Optimal. Leaf size=16 \[ \frac{x \left (d x^3\right )^n}{3 n+1} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0040014, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286, Rules used = {15, 30} \[ \frac{x \left (d x^3\right )^n}{3 n+1} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \left (d x^3\right )^n \, dx &=\left (x^{-3 n} \left (d x^3\right )^n\right ) \int x^{3 n} \, dx\\ &=\frac{x \left (d x^3\right )^n}{1+3 n}\\ \end{align*}
Mathematica [A] time = 0.0018816, size = 16, normalized size = 1. \[ \frac{x \left (d x^3\right )^n}{3 n+1} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 17, normalized size = 1.1 \begin{align*}{\frac{x \left ( d{x}^{3} \right ) ^{n}}{1+3\,n}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.13058, size = 23, normalized size = 1.44 \begin{align*} \frac{d^{n} x x^{3 \, n}}{3 \, n + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.37066, size = 31, normalized size = 1.94 \begin{align*} \frac{\left (d x^{3}\right )^{n} x}{3 \, n + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.1404, size = 22, normalized size = 1.38 \begin{align*} \frac{\left (d x^{3}\right )^{n} x}{3 \, n + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]