To integrate the given expression, we first note that the expression can be simplified by dividing the numerator by the denominator. This results in:
∫x3+3x2+4xx^3 + 3x^2 + 4xx3+3x2+4x / x^2 dx= ∫x+3+4/xx + 3 + 4/xx+3+4/x dx= ∫x dx + ∫3 dx + ∫4/x dx= 1/21/21/2x^2 + 3x + 4ln|x| + C
Therefore, the integral of x^3 + 3x^2 + 4x / x^2 dx is 1/21/21/2x^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:
∫x3+3x2+4xx^3 + 3x^2 + 4xx3+3x2+4x / x^2 dx
= ∫x+3+4/xx + 3 + 4/xx+3+4/x dx
= ∫x dx + ∫3 dx + ∫4/x dx
= 1/21/21/2x^2 + 3x + 4ln|x| + C
Therefore, the integral of x^3 + 3x^2 + 4x / x^2 dx is 1/21/21/2x^2 + 3x + 4ln|x| + C, where C is the constant of integration.