Let's compute the integral: $\int 4x^{3}dx$

ⓘ A constant factor stays in front of the integral. An antiderivative of x^n is x^(n+1)/(n+1), for n ≠ -1: $\int 4x^{3}dx$ = $4·\frac{x^4}{4}$

$4·\frac{x^4}{4}$

ⓘ Multiplying a fraction by a number multiplies its numerator: $4·\frac{x^4}{4}$ = $\frac{4x^4}{4}$■A fraction is simplified by dividing the numerator and the denominator by the same number: $\frac{4x^4}{4}$ = $x^4$

$x^4$

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