Optimal. Leaf size=16 \[ \frac{x^{2 (n+1)}}{2 (n+1)} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0025427, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {30} \[ \frac{x^{2 (n+1)}}{2 (n+1)} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 30
Rubi steps
\begin{align*} \int x^{1+2 n} \, dx &=\frac{x^{2 (1+n)}}{2 (1+n)}\\ \end{align*}
Mathematica [A] time = 0.0022625, size = 15, normalized size = 0.94 \[ \frac{x^{2 n+2}}{2 n+2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 15, normalized size = 0.9 \begin{align*}{\frac{{x}^{2+2\,n}}{2+2\,n}} \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 [A] time = 2.08276, size = 36, normalized size = 2.25 \begin{align*} \frac{x x^{2 \, n + 1}}{2 \,{\left (n + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.054665, size = 19, normalized size = 1.19 \begin{align*} \begin{cases} \frac{x^{2 n + 2}}{2 n + 2} & \text{for}\: 2 n + 1 \neq -1 \\\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 = 1.07528, size = 19, normalized size = 1.19 \begin{align*} \frac{x^{2 \, n + 2}}{2 \,{\left (n + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]