To integrate the given expression, we first note that the expression can be simplified by dividing the numerator by the denominator. This results in:
∫(x^3 + 3x^2 + 4x) / x^2 dx= ∫(x + 3 + 4/x) dx= ∫x dx + ∫3 dx + ∫4/x dx= (1/2)x^2 + 3x + 4ln|x| + C
Therefore, the integral of x^3 + 3x^2 + 4x / x^2 dx is (1/2)x^2 + 3x + 4ln|x| + C, where C is the constant of integration.
To integrate the given expression, we first note that the expression can be simplified by dividing the numerator by the denominator. This results in:
∫(x^3 + 3x^2 + 4x) / x^2 dx
= ∫(x + 3 + 4/x) dx
= ∫x dx + ∫3 dx + ∫4/x dx
= (1/2)x^2 + 3x + 4ln|x| + C
Therefore, the integral of x^3 + 3x^2 + 4x / x^2 dx is (1/2)x^2 + 3x + 4ln|x| + C, where C is the constant of integration.