Optimal. Leaf size=4 \[ \sin \left (x^3\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0097691, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {12, 3380, 2637} \[ \sin \left (x^3\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 3380
Rule 2637
Rubi steps
\begin{align*} \int 3 x^2 \cos \left (x^3\right ) \, dx &=3 \int x^2 \cos \left (x^3\right ) \, dx\\ &=\operatorname{Subst}\left (\int \cos (x) \, dx,x,x^3\right )\\ &=\sin \left (x^3\right )\\ \end{align*}
Mathematica [A] time = 0.0016308, size = 4, normalized size = 1. \[ \sin \left (x^3\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 5, normalized size = 1.3 \begin{align*} \sin \left ({x}^{3} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.940966, size = 5, normalized size = 1.25 \begin{align*} \sin \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 2.01688, size = 14, normalized size = 3.5 \begin{align*} \sin \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.292507, size = 3, normalized size = 0.75 \begin{align*} \sin{\left (x^{3} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.07257, size = 5, normalized size = 1.25 \begin{align*} \sin \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]