## Calculus (3rd Edition)

$$y= x^4+3$$
Given$$\frac{d y}{d x}=4 x^{3}, \quad y(1)=4$$ Since :\begin{align*} y&= \int 4x^3 dx\\ &= x^4+c \end{align*} at $x= 1,\ \ \ y= 4$, then $c= 3$, hence $$y= x^4+3$$