Find the general indefinite integral. (Use C for the constant of integration.)2 + 27x2 + 38x3 dx

To find the indefinite integral of the function 2 + 27x^2 + 38x^3 dx, we integrate each term separately.

The integral of a constant, like 2, with respect to x is simply that constant times x. So, the integral of 2 dx is 2x.

The integral of x^n dx, where n is any real number, is (1/(n+1))x^(n+1). So, the integral of 27x^2 dx is (27/3)x^3 = 9x^3.

Similarly, the integral of 38x^3 dx is (38/4)x^4 = 9.5x^4.

Adding these together, the indefinite integral of 2 + 27x^2 + 38x^3 dx is 2x + 9x^3 + 9.5x^4 + C, where C is the constant of integration.