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(4x1/2). 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(4x1/2) + 3x + C ]. After simplifying each individual term, our final answer is [ 2/5(x5) - 8x1/2 + 3x + C ]
