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in this video im going to show you how to integrate using u-substitution so were going to focus on the definite integrals how can we find the anti-derivative of 4x times x squared plus five raised to the third power so what do we need to do we need to define two things we need to identify the u variable and d u now whatever you select u to be du has to be the derivative if we select u to be 4x the derivative will be 4 and thats not going to get rid of x squared plus 5. we need to change all of the x variables into u variables now if we make u equal to x squared plus 5 d u is going to be 2x which can cancel the x and 4x and thats what we want to do so lets set u equal to x squared plus five d u is going to be 2x but times dx so what im going to do now is solve for dx in this equation so if i divide both sides by 2x dx is equal to du divided by 2x now what you need to do is replace this with u and replace the dx with du over 2x and it will all work out so lets go ahead and do that