalized size = 1.29 \begin{align*} \frac{b^{p}{\left (x^{2}\right )}^{p}}{2 \, p} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.69649, size = 23, normalized size = 1.64 \begin{align*} \frac{\left (b x^{2}\right )^{p}}{2 \, p} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.189575, size = 14, normalized size = 1. \begin{align*} \begin{cases} \frac{b^{p} \left (x^{2}\right )^{p}}{2 p} & \text{for}\: p \neq 0 \\\log{\left (x \right )} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.13755, size = 16, normalized size = 1.14 \begin{align*} \frac{\left (b x^{2}\right )^{p}}{2 \, p} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]