Solve the integral: int(x^3+4x^2+sinx)dx.

First, since there are terms with different factors of x summing together, we can separate these into three individual integrals as follows:int(x³ dx) + 4int(x²dx) + int(sinx dx)Then using the rules of integration given in the integral tables we solve for every term as:1/3 x² + 4/2 x - cos x + constant