Optimal. Leaf size=9 \[ -\frac{\cos \left (x^n\right )}{n} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0111279, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {3379, 2638} \[ -\frac{\cos \left (x^n\right )}{n} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 3379
Rule 2638
Rubi steps
\begin{align*} \int x^{-1+n} \sin \left (x^n\right ) \, dx &=\frac{\operatorname{Subst}\left (\int \sin (x) \, dx,x,x^n\right )}{n}\\ &=-\frac{\cos \left (x^n\right )}{n}\\ \end{align*}
Mathematica [A] time = 0.0137676, size = 9, normalized size = 1. \[ -\frac{\cos \left (x^n\right )}{n} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.005, size = 10, normalized size = 1.1 \begin{align*} -{\frac{\cos \left ({x}^{n} \right ) }{n}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.94586, size = 12, normalized size = 1.33 \begin{align*} -\frac{\cos \left (x^{n}\right )}{n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0.46481, size = 18, normalized size = 2. \begin{align*} -\frac{\cos \left (x^{n}\right )}{n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 17.818, size = 7, normalized size = 0.78 \begin{align*} - \frac{\cos{\left (x^{n} \right )}}{n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.07018, size = 12, normalized size = 1.33 \begin{align*} -\frac{\cos \left (x^{n}\right )}{n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]