Integrate 10x(x^1/2 - 2)dx

First, expand the brackets. This will give us 10x^3/2 - 20x. Now to integrate this expression we have to increase the power of each term by one and then divide them by the number which becomes the new power.10x^3/2 becomes 10*2/5x^5/2 and -2x becomes -20/2x^2 so what we get is 4x^5/2 - 10 x^2 + C. Where C is a constant which is added every time an expression is integrated.