⚠ xcos(4pi)x^2 is read as x*cos(4pi)*x^2: use * for multiplication, use ^ for a power

Before integrating, let's calculate: $x·\cos \left(4\pi \right)·x^2$

ⓘ cos and sin are periodic with period 2π: $\cos \left(4\pi \right)$ = $\cos \left(0\right)$■Multiplying powers with the same base adds the exponents: $x{x}^2$ = $x^3$

$x^3·\cos \left(0\right)$

ⓘ The cosine is the x-coordinate (horizontal axis) of the point reached on the unit circle after a rotation of $0$ radians from the horizontal axis pointing to the right, this is a remarkable value: $\cos \left(0\right)$ = $1$■Multiplying by 1 changes nothing: $x^3·1$ = $x^3$

$x^3$

Let's integrate: $\int x^{3}dx$

ⓘ An antiderivative of x^n is x^(n+1)/(n+1), for n ≠ -1: $\int x^{3}dx$ = $\frac{x^4}{4}$

$\frac{x^4}{4}$

▶Indefinite integrals are defined up to an additive constant C, so this yields: $\frac{x^4}{4}+C$