Find the integral of [ 2x^4 - (4/sqrt(x) ) + 3 ], giving each term in its simplest form

We begin by rewriting it in a more workable form: 2x⁴ - 4x^-1/2 + 3. Indices are easier to integrate than fractions.Now, we integrate each term separately. The first term is 2x⁴. We increase the power of 'x' by 1, and divide the whole term by it, giving us 1/5(2x⁵). We then do the same with the second term, giving us -2(4x^1/2). The third term doesn't appear to have an 'x' term, but it can be written as 3(x⁰), x⁰ being equal to 1. We then do the same to this term, resulting in 3x. As this is an indefinite integral, we add a '+ C' at the end. Our integral is now [ 1/5(2x⁵) - 2(4x^1/2) + 3x + C ]. After simplifying each individual term, our final answer is [ 2/5(x⁵) - 8x^1/2 + 3x + C ]