1. The problem statement, all variables and given/known data Hi I have a really hard time understanding when and how to use the Power rule when integrating My book states that if u is a function of x, then the power rule is given by: ∫urdu = (ur+1)/(r+1)+c First: I do understand that if u=2x Then the differential du=u'(x)dx =2 So ∫u^2*du = ƒ2*(2x)^2 = 2*[(2x)3/3] 2. Relevant equations What I don't understand: it seems that the power rule is only practical when I need to find the integral of a function ur multiplied by it's differential (which i can rarely find in any of the problems, so i don't understand why the power rule is important ) EXAMPLE What If I'm given a function f with the equation f(x)= (1/x+x)^2 and i need to find the integral of it using the power rule? I could define u=(1/x+x) and I do have u^2=(1/x+x)^2 but there is no differential du = d(1/x+x))dx multiplied to the function, , so Is it true that The only way Can integrate this function is by first multiplying (1/x+x)*(1/x+x) and then integrating the individual terms, or is there another way, perhaps using the power rule? So to me it seems like I can't use ∫u^2du =[(u)3/3] beause that would be the same as ∫(1/x+x)^2 d(1/x+x)^2) and that's not what I'm suppose to integrate. So when is the power rule usefull? Am I interpreting this wrong?