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so how can we find the indefinite integral of x times e raised to the x to do this we need to use something called integration by parts the integral of u dv is equal to u times v minus the integral of v d u so we need to determine u dv v and u and d u let me put it in a different order so which one should we set equal to u and which one should we set equal to dv its best to set u equal to x because if we do so d u will simply be equal to one times dx and when dealing with constants theyre a lot easier to integrate than variables so were going to make dv equal to e to the x dx now v is the integral of dv the integral of e to the x is simply e to the x so now using the formula u times v thats going to be x times e raised to the x minus the integral of v d u v is e to the x d u is 1 dx and the integral of e to the x is e to the x plus some constant c so this is the final answer thats the integral of x raised to the or x times e raised to the x lets try another problem lets integra
