Find ∫(8x^3+6x^(1/2)-5)dx Give your answer in the simplest form.

This is a simple C1 question on basic integration.I find it best to think of integration as 'anti-differentiation' and it's far more simple. Take each power, add one to it, before dividing into the coefficient. The first term is 8x³. In this case, the power is 3 and the coefficient is 8. So, take 3 and add 1 to it. This gives you a power of 4. Take the new power, then divide it into the coefficient. This leaves you with a new coefficient of 2. So, the new term is now 2x⁴. On the second term, the coefficient is 6 and the power is 1/2. Add 1 to the power and you get a new power of 3/2. Divide this into the coefficient and you get a new coefficient of 4. This means the second term is 4x^3/2. The next term is a constant of -5. This is best thought of as -5x⁰. So, the coefficient is 5 and the power is 0. Applying the same logic we have applied to everything else, this would give a new power of 1. Divide this new power into the coefficient of -5 which simply gives -5. This gives a new term of -5x¹ which is simply- 5x. During indefinite integration, you must never forget to end the new term with +C. This is because we cannot know if there were any constants.This should leave you with an answer of 2x⁴+4x^3/2-5x+C.This is easy to check by simply differentiating the new term. If, after applying differentiation, you are left with the original equation then you are correct.